%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT024-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n001.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 06:24:00 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT024-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.06/0.32 % Computer : n001.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Mon Sep 7 12:14:24 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(greater_type, type, (
% 0.13/0.39 greater: ( $i * $i ) > $o)).
% 0.13/0.39 tff(growth_rate_type, type, (
% 0.13/0.39 growth_rate: ( $i * $i ) > $i)).
% 0.13/0.39 tff(sk2_type, type, (
% 0.13/0.39 sk2: $i)).
% 0.13/0.39 tff(efficient_producers_type, type, (
% 0.13/0.39 efficient_producers: $i)).
% 0.13/0.39 tff(zero_type, type, (
% 0.13/0.39 zero: $i)).
% 0.13/0.39 tff(first_movers_type, type, (
% 0.13/0.39 first_movers: $i)).
% 0.13/0.39 tff(constant_type, type, (
% 0.13/0.39 constant: $i > $o)).
% 0.13/0.39 tff(number_of_organizations_type, type, (
% 0.13/0.39 number_of_organizations: ( $i * $i ) > $i)).
% 0.13/0.39 tff(sk1_type, type, (
% 0.13/0.39 sk1: $i)).
% 0.13/0.39 tff(resources_type, type, (
% 0.13/0.39 resources: ( $i * $i ) > $i)).
% 0.13/0.39 tff(equilibrium_type, type, (
% 0.13/0.39 equilibrium: $i > $i)).
% 0.13/0.39 tff(greater_or_equal_type, type, (
% 0.13/0.39 greater_or_equal: ( $i * $i ) > $o)).
% 0.13/0.39 tff(environment_type, type, (
% 0.13/0.39 environment: $i > $o)).
% 0.13/0.39 tff(subpopulations_type, type, (
% 0.13/0.39 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.39 tff(in_environment_type, type, (
% 0.13/0.39 in_environment: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,assumption,(~greater(zero, growth_rate(first_movers, sk2))), introduced(assumption)).
% 0.13/0.39 tff(2,assumption,(~greater(growth_rate(first_movers, sk2), zero)), introduced(assumption)).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (greater_or_equal(sk2, equilibrium(sk1)) <=> greater_or_equal(sk2, equilibrium(sk1))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(greater_or_equal(sk2, equilibrium(sk1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l6_41')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (greater_or_equal(sk2, equilibrium(sk1))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (environment(sk1) <=> environment(sk1)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(7,axiom,(environment(sk1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l6_39')).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (environment(sk1)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (^[B: $i, A: $i] : refl(((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A)))) <=> ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~greater_or_equal(B, equilibrium(A)))) | (~greater(equilibrium(A), B))) <=> ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![B: $i, A: $i] : (((~environment(A)) | (~greater_or_equal(B, equilibrium(A)))) | (~greater(equilibrium(A), B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.39 tff(14,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~greater_or_equal(B, equilibrium(A)))) | (~greater(equilibrium(A), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_equilibrium_26')).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.39 tff(17,plain,(
% 0.13/0.39 ![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (((~![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A))))) | ((~environment(sk1)) | (~greater(equilibrium(sk1), sk2)) | (~greater_or_equal(sk2, equilibrium(sk1))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A))))) | (~environment(sk1)) | (~greater(equilibrium(sk1), sk2)) | (~greater_or_equal(sk2, equilibrium(sk1))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((~![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A))))) | ((~environment(sk1)) | (~greater(equilibrium(sk1), sk2)) | (~greater_or_equal(sk2, equilibrium(sk1))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((~![B: $i, A: $i] : ((~environment(A)) | (~greater(equilibrium(A), B)) | (~greater_or_equal(B, equilibrium(A))))) | (~environment(sk1)) | (~greater(equilibrium(sk1), sk2)) | (~greater_or_equal(sk2, equilibrium(sk1)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (~greater(equilibrium(sk1), sk2)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[21, 18, 8, 5])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (subpopulations(first_movers, efficient_producers, sk1, sk2) <=> subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(24,axiom,(subpopulations(first_movers, efficient_producers, sk1, sk2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l6_40')).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(number_of_organizations(A, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(number_of_organizations(A, B), zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.39 tff(31,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(number_of_organizations(A, B), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_positive_number_of_organizations_25')).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.13/0.39 tff(34,plain,(
% 0.13/0.39 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.39 inference(skolemize,[status(sab)],[33])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(number_of_organizations(sk1, sk2), zero))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(number_of_organizations(sk1, sk2), zero))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(number_of_organizations(sk1, sk2), zero))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(number_of_organizations(A, B), zero))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(number_of_organizations(sk1, sk2), zero)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (greater(number_of_organizations(sk1, sk2), zero)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[38, 35, 8, 25])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (^[B: $i, A: $i] : refl((in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B)) <=> (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B)) <=> ![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.13/0.39 tff(45,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_time_point_occur_24')).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.13/0.40 tff(48,plain,(
