%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT034-2 : 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 06:24:02 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT034-2 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 7 12:33:09 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.44 % SZS status Unsatisfiable
% 0.13/0.44 % SZS output start Proof
% 0.13/0.44 tff(greater_type, type, (
% 0.13/0.44 greater: ( $i * $i ) > $o)).
% 0.13/0.44 tff(growth_rate_type, type, (
% 0.13/0.44 growth_rate: ( $i * $i ) > $i)).
% 0.13/0.44 tff(sk2_type, type, (
% 0.13/0.44 sk2: $i)).
% 0.13/0.44 tff(efficient_producers_type, type, (
% 0.13/0.44 efficient_producers: $i)).
% 0.13/0.44 tff(first_movers_type, type, (
% 0.13/0.44 first_movers: $i)).
% 0.13/0.44 tff(subpopulations_type, type, (
% 0.13/0.44 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.44 tff(sk1_type, type, (
% 0.13/0.44 sk1: $i)).
% 0.13/0.44 tff(appear_type, type, (
% 0.13/0.44 appear: ( $i * $i ) > $i)).
% 0.13/0.44 tff(in_environment_type, type, (
% 0.13/0.44 in_environment: ( $i * $i ) > $o)).
% 0.13/0.44 tff(critical_point_type, type, (
% 0.13/0.44 critical_point: $i > $i)).
% 0.13/0.44 tff(greater_or_equal_type, type, (
% 0.13/0.44 greater_or_equal: ( $i * $i ) > $o)).
% 0.13/0.44 tff(environment_type, type, (
% 0.13/0.44 environment: $i > $o)).
% 0.13/0.44 tff(selection_favors_type, type, (
% 0.13/0.44 selection_favors: ( $i * $i * $i ) > $o)).
% 0.13/0.44 tff(zero_type, type, (
% 0.13/0.44 zero: $i)).
% 0.13/0.44 tff(difference_type, type, (
% 0.13/0.44 difference: ( $i * $i ) > $i)).
% 0.13/0.44 tff(decreases_type, type, (
% 0.13/0.44 decreases: $i > $o)).
% 0.13/0.44 tff(disbanding_rate_type, type, (
% 0.13/0.44 disbanding_rate: ( $i * $i ) > $i)).
% 0.13/0.44 tff(founding_rate_type, type, (
% 0.13/0.44 founding_rate: ( $i * $i ) > $i)).
% 0.13/0.44 tff(1,assumption,(~in_environment(sk1, appear(efficient_producers, sk1))), introduced(assumption)).
% 0.13/0.44 tff(2,assumption,(critical_point(sk1) = appear(efficient_producers, sk1)), introduced(assumption)).
% 0.13/0.44 tff(3,plain,
% 0.13/0.44 (in_environment(sk1, critical_point(sk1)) <=> in_environment(sk1, appear(efficient_producers, sk1))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[2])).
% 0.13/0.44 tff(4,plain,
% 0.13/0.44 (in_environment(sk1, appear(efficient_producers, sk1)) <=> in_environment(sk1, critical_point(sk1))),
% 0.13/0.44 inference(symmetry,[status(thm)],[3])).
% 0.13/0.44 tff(5,plain,
% 0.13/0.44 ((~in_environment(sk1, appear(efficient_producers, sk1))) <=> (~in_environment(sk1, critical_point(sk1)))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[4])).
% 0.13/0.44 tff(6,plain,
% 0.13/0.44 (~in_environment(sk1, critical_point(sk1))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[1, 5])).
% 0.13/0.44 tff(7,plain,
% 0.13/0.44 (in_environment(sk1, critical_point(sk1)) <=> in_environment(sk1, critical_point(sk1))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(8,axiom,(in_environment(sk1, critical_point(sk1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t3_59')).
% 0.13/0.44 tff(9,plain,
% 0.13/0.44 (in_environment(sk1, critical_point(sk1))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.44 tff(10,plain,
% 0.13/0.44 ($false),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[9, 6])).
% 0.13/0.44 tff(11,plain,((~(critical_point(sk1) = appear(efficient_producers, sk1))) | in_environment(sk1, appear(efficient_producers, sk1))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.44 tff(12,plain,
% 0.13/0.44 (~(critical_point(sk1) = appear(efficient_producers, sk1))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[11, 1])).
% 0.13/0.44 tff(13,assumption,(~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))), introduced(assumption)).
% 0.13/0.44 tff(14,plain,
% 0.13/0.44 (^[B: $i] : refl(greater_or_equal(B, B) <=> greater_or_equal(B, B))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(15,plain,
% 0.13/0.44 (![B: $i] : greater_or_equal(B, B) <=> ![B: $i] : greater_or_equal(B, B)),
% 0.13/0.44 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.44 tff(16,plain,
% 0.13/0.44 (![B: $i] : greater_or_equal(B, B) <=> ![B: $i] : greater_or_equal(B, B)),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(17,plain,
% 0.13/0.44 (![B: $i, A: $i] : greater_or_equal(B, B) <=> ![B: $i] : greater_or_equal(B, B)),
% 0.13/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.13/0.44 tff(18,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : greater_or_equal(B, B)),
% 0.13/0.44 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.13/0.44 tff(19,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B)) <=> ![B: $i] : greater_or_equal(B, B)),
% 0.13/0.44 inference(transitivity,[status(thm)],[18, 17])).
% 0.13/0.44 tff(20,axiom,(![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_or_equal_52')).
