%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT037-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n007.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 06:24:03 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT037-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n007.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 7 12:42:12 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(decreases_type, type, (
% 0.13/0.39 decreases: $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 * $i ) > $i)).
% 0.13/0.39 tff(sk3_type, type, (
% 0.13/0.39 sk3: $i)).
% 0.13/0.39 tff(sk4_type, type, (
% 0.13/0.39 sk4: $i)).
% 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 * $i ) > $i)).
% 0.13/0.39 tff(zero_type, type, (
% 0.13/0.39 zero: $i)).
% 0.13/0.39 tff(efficient_producers_type, type, (
% 0.13/0.39 efficient_producers: $i)).
% 0.13/0.39 tff(first_movers_type, type, (
% 0.13/0.39 first_movers: $i)).
% 0.13/0.39 tff(resilience_type, type, (
% 0.13/0.39 resilience: $i > $i)).
% 0.13/0.39 tff(in_environment_type, type, (
% 0.13/0.39 in_environment: ( $i * $i ) > $o)).
% 0.13/0.39 tff(cardinality_at_time_type, type, (
% 0.13/0.39 cardinality_at_time: ( $i * $i ) > $i)).
% 0.13/0.39 tff(environment_type, type, (
% 0.13/0.39 environment: $i > $o)).
% 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(appear_type, type, (
% 0.13/0.39 appear: ( $i * $i ) > $i)).
% 0.13/0.39 tff(subpopulation_type, type, (
% 0.13/0.39 subpopulation: ( $i * $i * $i ) > $o)).
% 0.13/0.39 tff(constant_type, type, (
% 0.13/0.39 constant: $i > $o)).
% 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(an_organisation_type, type, (
% 0.13/0.39 an_organisation: $i)).
% 0.13/0.39 tff(1,assumption,(~decreases(number_of_organizations(sk3, sk1(sk4, sk3)))), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~greater(cardinality_at_time(efficient_producers, sk4), zero)) <=> (~greater(cardinality_at_time(efficient_producers, sk4), zero))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,axiom,(~greater(cardinality_at_time(efficient_producers, sk4), zero)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t6_54')).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (~greater(cardinality_at_time(efficient_producers, sk4), zero)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (in_environment(sk3, sk4) <=> in_environment(sk3, sk4)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(6,axiom,(in_environment(sk3, sk4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t6_52')).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (in_environment(sk3, sk4)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (environment(sk3) <=> environment(sk3)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(9,axiom,(environment(sk3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t6_51')).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (environment(sk3)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (^[B: $i, A: $i] : refl(((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (cardinality_at_time(efficient_producers, B) = zero)) <=> ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (cardinality_at_time(efficient_producers, B) = zero)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> (((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B))) | greater(cardinality_at_time(efficient_producers, B), zero)))), rewrite((((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B))) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))), (((((~environment(A)) | (~in_environment(A, B))) | (cardinality_at_time(efficient_producers, B) = zero)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (cardinality_at_time(efficient_producers, B) = zero)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.39 tff(16,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (cardinality_at_time(efficient_producers, B) = zero)) | greater(cardinality_at_time(efficient_producers, B), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_efficient_producers_exist_40')).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.39 tff(19,plain,(
% 0.13/0.39 ![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.13/0.39 inference(skolemize,[status(sab)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (((~![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | (greater(cardinality_at_time(efficient_producers, sk4), zero) | (cardinality_at_time(efficient_producers, sk4) = zero) | (~environment(sk3)) | (~in_environment(sk3, sk4)))) <=> ((~![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | greater(cardinality_at_time(efficient_producers, sk4), zero) | (cardinality_at_time(efficient_producers, sk4) = zero) | (~environment(sk3)) | (~in_environment(sk3, sk4)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (((cardinality_at_time(efficient_producers, sk4) = zero) | (~environment(sk3)) | (~in_environment(sk3, sk4)) | greater(cardinality_at_time(efficient_producers, sk4), zero)) <=> (greater(cardinality_at_time(efficient_producers, sk4), zero) | (cardinality_at_time(efficient_producers, sk4) = zero) | (~environment(sk3)) | (~in_environment(sk3, sk4)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (((~![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | ((cardinality_at_time(efficient_producers, sk4) = zero) | (~environment(sk3)) | (~in_environment(sk3, sk4)) | greater(cardinality_at_time(efficient_producers, sk4), zero))) <=> ((~![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | (greater(cardinality_at_time(efficient_producers, sk4), zero) | (cardinality_at_time(efficient_producers, sk4) = zero) | (~environment(sk3)) | (~in_environment(sk3, sk4))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (((~![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | ((cardinality_at_time(efficient_producers, sk4) = zero) | (~environment(sk3)) | (~in_environment(sk3, sk4)) | greater(cardinality_at_time(efficient_producers, sk4), zero))) <=> ((~![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | greater(cardinality_at_time(efficient_producers, sk4), zero) | (cardinality_at_time(efficient_producers, sk4) = zero) | (~environment(sk3)) | (~in_environment(sk3, sk4)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[23, 