% 0.13/0.40 ![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[47])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | in_environment(sk1, sk2))) <=> ((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | in_environment(sk1, sk2))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 ((in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1))) <=> ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | in_environment(sk1, sk2))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | in_environment(sk1, sk2)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[51])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | in_environment(sk1, sk2))),
% 0.13/0.40 inference(transitivity,[status(thm)],[52, 50])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | in_environment(sk1, sk2)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (in_environment(sk1, sk2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[55, 49, 8, 25])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (^[B: $i, A: $i] : refl(((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B))) <=> ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) <=> ((~environment(A)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)) <=> (((~environment(A)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B))) | greater(equilibrium(A), B)))), rewrite((((~environment(A)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B))) | greater(equilibrium(A), B)) <=> ((~environment(A)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)) <=> ((~environment(A)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)) | constant(resources(A, B))) <=> (((~environment(A)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B))) | constant(resources(A, B))))), rewrite((((~environment(A)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B))) | constant(resources(A, B))) <=> ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)) | constant(resources(A, B))) <=> ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (![B: $i, A: $i] : (((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)) | constant(resources(A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.13/0.40 tff(62,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)) | constant(resources(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a3_28')).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.13/0.40 tff(65,plain,(
% 0.13/0.40 ![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[64])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))) | ((~environment(sk1)) | greater(equilibrium(sk1), sk2) | (~in_environment(sk1, sk2)) | constant(resources(sk1, sk2)) | (~greater(number_of_organizations(sk1, sk2), zero)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))) | (~environment(sk1)) | greater(equilibrium(sk1), sk2) | (~in_environment(sk1, sk2)) | constant(resources(sk1, sk2)) | (~greater(number_of_organizations(sk1, sk2), zero)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (((~environment(sk1)) | greater(equilibrium(sk1), sk2) | constant(resources(sk1, sk2)) | (~greater(number_of_organizations(sk1, sk2), zero)) | (~in_environment(sk1, sk2))) <=> ((~environment(sk1)) | greater(equilibrium(sk1), sk2) | (~in_environment(sk1, sk2)) | constant(resources(sk1, sk2)) | (~greater(number_of_organizations(sk1, sk2), zero)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))) | ((~environment(sk1)) | greater(equilibrium(sk1), sk2) | constant(resources(sk1, sk2)) | (~greater(number_of_organizations(sk1, sk2), zero)) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))) | ((~environment(sk1)) | greater(equilibrium(sk1), sk2) | (~in_environment(sk1, sk2)) | constant(resources(sk1, sk2)) | (~greater(number_of_organizations(sk1, sk2), zero))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[68])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))) | ((~environment(sk1)) | greater(equilibrium(sk1), sk2) | constant(resources(sk1, sk2)) | (~greater(number_of_organizations(sk1, sk2), zero)) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))) | (~environment(sk1)) | greater(equilibrium(sk1), sk2) | (~in_environment(sk1, sk2)) | constant(resources(sk1, sk2)) | (~greater(number_of_organizations(sk1, sk2), zero)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[69, 67])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))) | ((~environment(sk1)) | greater(equilibrium(sk1), sk2) | constant(resources(sk1, sk2)) | (~greater(number_of_organizations(sk1, sk2), zero)) | (~in_environment(sk1, sk2)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : ((~environment(A)) | greater(equilibrium(A), B) | constant(resources(A, B)) | (~greater(number_of_organizations(A, B), zero)) | (~in_environment(A, B)))) | (~environment(sk1)) | greater(equilibrium(sk1), sk2) | (~in_environment(sk1, sk2)) | constant(resources(sk1, sk2)) | (~greater(number_of_organizations(sk1, sk2), zero))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (constant(resources(sk1, sk2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[72, 66, 8, 56, 39, 22])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 (^[B: $i, A: $i] : refl((constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B)))) <=> (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 (![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B)))) <=> ![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 (![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B)))) <=> ![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~constant(resources(A, B)))) <=> ((~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))), (((((~environment(A)) | (~in_environment(A, B))) | (~constant(resources(A, B)))) | constant(number_of_organizations(A, B))) <=> (((~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B)))) | constant(number_of_organizations(A, B))))), rewrite((((~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B)))) | constant(number_of_organizations(A, B))) <=> (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))), (((((~environment(A)) | (~in_environment(A, B))) | (~constant(resources(A, B)))) | constant(number_of_organizations(A, B))) <=> (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~constant(resources(A, B)))) | constant(number_of_organizations(A, B))) <=> ![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.13/0.40 tff(79,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~constant(resources(A, B)))) | constant(number_of_organizations(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a6_30')).