% 0.13/0.44 tff(21,plain,
% 0.13/0.44 (![B: $i] : greater_or_equal(B, B)),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.44 tff(22,plain,
% 0.13/0.44 (![B: $i] : greater_or_equal(B, B)),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.13/0.44 tff(23,plain,(
% 0.13/0.44 ![B: $i] : greater_or_equal(B, B)),
% 0.13/0.44 inference(skolemize,[status(sab)],[22])).
% 0.13/0.44 tff(24,plain,
% 0.13/0.44 (![B: $i] : greater_or_equal(B, B)),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.13/0.44 tff(25,plain,
% 0.13/0.44 ((~![B: $i] : greater_or_equal(B, B)) | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))),
% 0.13/0.44 inference(quant_inst,[status(thm)],[])).
% 0.13/0.44 tff(26,plain,
% 0.13/0.44 ($false),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[25, 24, 13])).
% 0.13/0.44 tff(27,plain,(greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.44 tff(28,plain,
% 0.13/0.44 (environment(sk1) <=> environment(sk1)),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(29,axiom,(environment(sk1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t3_58')).
% 0.13/0.44 tff(30,plain,
% 0.13/0.44 (environment(sk1)),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.44 tff(31,plain,
% 0.13/0.44 (^[B: $i, A: $i] : refl(((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(32,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[31])).
% 0.13/0.44 tff(33,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(34,plain,
% 0.13/0.44 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A))))), (((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) <=> (((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))))), rewrite((((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))), (((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))))), ((((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) | in_environment(A, B)) <=> (((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | in_environment(A, B)))), rewrite((((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | in_environment(A, B)) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))), ((((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) | in_environment(A, B)) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(35,plain,
% 0.13/0.44 (![B: $i, A: $i] : (((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) | in_environment(A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.44 tff(36,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) | in_environment(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_critical_time_points_46')).
% 0.13/0.44 tff(37,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.44 tff(38,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.13/0.44 tff(39,plain,(
% 0.13/0.44 ![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.13/0.44 inference(skolemize,[status(sab)],[38])).
% 0.13/0.44 tff(40,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.13/0.44 tff(41,plain,
% 0.13/0.44 (((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(42,plain,
% 0.13/0.44 (((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1)))) <=> ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(43,plain,
% 0.13/0.44 (((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[42])).
% 0.13/0.44 tff(44,plain,
% 0.13/0.44 (((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[43, 41])).
% 0.13/0.44 tff(45,plain,
% 0.13/0.44 ((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))))),
% 0.13/0.44 inference(quant_inst,[status(thm)],[])).
% 0.13/0.44 tff(46,plain,
% 0.13/0.44 ((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.44 tff(47,plain,
% 0.13/0.44 (in_environment(sk1, appear(efficient_producers, sk1)) | (~greater(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[46, 40, 30, 9, 27])).
% 0.13/0.44 tff(48,plain,
% 0.13/0.44 (~greater(critical_point(sk1), appear(efficient_producers, sk1))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[47, 1])).
% 0.13/0.44 tff(49,plain,
% 0.13/0.44 (^[A: $i] : refl((subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A))) <=> (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(50,plain,
% 0.13/0.44 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[49])).
% 0.13/0.45 tff(51,plain,
% 0.13/0.45 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(52,plain,
% 0.13/0.45 (^[A: $i] : rewrite((((~environment(A)) | (~in_environment(A, critical_point(A)))) | subpopulations(first_movers, efficient_producers, A, critical_point(A))) <=> (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(53,plain,
% 0.13/0.45 (![A: $i] : (((~environment(A)) | (~in_environment(A, critical_point(A)))) | subpopulations(first_movers, efficient_producers, A, critical_point(A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[52])).
% 0.13/0.45 tff(54,axiom,(![A: $i] : (((~environment(A)) | (~in_environment(A, critical_point(A)))) | subpopulations(first_movers, efficient_producers, A, critical_point(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_critical_point_means_FM_and_EP_35')).
% 0.13/0.45 tff(55,plain,
% 0.13/0.45 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.13/0.45 tff(56,plain,
% 0.13/0.45 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.13/0.45 tff(57,plain,(
% 0.13/0.45 ![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.13/0.45 inference(skolemize,[status(sab)],[56])).
% 0.13/0.45 tff(58,plain,
% 0.13/0.45 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.13/0.45 tff(59,plain,
% 0.13/0.45 (((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))) | (subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1)) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)))) <=> ((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))) | subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1)) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(60,plain,
% 0.13/0.45 ((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))) | (subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1)) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(61,plain,
% 0.13/0.45 ((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))) | subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1)) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.13/0.45 tff(62,plain,
% 0.13/0.45 (subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[61, 58, 30, 9])).
% 0.13/0.45 tff(63,plain,
% 0.13/0.45 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(64,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[63])).
% 0.13/0.45 tff(65,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(66,plain,
% 0.13/0.45 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater_or_equal(B, appear(efficient_producers, A))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(67,plain,
% 0.13/0.45 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater_or_equal(B, appear(efficient_producers, A))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[66])).
% 0.13/0.45 tff(68,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater_or_equal(B, appear(efficient_producers, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_FM_and_EP_members_EP_appeared_49')).
% 0.13/0.45 tff(69,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.13/0.45 tff(70,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.13/0.45 tff(71,plain,(
% 0.13/0.45 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.13/0.45 inference(skolemize,[status(sab)],[70])).