21])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((~![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | ((cardinality_at_time(efficient_producers, sk4) = zero) | (~environment(sk3)) | (~in_environment(sk3, sk4)) | greater(cardinality_at_time(efficient_producers, sk4), zero))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~![B: $i, A: $i] : ((cardinality_at_time(efficient_producers, B) = zero) | (~environment(A)) | (~in_environment(A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | greater(cardinality_at_time(efficient_producers, sk4), zero) | (cardinality_at_time(efficient_producers, sk4) = zero) | (~environment(sk3)) | (~in_environment(sk3, sk4))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (cardinality_at_time(efficient_producers, sk4) = zero),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[26, 20, 10, 7, 4])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (greater_or_equal(sk4, appear(efficient_producers, sk3)) <=> greater_or_equal(sk4, appear(efficient_producers, sk3))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(29,axiom,(greater_or_equal(sk4, appear(efficient_producers, sk3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t6_53')).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (greater_or_equal(sk4, appear(efficient_producers, sk3))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (^[B: $i, A: $i] : refl(((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A))) <=> ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A))) <=> ![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A))) <=> ![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~(cardinality_at_time(efficient_producers, B) = zero))) <=> ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)))), (((((~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~(cardinality_at_time(efficient_producers, B) = zero))) | in_environment(A, sk1(B, A))) <=> (((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A))) | in_environment(A, sk1(B, A))))), rewrite((((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A))) | in_environment(A, sk1(B, A))) <=> ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))), (((((~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~(cardinality_at_time(efficient_producers, B) = zero))) | in_environment(A, sk1(B, A))) <=> ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((((~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~(cardinality_at_time(efficient_producers, B) = zero))) | in_environment(A, sk1(B, A))) <=> ![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.39 tff(36,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~(cardinality_at_time(efficient_producers, B) = zero))) | in_environment(A, sk1(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_previous_negative_growth_29')).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.13/0.39 tff(39,plain,(
% 0.13/0.39 ![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[38])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (((~![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))) | ((~(cardinality_at_time(efficient_producers, sk4) = zero)) | (~greater_or_equal(sk4, appear(efficient_producers, sk3))) | (~environment(sk3)) | in_environment(sk3, sk1(sk4, sk3)))) <=> ((~![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))) | (~(cardinality_at_time(efficient_producers, sk4) = zero)) | (~greater_or_equal(sk4, appear(efficient_producers, sk3))) | (~environment(sk3)) | in_environment(sk3, sk1(sk4, sk3)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((~![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))) | ((~(cardinality_at_time(efficient_producers, sk4) = zero)) | (~greater_or_equal(sk4, appear(efficient_producers, sk3))) | (~environment(sk3)) | in_environment(sk3, sk1(sk4, sk3)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ((~![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | in_environment(A, sk1(B, A)))) | (~(cardinality_at_time(efficient_producers, sk4) = zero)) | (~greater_or_equal(sk4, appear(efficient_producers, sk3))) | (~environment(sk3)) | in_environment(sk3, sk1(sk4, sk3))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 ((~(cardinality_at_time(efficient_producers, sk4) = zero)) | in_environment(sk3, sk1(sk4, sk3))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[43, 40, 10, 30])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (in_environment(sk3, sk1(sk4, sk3))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[44, 27])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (^[B: $i, A: $i] : refl(((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B)))) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | (~greater(zero, growth_rate(sk2(B, A), B)))) <=> (((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B))) | (~greater(zero, growth_rate(sk2(B, A), B)))))), rewrite((((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B))) | (~greater(zero, growth_rate(sk2(B, A), B)))) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))), (((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | (~greater(zero, growth_rate(sk2(B, A), B)))) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | (~greater(zero, growth_rate(sk2(B, A), B)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.13/0.39 tff(51,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | (~greater(zero, growth_rate(sk2(B, A), B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_non_decreasing_35')).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.13/0.39 tff(54,plain,(