% 0.13/0.40 tff(80,plain,
% 0.13/0.40 (![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.13/0.40 tff(81,plain,
% 0.13/0.40 (![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.13/0.40 tff(82,plain,(
% 0.13/0.40 ![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[81])).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 (![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))) | (constant(number_of_organizations(sk1, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~constant(resources(sk1, sk2))))) <=> ((~![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))) | constant(number_of_organizations(sk1, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~constant(resources(sk1, sk2))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))) | (constant(number_of_organizations(sk1, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~constant(resources(sk1, sk2))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(86,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : (constant(number_of_organizations(A, B)) | (~environment(A)) | (~in_environment(A, B)) | (~constant(resources(A, B))))) | constant(number_of_organizations(sk1, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~constant(resources(sk1, sk2)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.13/0.40 tff(87,plain,
% 0.13/0.40 (constant(number_of_organizations(sk1, sk2)) | (~constant(resources(sk1, sk2)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[86, 83, 8, 56])).
% 0.13/0.40 tff(88,plain,
% 0.13/0.40 (constant(number_of_organizations(sk1, sk2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[87, 73])).
% 0.13/0.40 tff(89,plain,
% 0.13/0.40 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(90,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(92,plain,
% 0.13/0.40 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B))) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(first_movers, B))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(first_movers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(93,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.13/0.41 tff(94,axiom,(![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l7_36')).
% 0.13/0.41 tff(95,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.13/0.41 tff(96,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.13/0.41 tff(97,plain,(
% 0.13/0.41 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.41 inference(skolemize,[status(sab)],[96])).
% 0.13/0.41 tff(98,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.13/0.41 tff(99,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | ((growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(100,plain,
% 0.13/0.41 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | (growth_rate(efficient_producers, sk2) = zero)) <=> ((growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(101,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | (growth_rate(efficient_producers, sk2) = zero))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | ((growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[100])).
% 0.13/0.41 tff(102,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | (growth_rate(efficient_producers, sk2) = zero))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[101, 99])).
% 0.13/0.41 tff(103,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | (growth_rate(efficient_producers, sk2) = zero))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(104,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.13/0.41 tff(105,plain,
% 0.13/0.41 ((growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(zero, growth_rate(first_movers, sk2)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[104, 98, 8, 25])).
% 0.13/0.41 tff(106,plain,
% 0.13/0.41 ((growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(zero, growth_rate(first_movers, sk2))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[105, 88])).
% 0.13/0.41 tff(107,plain,
% 0.13/0.41 (growth_rate(efficient_producers, sk2) = zero),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[106, 2, 1])).
% 0.13/0.41 tff(108,plain,
% 0.13/0.41 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(109,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[108])).
% 0.13/0.41 tff(110,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(111,plain,
% 0.13/0.41 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(growth_rate(first_movers, B), zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(growth_rate(first_movers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B))) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(zero, growth_rate(first_movers, B))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(zero, growth_rate(first_movers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(112,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[111])).
% 0.13/0.41 tff(113,axiom,(![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l7_32')).
% 0.13/0.41 tff(114,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.13/0.41 tff(115,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.13/0.41 tff(116,plain,(
% 0.13/0.41 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[115])).