% 0.13/0.45 tff(72,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.13/0.45 tff(73,plain,
% 0.13/0.45 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(74,plain,
% 0.13/0.45 (((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))) <=> ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(75,plain,
% 0.13/0.45 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[74])).
% 0.13/0.45 tff(76,plain,
% 0.13/0.45 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.13/0.45 inference(transitivity,[status(thm)],[75, 73])).
% 0.13/0.45 tff(77,plain,
% 0.13/0.45 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(78,plain,
% 0.13/0.45 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.13/0.45 tff(79,plain,
% 0.13/0.45 (greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[78, 72, 30, 62])).
% 0.13/0.45 tff(80,plain,
% 0.13/0.45 (^[B: $i, A: $i] : refl((greater(A, B) | (A = B) | (~greater_or_equal(A, B))) <=> (greater(A, B) | (A = B) | (~greater_or_equal(A, B))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(81,plain,
% 0.13/0.45 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.13/0.45 tff(82,plain,
% 0.13/0.45 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(83,plain,
% 0.13/0.45 (^[B: $i, A: $i] : rewrite((((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> (greater(A, B) | (A = B) | (~greater_or_equal(A, B))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(84,plain,
% 0.13/0.45 (![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.13/0.45 tff(85,axiom,(![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_or_equal_50')).
% 0.13/0.45 tff(86,plain,
% 0.13/0.45 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.13/0.45 tff(87,plain,
% 0.13/0.45 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.13/0.45 tff(88,plain,(
% 0.13/0.45 ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.13/0.45 inference(skolemize,[status(sab)],[87])).
% 0.13/0.45 tff(89,plain,
% 0.13/0.45 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.13/0.45 tff(90,plain,
% 0.13/0.45 (((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | (greater(critical_point(sk1), appear(efficient_producers, sk1)) | (critical_point(sk1) = appear(efficient_producers, sk1)) | (~greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))))) <=> ((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | greater(critical_point(sk1), appear(efficient_producers, sk1)) | (critical_point(sk1) = appear(efficient_producers, sk1)) | (~greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(91,plain,
% 0.13/0.45 ((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | (greater(critical_point(sk1), appear(efficient_producers, sk1)) | (critical_point(sk1) = appear(efficient_producers, sk1)) | (~greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(92,plain,
% 0.13/0.45 ((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | greater(critical_point(sk1), appear(efficient_producers, sk1)) | (critical_point(sk1) = appear(efficient_producers, sk1)) | (~greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.13/0.45 tff(93,plain,
% 0.13/0.45 (greater(critical_point(sk1), appear(efficient_producers, sk1)) | (critical_point(sk1) = appear(efficient_producers, sk1))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[92, 89, 79])).
% 0.13/0.45 tff(94,plain,
% 0.13/0.45 ($false),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[93, 48, 12])).
% 0.13/0.45 tff(95,plain,(in_environment(sk1, appear(efficient_producers, sk1))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.45 tff(96,plain,
% 0.13/0.45 (^[A: $i] : refl(((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A)))) <=> ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A)))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(97,plain,
% 0.13/0.45 (![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A)))) <=> ![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[96])).
% 0.13/0.45 tff(98,plain,
% 0.13/0.45 (![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A)))) <=> ![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(99,plain,
% 0.13/0.45 (^[A: $i] : rewrite((((~environment(A)) | (~in_environment(A, appear(efficient_producers, A)))) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A))) <=> ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A)))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(100,plain,
% 0.13/0.45 (![A: $i] : (((~environment(A)) | (~in_environment(A, appear(efficient_producers, A)))) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A))) <=> ![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[99])).
% 0.13/0.45 tff(101,axiom,(![A: $i] : (((~environment(A)) | (~in_environment(A, appear(efficient_producers, A)))) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_FM_and_EP_when_EP_appears_36')).
% 0.13/0.45 tff(102,plain,
% 0.13/0.45 (![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.13/0.45 tff(103,plain,
% 0.13/0.45 (![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.13/0.45 tff(104,plain,(
% 0.13/0.45 ![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.13/0.45 inference(skolemize,[status(sab)],[103])).
% 0.13/0.45 tff(105,plain,
% 0.13/0.45 (![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.13/0.45 tff(106,plain,
% 0.13/0.45 (((~![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))) | ((~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)) | (~in_environment(sk1, appear(efficient_producers, sk1))))) <=> ((~![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))) | (~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)) | (~in_environment(sk1, appear(efficient_producers, sk1))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(107,plain,
% 0.13/0.45 ((~![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))) | ((~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)) | (~in_environment(sk1, appear(efficient_producers, sk1))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(108,plain,
% 0.13/0.45 ((~![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))) | (~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)) | (~in_environment(sk1, appear(efficient_producers, sk1)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.13/0.45 tff(109,plain,
% 0.13/0.45 (subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)) | (~in_environment(sk1, appear(efficient_producers, sk1)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[108, 105, 30])).
% 0.13/0.45 tff(110,plain,
% 0.13/0.45 (subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[109, 95])).
% 0.13/0.45 tff(111,plain,
% 0.13/0.45 (greater(critical_point(sk1), sk2) <=> greater(critical_point(sk1), sk2)),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(112,axiom,(greater(critical_point(sk1), sk2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t3_61')).