% 0.13/0.39 ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[53])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | (~greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | (~greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | (~greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | (~greater(zero, growth_rate(sk2(B, A), B))))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | (~greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 (decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | (~greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[58, 55, 10, 45])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 (~greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[59, 1])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 (^[B: $i, A: $i] : refl(((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A)))) <=> ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A)))) <=> ![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 (![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A)))) <=> ![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~(cardinality_at_time(efficient_producers, B) = zero))) <=> ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)))), (((((~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~(cardinality_at_time(efficient_producers, B) = zero))) | greater(zero, growth_rate(efficient_producers, sk1(B, A)))) <=> (((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A))) | greater(zero, growth_rate(efficient_producers, sk1(B, A)))))), rewrite((((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A))) | greater(zero, growth_rate(efficient_producers, sk1(B, A)))) <=> ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))), (((((~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~(cardinality_at_time(efficient_producers, B) = zero))) | greater(zero, growth_rate(efficient_producers, sk1(B, A)))) <=> ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((((~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~(cardinality_at_time(efficient_producers, B) = zero))) | greater(zero, growth_rate(efficient_producers, sk1(B, A)))) <=> ![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.13/0.40 tff(66,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~(cardinality_at_time(efficient_producers, B) = zero))) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_previous_negative_growth_31')).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.13/0.40 tff(69,plain,(
% 0.13/0.40 ![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[68])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))) | ((~(cardinality_at_time(efficient_producers, sk4) = zero)) | (~greater_or_equal(sk4, appear(efficient_producers, sk3))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3))))) <=> ((~![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))) | (~(cardinality_at_time(efficient_producers, sk4) = zero)) | (~greater_or_equal(sk4, appear(efficient_producers, sk3))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))) | ((~(cardinality_at_time(efficient_producers, sk4) = zero)) | (~greater_or_equal(sk4, appear(efficient_producers, sk3))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : ((~(cardinality_at_time(efficient_producers, B) = zero)) | (~greater_or_equal(B, appear(efficient_producers, A))) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, sk1(B, A))))) | (~(cardinality_at_time(efficient_producers, sk4) = zero)) | (~greater_or_equal(sk4, appear(efficient_producers, sk3))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 ((~(cardinality_at_time(efficient_producers, sk4) = zero)) | greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[73, 70, 10, 30])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 (greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[74, 27])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B))) <=> ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(79,plain,
% 0.13/0.40 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | greater(zero, growth_rate(C, B))) <=> ((~environment(A)) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | greater(zero, growth_rate(C, B))) | (~greater(resilience(D), resilience(C)))) <=> (((~environment(A)) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B))) | (~greater(resilience(D), resilience(C)))))), rewrite((((~environment(A)) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B))) | (~greater(resilience(D), resilience(C)))) <=> ((~environment(A)) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | greater(zero, growth_rate(C, B))) | (~greater(resilience(D), resilience(C)))) <=> ((~environment(A)) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | greater(zero, growth_rate(C, B))) | (~greater(resilience(D), resilience(C)))) | (~greater(zero, growth_rate(D, B)))) <=> (((~environment(A)) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B))) | (~greater(zero, growth_rate(D, B)))))), rewrite((((~environment(A)) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B))) | (~greater(zero, growth_rate(D, B)))) <=> ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))), ((((((~environment(A)) | (~in_environment(A, B))) | greater(zero, growth_rate(C, B))) | (~greater(resilience(D), resilience(C)))) | (~greater(zero, growth_rate(D, B)))) <=> ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(80,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : (((((~environment(A)) | (~in_environment(A, B))) | greater(zero, growth_rate(C, B))) | (~greater(resilience(D), resilience(C)))) | (~greater(zero, growth_rate(D, B)))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.13/0.40 tff(81,axiom,(![B: $i, D: $i, A: $i, C: $i] : (((((~environment(A)) | (~in_environment(A, B))) | greater(zero, growth_rate(C, B))) | (~greater(resilience(D), resilience(C)))) | (~greater(zero, growth_rate(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a12_48')).