% 0.13/0.41 tff(117,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.13/0.41 tff(118,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | (greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(119,plain,
% 0.13/0.42 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2)))) <=> (greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(120,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | (greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[119])).
% 0.13/0.42 tff(121,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[120, 118])).
% 0.13/0.42 tff(122,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(123,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.13/0.42 tff(124,plain,
% 0.13/0.42 (greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(first_movers, sk2)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[123, 117, 8, 25])).
% 0.13/0.42 tff(125,plain,
% 0.13/0.42 (greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(first_movers, sk2))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[124, 88])).
% 0.13/0.42 tff(126,plain,
% 0.13/0.42 (growth_rate(first_movers, sk2) = zero),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[125, 2, 1])).
% 0.13/0.42 tff(127,plain,
% 0.13/0.42 (((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))) <=> ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(128,axiom,((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l6_42')).
% 0.13/0.42 tff(129,plain,
% 0.13/0.42 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.13/0.42 tff(130,plain,
% 0.13/0.42 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[129, 127])).
% 0.13/0.42 tff(131,plain,
% 0.13/0.42 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.13/0.42 tff(132,plain,
% 0.13/0.42 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.13/0.42 tff(133,plain,
% 0.13/0.42 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[132, 127])).
% 0.13/0.42 tff(134,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[133, 126, 107])).
% 0.13/0.42 tff(135,plain,(greater(growth_rate(first_movers, sk2), zero) | greater(zero, growth_rate(first_movers, sk2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.42 tff(136,plain,
% 0.13/0.42 (greater(growth_rate(first_movers, sk2), zero)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[135, 1])).
% 0.13/0.42 tff(137,plain,
% 0.13/0.42 (((~greater(zero, growth_rate(efficient_producers, sk2))) | (~greater(growth_rate(first_movers, sk2), zero))) <=> ((~greater(zero, growth_rate(efficient_producers, sk2))) | (~greater(growth_rate(first_movers, sk2), zero)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(138,plain,
% 0.13/0.42 (((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))) <=> ((~greater(zero, growth_rate(efficient_producers, sk2))) | (~greater(growth_rate(first_movers, sk2), zero)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(139,axiom,((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l6_43')).
% 0.13/0.42 tff(140,plain,
% 0.13/0.42 ((~greater(zero, growth_rate(efficient_producers, sk2))) | (~greater(growth_rate(first_movers, sk2), zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.13/0.42 tff(141,plain,
% 0.13/0.42 ((~greater(zero, growth_rate(efficient_producers, sk2))) | (~greater(growth_rate(first_movers, sk2), zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[140, 137])).
% 0.13/0.42 tff(142,plain,
% 0.13/0.42 (~greater(zero, growth_rate(efficient_producers, sk2))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[141, 136])).
% 0.13/0.42 tff(143,plain,
% 0.13/0.42 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(144,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[143])).
% 0.13/0.42 tff(145,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(146,plain,
% 0.13/0.42 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(first_movers, B))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(first_movers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(147,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[146])).
% 0.13/0.42 tff(148,axiom,(![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l7_38')).
% 0.13/0.42 tff(149,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.13/0.43 tff(150,plain,
% 0.13/0.43 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.13/0.43 tff(151,plain,(
% 0.13/0.43 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.43 inference(skolemize,[status(sab)],[150])).
% 0.13/0.43 tff(152,plain,
% 0.13/0.43 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.13/0.43 tff(153,plain,
% 0.13/0.43 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(154,plain,
% 0.13/0.43 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)) | (growth_rate(efficient_producers, sk2) = zero)) <=> ((growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(155,plain,
% 0.13/0.43 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)) | (growth_rate(efficient_producers, sk2) = zero))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[154])).
% 0.13/0.43 tff(156,plain,
% 0.13/0.43 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)) | (growth_rate(efficient_producers, sk2) = zero))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[155, 153])).
% 0.13/0.43 tff(157,plain,
% 0.13/0.43 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)) | (growth_rate(efficient_producers, sk2) = zero))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(158,plain,
% 0.13/0.43 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.13/0.43 tff(159,plain,
% 0.13/0.43 ((growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[158, 152, 8, 25])).
% 0.13/0.43 tff(160,plain,
% 0.13/0.43 ((growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[159, 88])).