% 0.13/0.45 tff(113,plain,
% 0.13/0.45 (greater(critical_point(sk1), sk2)),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.13/0.45 tff(114,plain,
% 0.13/0.45 (^[B: $i, A: $i] : refl(((~greater(A, B)) | greater_or_equal(A, B)) <=> ((~greater(A, B)) | greater_or_equal(A, B)))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(115,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[114])).
% 0.13/0.45 tff(116,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(117,axiom,(![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_or_equal_51')).
% 0.13/0.45 tff(118,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.13/0.45 tff(119,plain,(
% 0.13/0.45 ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.13/0.45 inference(skolemize,[status(sab)],[118])).
% 0.13/0.45 tff(120,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.13/0.45 tff(121,plain,
% 0.13/0.45 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(critical_point(sk1), sk2)) | greater_or_equal(critical_point(sk1), sk2))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(critical_point(sk1), sk2)) | greater_or_equal(critical_point(sk1), sk2))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(122,plain,
% 0.13/0.45 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(critical_point(sk1), sk2)) | greater_or_equal(critical_point(sk1), sk2))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(123,plain,
% 0.13/0.45 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(critical_point(sk1), sk2)) | greater_or_equal(critical_point(sk1), sk2)),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.13/0.45 tff(124,plain,
% 0.13/0.45 (greater_or_equal(critical_point(sk1), sk2)),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[123, 120, 113])).
% 0.13/0.45 tff(125,plain,
% 0.13/0.45 (greater_or_equal(sk2, appear(efficient_producers, sk1)) <=> greater_or_equal(sk2, appear(efficient_producers, sk1))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(126,axiom,(greater_or_equal(sk2, appear(efficient_producers, sk1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t3_60')).
% 0.13/0.45 tff(127,plain,
% 0.13/0.45 (greater_or_equal(sk2, appear(efficient_producers, sk1))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.13/0.45 tff(128,plain,
% 0.13/0.45 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(129,plain,
% 0.13/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[128])).
% 0.13/0.45 tff(130,plain,
% 0.13/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(131,plain,
% 0.13/0.45 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) <=> (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(D, B))))), rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(D, B))) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) <=> (((~environment(A)) | (~greater_or_equal(D, B)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(C, D))))), rewrite((((~environment(A)) | (~greater_or_equal(D, B)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(C, D))) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B)))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) | subpopulations(first_movers, efficient_producers, A, D)) <=> (((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | subpopulations(first_movers, efficient_producers, A, D)))), rewrite((((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | subpopulations(first_movers, efficient_producers, A, D)) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) | subpopulations(first_movers, efficient_producers, A, D)) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))))),
% 0.13/0.46 inference(bind,[status(th)],[])).
% 0.13/0.46 tff(132,plain,
% 0.13/0.46 (![B: $i, D: $i, A: $i, C: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) | subpopulations(first_movers, efficient_producers, A, D)) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.46 inference(quant_intro,[status(thm)],[131])).
% 0.13/0.46 tff(133,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) | subpopulations(first_movers, efficient_producers, A, D))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a10_56')).
% 0.13/0.46 tff(134,plain,
% 0.13/0.46 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.13/0.46 tff(135,plain,
% 0.13/0.46 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.13/0.46 tff(136,plain,(
% 0.13/0.46 ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.46 inference(skolemize,[status(sab)],[135])).
% 0.13/0.46 tff(137,plain,
% 0.13/0.46 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.13/0.46 tff(138,plain,
% 0.13/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(139,plain,
% 0.13/0.46 (((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)))) <=> ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(140,plain,
% 0.13/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)))))),
% 0.13/0.46 inference(monotonicity,[status(thm)],[139])).
% 0.13/0.46 tff(141,plain,
% 0.13/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))),
% 0.13/0.46 inference(transitivity,[status(thm)],[140, 138])).
% 0.13/0.46 tff(142,plain,
% 0.13/0.46 ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))),
% 0.13/0.46 inference(quant_inst,[status(thm)],[])).
% 0.13/0.46 tff(143,plain,
% 0.13/0.46 ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.13/0.46 tff(144,plain,
% 0.13/0.46 (subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[143, 137, 30, 127, 62, 124])).
% 0.13/0.46 tff(145,plain,
% 0.13/0.46 (subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[144, 110])).
% 0.13/0.46 tff(146,plain,
% 0.13/0.46 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B)))),
% 0.13/0.46 inference(bind,[status(th)],[])).
% 0.13/0.46 tff(147,plain,
% 0.13/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.46 inference(quant_intro,[status(thm)],[146])).
% 0.13/0.46 tff(148,plain,
% 0.13/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(149,plain,
% 0.13/0.46 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | subpopulations(efficient_producers, first_movers, A, B)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B)))),
% 0.13/0.46 inference(bind,[status(th)],[])).
% 0.13/0.46 tff(150,plain,
% 0.13/0.46 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | subpopulations(efficient_producers, first_movers, A, B)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.46 inference(quant_intro,[status(thm)],[149])).
% 0.13/0.46 tff(151,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | subpopulations(efficient_producers, first_movers, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_symmetry_of_subpopulations_48')).
% 0.13/0.46 tff(152,plain,
% 0.13/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.13/0.46 tff(153,plain,
% 0.13/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.13/0.46 tff(154,plain,(
% 0.13/0.46 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.46 inference(skolemize,[status(sab)],[153])).