% 0.13/0.40 tff(82,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.13/0.40 tff(84,plain,(
% 0.13/0.40 ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[83])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.13/0.40 tff(86,plain,
% 0.13/0.40 (((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))) | (~in_environment(sk3, sk1(sk4, sk3))) | greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))) | (~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))) | (~environment(sk3)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))) | (~in_environment(sk3, sk1(sk4, sk3))) | greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))) | (~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(87,plain,
% 0.13/0.40 (((~environment(sk3)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))) | (~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))) | greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))) | (~in_environment(sk3, sk1(sk4, sk3)))) <=> ((~environment(sk3)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))) | (~in_environment(sk3, sk1(sk4, sk3))) | greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))) | (~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(88,plain,
% 0.13/0.40 (((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))) | (~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))) | greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))) | (~in_environment(sk3, sk1(sk4, sk3))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))) | (~in_environment(sk3, sk1(sk4, sk3))) | greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))) | (~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[87])).
% 0.13/0.40 tff(89,plain,
% 0.13/0.40 (((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))) | (~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))) | greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))) | (~in_environment(sk3, sk1(sk4, sk3))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))) | (~environment(sk3)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))) | (~in_environment(sk3, sk1(sk4, sk3))) | greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))) | (~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[88, 86])).
% 0.13/0.40 tff(90,plain,
% 0.13/0.40 ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))) | (~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))) | greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))) | (~in_environment(sk3, sk1(sk4, sk3))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(zero, growth_rate(D, B))) | (~greater(resilience(D), resilience(C))) | greater(zero, growth_rate(C, B)) | (~in_environment(A, B)))) | (~environment(sk3)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))) | (~in_environment(sk3, sk1(sk4, sk3))) | greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))) | (~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.13/0.40 tff(92,plain,
% 0.13/0.40 (~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[91, 85, 10, 75, 45, 60])).
% 0.13/0.40 tff(93,assumption,(sk2(sk1(sk4, sk3), sk3) = first_movers), introduced(assumption)).
% 0.13/0.40 tff(94,plain,
% 0.13/0.40 (resilience(sk2(sk1(sk4, sk3), sk3)) = resilience(first_movers)),
% 0.13/0.40 inference(monotonicity,[status(thm)],[93])).
% 0.13/0.40 tff(95,plain,
% 0.13/0.40 (greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3))) <=> greater(resilience(efficient_producers), resilience(first_movers))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[94])).
% 0.13/0.40 tff(96,plain,
% 0.13/0.40 (greater(resilience(efficient_producers), resilience(first_movers)) <=> greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))),
% 0.13/0.40 inference(symmetry,[status(thm)],[95])).
% 0.13/0.40 tff(97,plain,
% 0.13/0.40 (greater(resilience(efficient_producers), resilience(first_movers)) <=> greater(resilience(efficient_producers), resilience(first_movers))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(98,axiom,(greater(resilience(efficient_producers), resilience(first_movers))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a2_49')).
% 0.13/0.40 tff(99,plain,
% 0.13/0.40 (greater(resilience(efficient_producers), resilience(first_movers))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.13/0.40 tff(100,plain,
% 0.13/0.40 (greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.13/0.40 tff(101,assumption,(~greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))), introduced(assumption)).
% 0.13/0.40 tff(102,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.13/0.40 tff(103,plain,((~(sk2(sk1(sk4, sk3), sk3) = first_movers)) | greater(resilience(efficient_producers), resilience(sk2(sk1(sk4, sk3), sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(104,plain,
% 0.13/0.40 (~(sk2(sk1(sk4, sk3), sk3) = first_movers)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[103, 92])).
% 0.13/0.40 tff(105,plain,
% 0.13/0.40 (^[B: $i, A: $i] : refl(((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B))) <=> ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(106,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[105])).
% 0.13/0.40 tff(107,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(108,plain,
% 0.13/0.40 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | subpopulation(sk2(B, A), A, B)) <=> (((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B))) | subpopulation(sk2(B, A), A, B)))), rewrite((((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B))) | subpopulation(sk2(B, A), A, B)) <=> ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | subpopulation(sk2(B, A), A, B)) <=> ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(109,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | subpopulation(sk2(B, A), A, B)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[108])).
% 0.13/0.40 tff(110,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | subpopulation(sk2(B, A), A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_non_decreasing_33')).
% 0.13/0.40 tff(111,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.13/0.40 tff(112,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.13/0.40 tff(113,plain,(
% 0.13/0.40 ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[112])).
% 0.13/0.40 tff(114,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.13/0.40 tff(115,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(116,plain,
% 0.13/0.40 (((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3)) | decreases(number_of_organizations(sk3, sk1(sk4, sk3)))) <=> ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(117,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3)) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[116])).
% 0.13/0.40 tff(118,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3)) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[117, 115])).