% 0.13/0.43 tff(161,plain,
% 0.13/0.43 (growth_rate(efficient_producers, sk2) = zero),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[160, 142, 1])).
% 0.13/0.43 tff(162,plain,
% 0.13/0.43 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(163,plain,
% 0.13/0.43 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[162])).
% 0.13/0.43 tff(164,plain,
% 0.13/0.43 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(165,plain,
% 0.13/0.43 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(zero, growth_rate(efficient_producers, B))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(166,plain,
% 0.13/0.43 (![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[165])).
% 0.13/0.43 tff(167,axiom,(![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l7_34')).
% 0.13/0.43 tff(168,plain,
% 0.13/0.43 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.13/0.43 tff(169,plain,
% 0.13/0.43 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.13/0.43 tff(170,plain,(
% 0.13/0.43 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.43 inference(skolemize,[status(sab)],[169])).
% 0.13/0.43 tff(171,plain,
% 0.13/0.43 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.13/0.43 tff(172,plain,
% 0.13/0.43 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | ((growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(173,plain,
% 0.13/0.44 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2))) <=> ((growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(174,plain,
% 0.13/0.44 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | ((growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[173])).
% 0.13/0.44 tff(175,plain,
% 0.13/0.44 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[174, 172])).
% 0.13/0.44 tff(176,plain,
% 0.13/0.44 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(zero, growth_rate(first_movers, sk2)) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.13/0.44 inference(quant_inst,[status(thm)],[])).
% 0.13/0.44 tff(177,plain,
% 0.13/0.44 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.13/0.44 tff(178,plain,
% 0.13/0.44 ((growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[177, 171, 8, 25])).
% 0.13/0.44 tff(179,plain,
% 0.13/0.44 ((growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(zero, growth_rate(first_movers, sk2))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[178, 88])).
% 0.13/0.44 tff(180,plain,
% 0.13/0.44 (growth_rate(first_movers, sk2) = zero),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[179, 142, 1])).
% 0.13/0.44 tff(181,plain,
% 0.13/0.44 ($false),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[133, 180, 161])).
% 0.13/0.44 tff(182,plain,(greater(zero, growth_rate(first_movers, sk2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.44 tff(183,plain,
% 0.13/0.44 (((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))) <=> ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(184,axiom,((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l6_44')).
% 0.13/0.44 tff(185,plain,
% 0.13/0.44 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.13/0.44 tff(186,plain,
% 0.13/0.44 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[185, 183])).
% 0.13/0.44 tff(187,plain,
% 0.13/0.44 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[186, 183])).
% 0.13/0.44 tff(188,plain,
% 0.13/0.44 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.13/0.44 tff(189,plain,
% 0.13/0.44 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[188, 183])).
% 0.13/0.44 tff(190,plain,
% 0.13/0.44 (~greater(growth_rate(efficient_producers, sk2), zero)),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[189, 182])).
% 0.13/0.44 tff(191,assumption,(~(growth_rate(first_movers, sk2) = zero)), introduced(assumption)).
% 0.13/0.44 tff(192,plain,
% 0.13/0.44 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(193,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[192])).
% 0.13/0.44 tff(194,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(195,plain,
% 0.13/0.44 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(zero, growth_rate(efficient_producers, B))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(growth_rate(efficient_producers, B), zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))) | greater(growth_rate(efficient_producers, B), zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B))) | greater(growth_rate(efficient_producers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(growth_rate(efficient_producers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(196,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(growth_rate(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[195])).
% 0.13/0.44 tff(197,axiom,(![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(growth_rate(efficient_producers, B), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l7_33')).
% 0.13/0.44 tff(198,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.13/0.44 tff(199,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.13/0.44 tff(200,plain,(
% 0.13/0.44 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.44 inference(skolemize,[status(sab)],[199])).
% 0.13/0.44 tff(201,plain,
% 0.13/0.44 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[200, 193])).
% 0.13/0.44 tff(202,plain,
% 0.13/0.44 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | ((growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(203,plain,
% 0.13/0.44 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2))) <=> ((growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(204,plain,
% 0.13/0.44 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | ((growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[203])).
% 0.13/0.44 tff(205,plain,
% 0.13/0.44 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[204, 202])).