% 0.13/0.46 tff(155,plain,
% 0.13/0.47 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.13/0.47 tff(156,plain,
% 0.13/0.47 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2))),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(157,plain,
% 0.13/0.47 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | subpopulations(efficient_producers, first_movers, sk1, sk2)) <=> ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2))),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(158,plain,
% 0.13/0.47 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | subpopulations(efficient_producers, first_movers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2)))),
% 0.13/0.47 inference(monotonicity,[status(thm)],[157])).
% 0.13/0.47 tff(159,plain,
% 0.13/0.47 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | subpopulations(efficient_producers, first_movers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2))),
% 0.13/0.47 inference(transitivity,[status(thm)],[158, 156])).
% 0.13/0.47 tff(160,plain,
% 0.13/0.47 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | subpopulations(efficient_producers, first_movers, sk1, sk2))),
% 0.13/0.47 inference(quant_inst,[status(thm)],[])).
% 0.13/0.47 tff(161,plain,
% 0.13/0.47 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2)),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.13/0.47 tff(162,plain,
% 0.13/0.47 (subpopulations(efficient_producers, first_movers, sk1, sk2)),
% 0.13/0.47 inference(unit_resolution,[status(thm)],[161, 155, 30, 145])).
% 0.13/0.47 tff(163,plain,
% 0.13/0.47 ((~selection_favors(first_movers, efficient_producers, sk2)) <=> (~selection_favors(first_movers, efficient_producers, sk2))),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(164,axiom,(~selection_favors(first_movers, efficient_producers, sk2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t3_62')).
% 0.13/0.47 tff(165,plain,
% 0.13/0.47 (~selection_favors(first_movers, efficient_producers, sk2)),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.13/0.47 tff(166,plain,
% 0.13/0.47 (^[B: $i, D: $i, A: $i, C: $i] : refl((selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))))),
% 0.13/0.47 inference(bind,[status(th)],[])).
% 0.13/0.47 tff(167,plain,
% 0.13/0.47 (![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> ![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.47 inference(quant_intro,[status(thm)],[166])).
% 0.13/0.47 tff(168,plain,
% 0.13/0.47 (![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> ![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(169,plain,
% 0.13/0.47 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(growth_rate(C, D), growth_rate(B, D)))) <=> ((~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(growth_rate(C, D), growth_rate(B, D)))) | selection_favors(C, B, D)) <=> (((~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))) | selection_favors(C, B, D)))), rewrite((((~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))) | selection_favors(C, B, D)) <=> (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(growth_rate(C, D), growth_rate(B, D)))) | selection_favors(C, B, D)) <=> (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))))),
% 0.13/0.47 inference(bind,[status(th)],[])).
% 0.13/0.47 tff(170,plain,
% 0.13/0.47 (![B: $i, D: $i, A: $i, C: $i] : ((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(growth_rate(C, D), growth_rate(B, D)))) | selection_favors(C, B, D)) <=> ![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.47 inference(quant_intro,[status(thm)],[169])).
% 0.13/0.47 tff(171,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(growth_rate(C, D), growth_rate(B, D)))) | selection_favors(C, B, D))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp1_high_growth_rates_33')).
% 0.13/0.47 tff(172,plain,
% 0.13/0.47 (![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.13/0.47 tff(173,plain,
% 0.13/0.47 (![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.13/0.47 tff(174,plain,(
% 0.13/0.47 ![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.47 inference(skolemize,[status(sab)],[173])).
% 0.13/0.47 tff(175,plain,
% 0.13/0.47 (![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.13/0.47 tff(176,plain,
% 0.13/0.47 (((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)))),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(177,plain,
% 0.13/0.47 ((selection_favors(first_movers, efficient_producers, sk2) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)) | (~environment(sk1))) <=> (selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)))),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(178,plain,
% 0.13/0.47 (((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (selection_favors(first_movers, efficient_producers, sk2) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2))))),
% 0.13/0.47 inference(monotonicity,[status(thm)],[177])).
% 0.13/0.47 tff(179,plain,
% 0.13/0.47 (((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (selection_favors(first_movers, efficient_producers, sk2) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)))),
% 0.13/0.47 inference(transitivity,[status(thm)],[178, 176])).
% 0.13/0.47 tff(180,plain,
% 0.13/0.47 ((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (selection_favors(first_movers, efficient_producers, sk2) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)) | (~environment(sk1)))),
% 0.13/0.47 inference(quant_inst,[status(thm)],[])).
% 0.13/0.47 tff(181,plain,
% 0.13/0.47 ((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.13/0.47 tff(182,plain,
% 0.13/0.47 (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))),
% 0.13/0.47 inference(unit_resolution,[status(thm)],[181, 175, 30, 165, 162])).
% 0.13/0.47 tff(183,plain,
% 0.13/0.47 (^[B: $i, A: $i] : refl(((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))),
% 0.13/0.47 inference(bind,[status(th)],[])).
% 0.13/0.47 tff(184,plain,
% 0.13/0.47 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.47 inference(quant_intro,[status(thm)],[183])).
% 0.13/0.47 tff(185,plain,
% 0.13/0.47 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(186,plain,
% 0.13/0.47 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))))) <=> ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))),
% 0.13/0.47 inference(bind,[status(th)],[])).
% 0.13/0.47 tff(187,plain,
% 0.13/0.47 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))))) <=> ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.47 inference(quant_intro,[status(thm)],[186])).
% 0.13/0.47 tff(188,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l3_34')).
% 0.13/0.47 tff(189,plain,
% 0.13/0.47 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.13/0.47 tff(190,plain,
% 0.13/0.47 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.13/0.47 tff(191,plain,(
% 0.13/0.47 ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.47 inference(skolemize,[status(sab)],[190])).