% 0.13/0.40 tff(119,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3)) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(120,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | subpopulation(sk2(B, A), A, B) | decreases(number_of_organizations(A, B)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.13/0.40 tff(121,plain,
% 0.13/0.40 (decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[120, 114, 10, 45])).
% 0.13/0.40 tff(122,plain,
% 0.13/0.40 (subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[121, 1])).
% 0.13/0.40 tff(123,plain,
% 0.13/0.40 (^[B: $i, A: $i] : refl(((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero)) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(124,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[123])).
% 0.13/0.40 tff(125,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(126,plain,
% 0.13/0.40 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | greater(cardinality_at_time(sk2(B, A), B), zero)) <=> (((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B))) | greater(cardinality_at_time(sk2(B, A), B), zero)))), rewrite((((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B))) | greater(cardinality_at_time(sk2(B, A), B), zero)) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))), (((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | greater(cardinality_at_time(sk2(B, A), B), zero)) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(127,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | greater(cardinality_at_time(sk2(B, A), B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[126])).
% 0.13/0.40 tff(128,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | decreases(number_of_organizations(A, B))) | greater(cardinality_at_time(sk2(B, A), B), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_non_decreasing_34')).
% 0.13/0.40 tff(129,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.13/0.40 tff(130,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.13/0.40 tff(131,plain,(
% 0.13/0.40 ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))),
% 0.13/0.40 inference(skolemize,[status(sab)],[130])).
% 0.13/0.40 tff(132,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.13/0.40 tff(133,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | greater(cardinality_at_time(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)), zero))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | greater(cardinality_at_time(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)), zero))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(134,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | greater(cardinality_at_time(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)), zero))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(135,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(number_of_organizations(A, B)) | greater(cardinality_at_time(sk2(B, A), B), zero))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | greater(cardinality_at_time(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)), zero)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.13/0.40 tff(136,plain,
% 0.13/0.40 (decreases(number_of_organizations(sk3, sk1(sk4, sk3))) | greater(cardinality_at_time(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)), zero)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[135, 132, 10, 45])).
% 0.13/0.40 tff(137,plain,
% 0.13/0.40 (greater(cardinality_at_time(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)), zero)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[136, 1])).
% 0.13/0.40 tff(138,plain,
% 0.13/0.40 (^[B: $i, A: $i, C: $i] : refl(((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C))) <=> ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(139,plain,
% 0.13/0.40 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[138])).
% 0.13/0.40 tff(140,plain,
% 0.13/0.40 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(141,plain,
% 0.13/0.40 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulation(B, A, C))) | (~greater(cardinality_at_time(B, C), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))), (((((~environment(A)) | (~subpopulation(B, A, C))) | (~greater(cardinality_at_time(B, C), zero))) | (B = efficient_producers)) <=> (((~environment(A)) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C))) | (B = efficient_producers)))), rewrite((((~environment(A)) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C))) | (B = efficient_producers)) <=> ((~environment(A)) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))), (((((~environment(A)) | (~subpopulation(B, A, C))) | (~greater(cardinality_at_time(B, C), zero))) | (B = efficient_producers)) <=> ((~environment(A)) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C))))), ((((((~environment(A)) | (~subpopulation(B, A, C))) | (~greater(cardinality_at_time(B, C), zero))) | (B = efficient_producers)) | (B = first_movers)) <=> (((~environment(A)) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C))) | (B = first_movers)))), rewrite((((~environment(A)) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C))) | (B = first_movers)) <=> ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))), ((((((~environment(A)) | (~subpopulation(B, A, C))) | (~greater(cardinality_at_time(B, C), zero))) | (B = efficient_producers)) | (B = first_movers)) <=> ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(142,plain,
% 0.13/0.40 (![B: $i, A: $i, C: $i] : (((((~environment(A)) | (~subpopulation(B, A, C))) | (~greater(cardinality_at_time(B, C), zero))) | (B = efficient_producers)) | (B = first_movers)) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[141])).
% 0.13/0.40 tff(143,axiom,(![B: $i, A: $i, C: $i] : (((((~environment(A)) | (~subpopulation(B, A, C))) | (~greater(cardinality_at_time(B, C), zero))) | (B = efficient_producers)) | (B = first_movers))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a9_50')).
% 0.13/0.40 tff(144,plain,
% 0.13/0.40 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.13/0.40 tff(145,plain,
% 0.13/0.40 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.13/0.40 tff(146,plain,(
% 0.13/0.40 ![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[145])).