% 0.13/0.45 tff(206,plain,
% 0.13/0.45 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(207,plain,
% 0.13/0.45 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)))) | (growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.13/0.45 tff(208,plain,
% 0.13/0.45 ((growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[207, 201, 8, 25])).
% 0.13/0.45 tff(209,plain,
% 0.13/0.45 ((growth_rate(first_movers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero)),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[208, 88])).
% 0.13/0.45 tff(210,plain,
% 0.13/0.45 (greater(zero, growth_rate(efficient_producers, sk2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[209, 191, 190])).
% 0.13/0.45 tff(211,plain,
% 0.13/0.45 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(212,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[211])).
% 0.13/0.45 tff(213,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(214,plain,
% 0.13/0.45 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(growth_rate(first_movers, B), zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(growth_rate(first_movers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(growth_rate(efficient_producers, B), zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B)))) | greater(growth_rate(efficient_producers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(215,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[214])).
% 0.13/0.45 tff(216,axiom,(![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l7_31')).
% 0.13/0.45 tff(217,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.13/0.45 tff(218,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.13/0.45 tff(219,plain,(
% 0.13/0.45 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.45 inference(skolemize,[status(sab)],[218])).
% 0.13/0.45 tff(220,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.13/0.45 tff(221,plain,
% 0.13/0.45 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | (greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(222,plain,
% 0.13/0.45 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2)))) <=> (greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(223,plain,
% 0.13/0.45 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | (greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[222])).
% 0.13/0.45 tff(224,plain,
% 0.13/0.45 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[223, 221])).
% 0.13/0.45 tff(225,plain,
% 0.13/0.45 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(226,plain,
% 0.13/0.45 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~constant(number_of_organizations(A, B))))) | greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.24/0.46 tff(227,plain,
% 0.24/0.46 (greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[226, 220, 8, 25])).
% 0.24/0.46 tff(228,plain,
% 0.24/0.46 (greater(growth_rate(first_movers, sk2), zero) | (growth_rate(first_movers, sk2) = zero) | greater(growth_rate(efficient_producers, sk2), zero)),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[227, 88])).
% 0.24/0.46 tff(229,plain,
% 0.24/0.46 (greater(growth_rate(first_movers, sk2), zero)),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[228, 191, 190])).
% 0.24/0.46 tff(230,plain,
% 0.24/0.46 ($false),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[141, 229, 210])).
% 0.24/0.46 tff(231,plain,(growth_rate(first_movers, sk2) = zero), inference(lemma,lemma(discharge,[]))).
% 0.24/0.46 tff(232,plain,
% 0.24/0.46 (~(growth_rate(efficient_producers, sk2) = zero)),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[133, 231])).
% 0.24/0.46 tff(233,plain,
% 0.24/0.46 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(234,plain,
% 0.24/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[233])).
% 0.24/0.46 tff(235,plain,
% 0.24/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(236,plain,
% 0.24/0.46 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(growth_rate(efficient_producers, B), zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(efficient_producers, B), zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(growth_rate(efficient_producers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(237,plain,
% 0.24/0.46 (![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(growth_rate(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[236])).
% 0.24/0.46 tff(238,axiom,(![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(growth_rate(efficient_producers, B), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l7_37')).
% 0.24/0.46 tff(239,plain,
% 0.24/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.24/0.46 tff(240,plain,
% 0.24/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[239, 235])).
% 0.24/0.46 tff(241,plain,(
% 0.24/0.46 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.46 inference(skolemize,[status(sab)],[240])).
% 0.24/0.46 tff(242,plain,
% 0.24/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[241, 234])).
% 0.24/0.46 tff(243,plain,
% 0.24/0.46 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(244,plain,
% 0.24/0.46 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)) | (growth_rate(efficient_producers, sk2) = zero)) <=> ((growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(245,plain,
% 0.24/0.46 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)) | (growth_rate(efficient_producers, sk2) = zero))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))))),
% 0.24/0.46 inference(monotonicity,[status(thm)],[244])).
% 0.24/0.46 tff(246,plain,
% 0.24/0.46 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)) | (growth_rate(efficient_producers, sk2) = zero))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.24/0.46 inference(transitivity,[status(thm)],[245, 243])).