% 0.13/0.47 tff(192,plain,
% 0.13/0.47 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.13/0.47 tff(193,plain,
% 0.13/0.47 (((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(194,plain,
% 0.13/0.47 (((~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1))) <=> ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(195,plain,
% 0.13/0.47 (((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))))),
% 0.13/0.47 inference(monotonicity,[status(thm)],[194])).
% 0.13/0.47 tff(196,plain,
% 0.13/0.47 (((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))),
% 0.13/0.47 inference(transitivity,[status(thm)],[195, 193])).
% 0.13/0.47 tff(197,plain,
% 0.13/0.47 ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))),
% 0.13/0.47 inference(quant_inst,[status(thm)],[])).
% 0.13/0.47 tff(198,plain,
% 0.13/0.47 ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.13/0.47 tff(199,plain,
% 0.13/0.47 (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))),
% 0.13/0.47 inference(unit_resolution,[status(thm)],[198, 192, 30, 145])).
% 0.13/0.47 tff(200,plain,
% 0.13/0.47 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))))),
% 0.13/0.48 inference(bind,[status(th)],[])).
% 0.13/0.48 tff(201,plain,
% 0.13/0.48 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.13/0.48 inference(quant_intro,[status(thm)],[200])).
% 0.13/0.48 tff(202,plain,
% 0.13/0.48 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(203,plain,
% 0.13/0.48 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))))),
% 0.13/0.48 inference(bind,[status(th)],[])).
% 0.13/0.48 tff(204,plain,
% 0.13/0.48 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.13/0.48 inference(quant_intro,[status(thm)],[203])).
% 0.13/0.48 tff(205,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a12_57')).
% 0.13/0.48 tff(206,plain,
% 0.13/0.48 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.13/0.48 tff(207,plain,
% 0.13/0.48 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.13/0.48 tff(208,plain,(
% 0.13/0.48 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.13/0.48 inference(skolemize,[status(sab)],[207])).
% 0.13/0.48 tff(209,plain,
% 0.13/0.48 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[208, 201])).
% 0.13/0.48 tff(210,plain,
% 0.13/0.48 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(211,plain,
% 0.13/0.48 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))) <=> ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(212,plain,
% 0.13/0.48 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))))),
% 0.13/0.48 inference(monotonicity,[status(thm)],[211])).
% 0.13/0.48 tff(213,plain,
% 0.13/0.48 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))),
% 0.13/0.48 inference(transitivity,[status(thm)],[212, 210])).
% 0.13/0.48 tff(214,plain,
% 0.13/0.48 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))),
% 0.13/0.48 inference(quant_inst,[status(thm)],[])).
% 0.13/0.48 tff(215,plain,
% 0.13/0.48 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.13/0.48 tff(216,plain,
% 0.13/0.48 (decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))),
% 0.13/0.48 inference(unit_resolution,[status(thm)],[215, 209, 30, 145])).
% 0.13/0.48 tff(217,plain,
% 0.13/0.48 (^[A: $i] : refl((decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))) <=> (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))))),
% 0.13/0.48 inference(bind,[status(th)],[])).
% 0.13/0.48 tff(218,plain,
% 0.13/0.48 (![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))) <=> ![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.13/0.48 inference(quant_intro,[status(thm)],[217])).
% 0.13/0.48 tff(219,plain,
% 0.13/0.48 (![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))) <=> ![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(220,plain,
% 0.13/0.48 (^[A: $i] : trans(monotonicity(rewrite(((~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A)))) <=> (decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))), ((((~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A)))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) <=> ((decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))))), rewrite(((decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) <=> (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))), ((((~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A)))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) <=> (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))))),
% 0.13/0.48 inference(bind,[status(th)],[])).
% 0.13/0.48 tff(221,plain,
% 0.13/0.48 (![A: $i] : (((~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A)))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) <=> ![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.13/0.48 inference(quant_intro,[status(thm)],[220])).
% 0.13/0.48 tff(222,axiom,(![A: $i] : (((~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A)))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_difference_between_founding_rates_37')).
% 0.13/0.48 tff(223,plain,
% 0.13/0.48 (![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.13/0.48 tff(224,plain,
% 0.13/0.48 (![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.13/0.48 tff(225,plain,(
% 0.13/0.48 ![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.13/0.48 inference(skolemize,[status(sab)],[224])).
% 0.13/0.48 tff(226,plain,
% 0.13/0.48 (![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[225, 218])).
% 0.13/0.48 tff(227,plain,
% 0.13/0.48 (((~![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))) | (decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))))) <=> ((~![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))) | decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))))),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(228,plain,
% 0.13/0.48 ((~![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))) | (decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))))),
% 0.13/0.48 inference(quant_inst,[status(thm)],[])).
% 0.13/0.48 tff(229,plain,
% 0.13/0.48 ((~![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))) | decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.13/0.48 tff(230,plain,
% 0.13/0.48 (decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))),
% 0.13/0.48 inference(unit_resolution,[status(thm)],[229, 226, 216, 199])).
% 0.13/0.48 tff(231,plain,
% 0.13/0.48 (^[A: $i] : refl(((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A))))) <=> ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A))))))),
% 0.13/0.48 inference(bind,[status(th)],[])).
% 0.13/0.48 tff(232,plain,
% 0.13/0.48 (![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A))))) <=> ![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))),
% 0.13/0.48 inference(quant_intro,[status(thm)],[231])).