% 0.13/0.40 tff(147,plain,
% 0.13/0.40 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.13/0.40 tff(148,plain,
% 0.13/0.40 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))) | ((~environment(sk3)) | (sk2(sk1(sk4, sk3), sk3) = first_movers) | (sk2(sk1(sk4, sk3), sk3) = efficient_producers) | (~greater(cardinality_at_time(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)), zero)) | (~subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))) | (~environment(sk3)) | (sk2(sk1(sk4, sk3), sk3) = first_movers) | (sk2(sk1(sk4, sk3), sk3) = efficient_producers) | (~greater(cardinality_at_time(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)), zero)) | (~subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(149,plain,
% 0.13/0.40 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))) | ((~environment(sk3)) | (sk2(sk1(sk4, sk3), sk3) = first_movers) | (sk2(sk1(sk4, sk3), sk3) = efficient_producers) | (~greater(cardinality_at_time(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)), zero)) | (~subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(150,plain,
% 0.13/0.40 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (B = first_movers) | (B = efficient_producers) | (~greater(cardinality_at_time(B, C), zero)) | (~subpopulation(B, A, C)))) | (~environment(sk3)) | (sk2(sk1(sk4, sk3), sk3) = first_movers) | (sk2(sk1(sk4, sk3), sk3) = efficient_producers) | (~greater(cardinality_at_time(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)), zero)) | (~subpopulation(sk2(sk1(sk4, sk3), sk3), sk3, sk1(sk4, sk3)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.13/0.40 tff(151,plain,
% 0.13/0.40 ((sk2(sk1(sk4, sk3), sk3) = first_movers) | (sk2(sk1(sk4, sk3), sk3) = efficient_producers)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[150, 147, 10, 137, 122])).
% 0.13/0.40 tff(152,plain,
% 0.13/0.40 (sk2(sk1(sk4, sk3), sk3) = efficient_producers),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[151, 104])).
% 0.13/0.40 tff(153,plain,
% 0.13/0.40 (growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)) = growth_rate(efficient_producers, sk1(sk4, sk3))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[152])).
% 0.13/0.40 tff(154,plain,
% 0.13/0.40 (greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3))) <=> greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[153])).
% 0.13/0.40 tff(155,plain,
% 0.13/0.40 (greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3))) <=> greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)))),
% 0.13/0.40 inference(symmetry,[status(thm)],[154])).
% 0.13/0.40 tff(156,plain,
% 0.13/0.40 (greater(zero, growth_rate(sk2(sk1(sk4, sk3), sk3), sk1(sk4, sk3)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[75, 155])).
% 0.13/0.40 tff(157,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[60, 156])).
% 0.13/0.40 tff(158,plain,(decreases(number_of_organizations(sk3, sk1(sk4, sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(159,plain,
% 0.13/0.40 (^[B: $i, A: $i] : refl(((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B)))) <=> ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(160,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[159])).
% 0.13/0.40 tff(161,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(162,plain,
% 0.13/0.40 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~decreases(resources(A, B)))) <=> ((~environment(A)) | (~in_environment(A, B)) | (~decreases(resources(A, B))))), (((((~environment(A)) | (~in_environment(A, B))) | (~decreases(resources(A, B)))) | (~decreases(number_of_organizations(A, B)))) <=> (((~environment(A)) | (~in_environment(A, B)) | (~decreases(resources(A, B)))) | (~decreases(number_of_organizations(A, B)))))), rewrite((((~environment(A)) | (~in_environment(A, B)) | (~decreases(resources(A, B)))) | (~decreases(number_of_organizations(A, B)))) <=> ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))), (((((~environment(A)) | (~in_environment(A, B))) | (~decreases(resources(A, B)))) | (~decreases(number_of_organizations(A, B)))) <=> ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(163,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~decreases(resources(A, B)))) | (~decreases(number_of_organizations(A, B)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[162])).
% 0.13/0.41 tff(164,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~decreases(resources(A, B)))) | (~decreases(number_of_organizations(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a6_46')).
% 0.13/0.41 tff(165,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.13/0.41 tff(166,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.13/0.41 tff(167,plain,(
% 0.13/0.41 ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[166])).
% 0.13/0.41 tff(168,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[167, 160])).