% 0.24/0.46 tff(247,plain,
% 0.24/0.46 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | greater(zero, growth_rate(efficient_producers, sk2)) | (growth_rate(efficient_producers, sk2) = zero))),
% 0.24/0.46 inference(quant_inst,[status(thm)],[])).
% 0.24/0.46 tff(248,plain,
% 0.24/0.46 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | (~constant(number_of_organizations(A, B))) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.24/0.46 tff(249,plain,
% 0.24/0.46 ((growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[248, 242, 8, 25])).
% 0.24/0.46 tff(250,plain,
% 0.24/0.46 ((growth_rate(efficient_producers, sk2) = zero) | greater(zero, growth_rate(efficient_producers, sk2)) | greater(growth_rate(efficient_producers, sk2), zero)),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[249, 88])).
% 0.24/0.46 tff(251,plain,
% 0.24/0.46 (greater(zero, growth_rate(efficient_producers, sk2))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[250, 232, 190])).
% 0.24/0.46 tff(252,plain,
% 0.24/0.46 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(253,plain,
% 0.24/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[252])).
% 0.24/0.46 tff(254,plain,
% 0.24/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(255,plain,
% 0.24/0.46 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(efficient_producers, B), zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))))),
% 0.24/0.47 inference(bind,[status(th)],[])).
% 0.24/0.47 tff(256,plain,
% 0.24/0.47 (![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.47 inference(quant_intro,[status(thm)],[255])).
% 0.24/0.47 tff(257,axiom,(![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~constant(number_of_organizations(A, B)))) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l7_35')).
% 0.24/0.47 tff(258,plain,
% 0.24/0.47 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.47 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.24/0.47 tff(259,plain,
% 0.24/0.47 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.47 inference(modus_ponens,[status(thm)],[258, 254])).
% 0.24/0.47 tff(260,plain,(
% 0.24/0.47 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.47 inference(skolemize,[status(sab)],[259])).
% 0.24/0.47 tff(261,plain,
% 0.24/0.47 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))),
% 0.24/0.47 inference(modus_ponens,[status(thm)],[260, 253])).
% 0.24/0.47 tff(262,plain,
% 0.24/0.47 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | ((growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(263,plain,
% 0.24/0.47 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | greater(growth_rate(first_movers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | (growth_rate(efficient_producers, sk2) = zero)) <=> ((growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(264,plain,
% 0.24/0.47 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | greater(growth_rate(first_movers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | (growth_rate(efficient_producers, sk2) = zero))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | ((growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))))),
% 0.24/0.48 inference(monotonicity,[status(thm)],[263])).
% 0.24/0.48 tff(265,plain,
% 0.24/0.48 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | greater(growth_rate(first_movers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | (growth_rate(efficient_producers, sk2) = zero))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2))))),
% 0.24/0.48 inference(transitivity,[status(thm)],[264, 262])).
% 0.24/0.48 tff(266,plain,
% 0.24/0.48 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater(growth_rate(efficient_producers, sk2), zero) | greater(growth_rate(first_movers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2))) | (growth_rate(efficient_producers, sk2) = zero))),
% 0.24/0.48 inference(quant_inst,[status(thm)],[])).
% 0.24/0.48 tff(267,plain,
% 0.24/0.48 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~constant(number_of_organizations(A, B))) | (growth_rate(efficient_producers, B) = zero))) | (growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.24/0.48 tff(268,plain,
% 0.24/0.48 ((growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(growth_rate(efficient_producers, sk2), zero) | (~constant(number_of_organizations(sk1, sk2)))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[267, 261, 8, 25])).
% 0.24/0.48 tff(269,plain,
% 0.24/0.48 ((growth_rate(efficient_producers, sk2) = zero) | greater(growth_rate(first_movers, sk2), zero) | greater(growth_rate(efficient_producers, sk2), zero)),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[268, 88])).
% 0.24/0.48 tff(270,plain,
% 0.24/0.48 (greater(growth_rate(first_movers, sk2), zero)),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[269, 232, 190])).
% 0.24/0.48 tff(271,plain,
% 0.24/0.48 ($false),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[141, 270, 251])).
% 0.24/0.48 % SZS output end Proof
% 0.24/0.48 % E exiting
%------------------------------------------------------------------------------