% 0.13/0.48 tff(233,plain,
% 0.13/0.48 (![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A))))) <=> ![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(234,plain,
% 0.13/0.48 (![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A))))) <=> ![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))),
% 0.13/0.48 inference(elim_unused_vars,[status(thm)],[])).
% 0.13/0.48 tff(235,plain,
% 0.13/0.48 (![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))),
% 0.13/0.48 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.13/0.48 tff(236,plain,
% 0.13/0.48 (![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A)))) <=> ![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))),
% 0.13/0.48 inference(transitivity,[status(thm)],[235, 234])).
% 0.13/0.48 tff(237,plain,
% 0.13/0.48 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~(B = critical_point(A)))) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))) <=> ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A)))))),
% 0.13/0.48 inference(bind,[status(th)],[])).
% 0.13/0.48 tff(238,plain,
% 0.13/0.48 (![B: $i, A: $i] : (((~environment(A)) | (~(B = critical_point(A)))) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))),
% 0.13/0.48 inference(quant_intro,[status(thm)],[237])).
% 0.13/0.48 tff(239,plain,
% 0.13/0.48 (![B: $i, A: $i] : (((~environment(A)) | (~(B = critical_point(A)))) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))) <=> ![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))),
% 0.13/0.48 inference(transitivity,[status(thm)],[238, 236])).
% 0.13/0.48 tff(240,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~(B = critical_point(A)))) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_54')).
% 0.13/0.48 tff(241,plain,
% 0.13/0.48 (![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.13/0.48 tff(242,plain,
% 0.13/0.48 (![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[241, 233])).
% 0.13/0.48 tff(243,plain,(
% 0.13/0.48 ![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))),
% 0.13/0.48 inference(skolemize,[status(sab)],[242])).
% 0.13/0.48 tff(244,plain,
% 0.13/0.48 (![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[243, 232])).
% 0.13/0.48 tff(245,plain,
% 0.13/0.48 (((~![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))) | ((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))))) <=> ((~![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))) | (~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))))),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(246,plain,
% 0.13/0.48 ((~![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))) | ((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))))),
% 0.13/0.48 inference(quant_inst,[status(thm)],[])).
% 0.13/0.48 tff(247,plain,
% 0.13/0.48 ((~![A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, critical_point(A)), growth_rate(first_movers, critical_point(A)))))) | (~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.13/0.48 tff(248,plain,
% 0.13/0.48 (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))),
% 0.13/0.48 inference(unit_resolution,[status(thm)],[247, 244, 30])).
% 0.13/0.48 tff(249,plain,
% 0.13/0.48 (^[A: $i] : refl(((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) <=> ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))))),
% 0.13/0.48 inference(bind,[status(th)],[])).
% 0.13/0.48 tff(250,plain,
% 0.13/0.48 (![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) <=> ![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[249])).
% 0.13/0.49 tff(251,plain,
% 0.13/0.49 (![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) <=> ![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(252,axiom,(![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_negative_growth_rate_difference_39')).
% 0.13/0.49 tff(253,plain,
% 0.13/0.49 (![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.13/0.49 tff(254,plain,(
% 0.13/0.49 ![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))),
% 0.13/0.49 inference(skolemize,[status(sab)],[253])).
% 0.13/0.49 tff(255,plain,
% 0.13/0.49 (![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[254, 250])).
% 0.13/0.49 tff(256,plain,
% 0.13/0.49 (((~![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))) | ((~greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))) | greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1))))) <=> ((~![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))) | (~greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))) | greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1))))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(257,plain,
% 0.13/0.49 ((~![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))) | ((~greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))) | greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1))))),
% 0.13/0.49 inference(quant_inst,[status(thm)],[])).
% 0.13/0.49 tff(258,plain,
% 0.13/0.49 ((~![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))) | (~greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))) | greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.13/0.49 tff(259,plain,
% 0.13/0.49 (~greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[258, 255, 248])).
% 0.13/0.49 tff(260,plain,
% 0.13/0.49 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(261,plain,
% 0.13/0.49 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[260])).
% 0.13/0.49 tff(262,plain,
% 0.13/0.49 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(263,plain,
% 0.13/0.49 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(264,plain,
% 0.13/0.49 (![B: $i, A: $i] : ((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[263])).
% 0.13/0.49 tff(265,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_relationship_of_growth_rates_53')).
% 0.13/0.49 tff(266,plain,
% 0.13/0.49 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.13/0.49 tff(267,plain,
% 0.13/0.49 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[266, 262])).
% 0.13/0.49 tff(268,plain,(
% 0.13/0.49 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.13/0.49 inference(skolemize,[status(sab)],[267])).
% 0.13/0.49 tff(269,plain,
% 0.13/0.49 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[268, 261])).
% 0.13/0.49 tff(270,plain,
% 0.13/0.49 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | ((~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(271,plain,
% 0.13/0.49 (((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))) <=> ((~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(272,plain,
% 0.13/0.49 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | ((~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))))),
% 0.13/0.49 inference(monotonicity,[status(thm)],[271])).
% 0.13/0.49 tff(273,plain,
% 0.13/0.49 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))),
% 0.13/0.49 inference(transitivity,[status(thm)],[272, 270])).
% 0.13/0.49 tff(274,plain,
% 0.13/0.49 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))),
% 0.13/0.49 inference(quant_inst,[status(thm)],[])).