% 0.13/0.41 tff(169,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~decreases(number_of_organizations(sk3, sk1(sk4, sk3)))) | (~decreases(resources(sk3, sk1(sk4, sk3)))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~decreases(number_of_organizations(sk3, sk1(sk4, sk3)))) | (~decreases(resources(sk3, sk1(sk4, sk3)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(170,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~decreases(number_of_organizations(sk3, sk1(sk4, sk3)))) | (~decreases(resources(sk3, sk1(sk4, sk3)))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(171,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~decreases(number_of_organizations(A, B))) | (~decreases(resources(A, B))))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~decreases(number_of_organizations(sk3, sk1(sk4, sk3)))) | (~decreases(resources(sk3, sk1(sk4, sk3))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.13/0.41 tff(172,plain,
% 0.13/0.41 ((~decreases(number_of_organizations(sk3, sk1(sk4, sk3)))) | (~decreases(resources(sk3, sk1(sk4, sk3))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[171, 168, 10, 45])).
% 0.13/0.41 tff(173,plain,
% 0.13/0.41 (~decreases(resources(sk3, sk1(sk4, sk3)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[172, 158])).
% 0.13/0.41 tff(174,plain,
% 0.13/0.41 (^[B: $i, A: $i] : refl((subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B))) <=> (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(175,plain,
% 0.13/0.41 (![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B))) <=> ![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[174])).
% 0.13/0.41 tff(176,plain,
% 0.13/0.41 (![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B))) <=> ![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(177,plain,
% 0.13/0.41 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~in_environment(A, B))) | subpopulation(efficient_producers, A, B)) <=> (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(178,plain,
% 0.13/0.41 (![B: $i, A: $i] : (((~environment(A)) | (~in_environment(A, B))) | subpopulation(efficient_producers, A, B)) <=> ![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[177])).
% 0.13/0.41 tff(179,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~in_environment(A, B))) | subpopulation(efficient_producers, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_subpopulations_38')).
% 0.13/0.41 tff(180,plain,
% 0.13/0.41 (![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.13/0.41 tff(181,plain,
% 0.13/0.41 (![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.13/0.41 tff(182,plain,(
% 0.13/0.41 ![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[181])).
% 0.13/0.41 tff(183,plain,
% 0.13/0.41 (![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[182, 175])).
% 0.13/0.41 tff(184,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | subpopulation(efficient_producers, sk3, sk1(sk4, sk3)))) <=> ((~![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | subpopulation(efficient_producers, sk3, sk1(sk4, sk3)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(185,plain,
% 0.13/0.41 ((subpopulation(efficient_producers, sk3, sk1(sk4, sk3)) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3)))) <=> ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | subpopulation(efficient_producers, sk3, sk1(sk4, sk3)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(186,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))) | (subpopulation(efficient_producers, sk3, sk1(sk4, sk3)) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))))) <=> ((~![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | subpopulation(efficient_producers, sk3, sk1(sk4, sk3))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[185])).
% 0.13/0.41 tff(187,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))) | (subpopulation(efficient_producers, sk3, sk1(sk4, sk3)) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))))) <=> ((~![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | subpopulation(efficient_producers, sk3, sk1(sk4, sk3)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[186, 184])).
% 0.13/0.41 tff(188,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))) | (subpopulation(efficient_producers, sk3, sk1(sk4, sk3)) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(189,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : (subpopulation(efficient_producers, A, B) | (~environment(A)) | (~in_environment(A, B)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | subpopulation(efficient_producers, sk3, sk1(sk4, sk3))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.13/0.41 tff(190,plain,
% 0.13/0.41 (subpopulation(efficient_producers, sk3, sk1(sk4, sk3))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[189, 183, 10, 45])).
% 0.13/0.41 tff(191,plain,
% 0.13/0.41 (^[B: $i, A: $i] : refl(((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B)))) <=> ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(192,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B)))) <=> ![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[191])).
% 0.13/0.41 tff(193,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B)))) <=> ![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(194,axiom,(![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_empty_not_decreasing_39')).
% 0.13/0.41 tff(195,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.13/0.41 tff(196,plain,(
% 0.13/0.41 ![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[195])).
% 0.13/0.41 tff(197,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.13/0.41 tff(198,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B))))) | ((~(cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))))) <=> ((~![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B))))) | (~(cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(199,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B))))) | ((~(cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3)))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(200,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~(cardinality_at_time(A, B) = zero)) | (~greater(zero, growth_rate(A, B))))) | (~(cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, sk1(sk4, sk3))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.13/0.41 tff(201,plain,
% 0.13/0.41 (~(cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[200, 197, 75])).
% 0.13/0.41 tff(202,plain,
% 0.13/0.41 (^[B: $i, A: $i, C: $i] : refl(((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A))) <=> ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(203,plain,
% 0.13/0.41 (![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[202])).