% 0.13/0.49 tff(275,plain,
% 0.13/0.49 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.13/0.50 tff(276,plain,
% 0.13/0.50 (greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[275, 269, 30, 62])).
% 0.13/0.50 tff(277,plain,
% 0.13/0.50 (greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[276, 259])).
% 0.13/0.50 tff(278,plain,
% 0.13/0.50 (^[B: $i, A: $i, C: $i] : refl(((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) <=> ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(279,plain,
% 0.13/0.50 (![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[278])).
% 0.13/0.50 tff(280,plain,
% 0.13/0.50 (![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(281,plain,
% 0.13/0.50 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) <=> ((~environment(A)) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) <=> (((~environment(A)) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~greater_or_equal(C, appear(efficient_producers, A)))))), rewrite((((~environment(A)) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~greater_or_equal(C, appear(efficient_producers, A)))) <=> ((~environment(A)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) <=> ((~environment(A)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) <=> (((~environment(A)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~greater(B, C))))), rewrite((((~environment(A)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~greater(B, C))) <=> ((~environment(A)) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) <=> ((~environment(A)) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) <=> (((~environment(A)) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))))), rewrite((((~environment(A)) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) <=> ((~environment(A)) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))), (((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) <=> ((~environment(A)) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))))), ((((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero)) <=> (((~environment(A)) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero)))), rewrite((((~environment(A)) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero)) <=> ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))), ((((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero)) <=> ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(282,plain,
% 0.13/0.50 (![B: $i, A: $i, C: $i] : (((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero)) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[281])).
% 0.13/0.50 tff(283,axiom,(![B: $i, A: $i, C: $i] : (((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_decreasing_function_38')).
% 0.13/0.50 tff(284,plain,
% 0.13/0.50 (![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.13/0.50 tff(285,plain,
% 0.13/0.50 (![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[284, 280])).
% 0.13/0.50 tff(286,plain,(
% 0.13/0.50 ![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.13/0.50 inference(skolemize,[status(sab)],[285])).
% 0.13/0.50 tff(287,plain,
% 0.13/0.50 (![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[286, 279])).
% 0.13/0.50 tff(288,plain,
% 0.13/0.50 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(289,plain,
% 0.13/0.50 (((~environment(sk1)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater(critical_point(sk1), sk2)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)) | (~in_environment(sk1, critical_point(sk1)))) <=> ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(290,plain,
% 0.13/0.50 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | ((~environment(sk1)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater(critical_point(sk1), sk2)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)) | (~in_environment(sk1, critical_point(sk1))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero))))),
% 0.13/0.50 inference(monotonicity,[status(thm)],[289])).
% 0.13/0.50 tff(291,plain,
% 0.13/0.50 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | ((~environment(sk1)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater(critical_point(sk1), sk2)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)) | (~in_environment(sk1, critical_point(sk1))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)))),
% 0.13/0.51 inference(transitivity,[status(thm)],[290, 288])).
% 0.13/0.51 tff(292,plain,
% 0.13/0.51 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | ((~environment(sk1)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater(critical_point(sk1), sk2)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)) | (~in_environment(sk1, critical_point(sk1))))),
% 0.13/0.51 inference(quant_inst,[status(thm)],[])).
% 0.13/0.51 tff(293,plain,
% 0.13/0.51 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero))),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.13/0.51 tff(294,plain,
% 0.13/0.51 (greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[293, 287, 30, 9, 127, 113])).
% 0.13/0.51 tff(295,plain,
% 0.13/0.51 (greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[294, 277])).
% 0.13/0.51 tff(296,plain,
% 0.13/0.51 (greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero)),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[295, 230])).
% 0.13/0.51 tff(297,plain,
% 0.13/0.51 (^[A: $i] : refl(((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) <=> ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A))))),
% 0.13/0.51 inference(bind,[status(th)],[])).
% 0.13/0.51 tff(298,plain,
% 0.13/0.51 (![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) <=> ![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))),
% 0.13/0.51 inference(quant_intro,[status(thm)],[297])).
% 0.13/0.51 tff(299,plain,
% 0.13/0.51 (![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) <=> ![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))),
% 0.13/0.51 inference(rewrite,[status(thm)],[])).
% 0.13/0.51 tff(300,axiom,(![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_positive_growth_rate_difference_41')).
% 0.13/0.51 tff(301,plain,
% 0.13/0.51 (![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.13/0.51 tff(302,plain,(
% 0.13/0.51 ![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))),
% 0.13/0.51 inference(skolemize,[status(sab)],[301])).
% 0.13/0.51 tff(303,plain,
% 0.13/0.51 (![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.13/0.51 tff(304,plain,
% 0.13/0.51 (((~![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | ((~greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero)) | greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) <=> ((~![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | (~greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero)) | greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))),
% 0.13/0.51 inference(rewrite,[status(thm)],[])).
% 0.13/0.51 tff(305,plain,
% 0.13/0.51 ((~![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | ((~greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero)) | greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))),
% 0.13/0.51 inference(quant_inst,[status(thm)],[])).
% 0.13/0.51 tff(306,plain,
% 0.13/0.51 ((~![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | (~greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero)) | greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.13/0.51 tff(307,plain,
% 0.13/0.51 ($false),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[306, 303, 296, 182])).
% 0.13/0.51 % SZS output end Proof
% 0.13/0.51 % E exiting
%------------------------------------------------------------------------------