% 0.13/0.41 tff(204,plain,
% 0.13/0.41 (![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(205,plain,
% 0.13/0.41 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~(number_of_organizations(A, B) = zero))) <=> ((~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | (~(number_of_organizations(A, B) = zero))) | (~subpopulation(C, A, B))) <=> (((~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A))) | (~subpopulation(C, A, B))))), rewrite((((~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A))) | (~subpopulation(C, A, B))) <=> ((~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | (~(number_of_organizations(A, B) = zero))) | (~subpopulation(C, A, B))) <=> ((~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~(number_of_organizations(A, B) = zero))) | (~subpopulation(C, A, B))) | (cardinality_at_time(C, B) = zero)) <=> (((~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A))) | (cardinality_at_time(C, B) = zero)))), rewrite((((~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A))) | (cardinality_at_time(C, B) = zero)) <=> ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))), ((((((~environment(A)) | (~in_environment(A, B))) | (~(number_of_organizations(A, B) = zero))) | (~subpopulation(C, A, B))) | (cardinality_at_time(C, B) = zero)) <=> ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(206,plain,
% 0.13/0.41 (![B: $i, A: $i, C: $i] : (((((~environment(A)) | (~in_environment(A, B))) | (~(number_of_organizations(A, B) = zero))) | (~subpopulation(C, A, B))) | (cardinality_at_time(C, B) = zero)) <=> ![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[205])).
% 0.13/0.41 tff(207,axiom,(![B: $i, A: $i, C: $i] : (((((~environment(A)) | (~in_environment(A, B))) | (~(number_of_organizations(A, B) = zero))) | (~subpopulation(C, A, B))) | (cardinality_at_time(C, B) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_no_members_36')).
% 0.13/0.41 tff(208,plain,
% 0.13/0.41 (![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.13/0.41 tff(209,plain,
% 0.13/0.41 (![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.13/0.41 tff(210,plain,(
% 0.13/0.41 ![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[209])).
% 0.13/0.41 tff(211,plain,
% 0.13/0.41 (![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.13/0.41 tff(212,plain,
% 0.13/0.41 (((~![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk3)) | (cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero) | (~in_environment(sk3, sk1(sk4, sk3))) | (~subpopulation(efficient_producers, sk3, sk1(sk4, sk3))) | (~(number_of_organizations(sk3, sk1(sk4, sk3)) = zero)))) <=> ((~![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk3)) | (cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero) | (~in_environment(sk3, sk1(sk4, sk3))) | (~subpopulation(efficient_producers, sk3, sk1(sk4, sk3))) | (~(number_of_organizations(sk3, sk1(sk4, sk3)) = zero)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(213,plain,
% 0.13/0.41 (((cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero) | (~subpopulation(efficient_producers, sk3, sk1(sk4, sk3))) | (~(number_of_organizations(sk3, sk1(sk4, sk3)) = zero)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~environment(sk3))) <=> ((~environment(sk3)) | (cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero) | (~in_environment(sk3, sk1(sk4, sk3))) | (~subpopulation(efficient_producers, sk3, sk1(sk4, sk3))) | (~(number_of_organizations(sk3, sk1(sk4, sk3)) = zero)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(214,plain,
% 0.13/0.41 (((~![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))) | ((cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero) | (~subpopulation(efficient_producers, sk3, sk1(sk4, sk3))) | (~(number_of_organizations(sk3, sk1(sk4, sk3)) = zero)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~environment(sk3)))) <=> ((~![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk3)) | (cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero) | (~in_environment(sk3, sk1(sk4, sk3))) | (~subpopulation(efficient_producers, sk3, sk1(sk4, sk3))) | (~(number_of_organizations(sk3, sk1(sk4, sk3)) = zero))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[213])).
% 0.13/0.41 tff(215,plain,
% 0.13/0.41 (((~![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))) | ((cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero) | (~subpopulation(efficient_producers, sk3, sk1(sk4, sk3))) | (~(number_of_organizations(sk3, sk1(sk4, sk3)) = zero)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~environment(sk3)))) <=> ((~![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk3)) | (cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero) | (~in_environment(sk3, sk1(sk4, sk3))) | (~subpopulation(efficient_producers, sk3, sk1(sk4, sk3))) | (~(number_of_organizations(sk3, sk1(sk4, sk3)) = zero)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[214, 212])).
% 0.13/0.41 tff(216,plain,
% 0.13/0.41 ((~![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))) | ((cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero) | (~subpopulation(efficient_producers, sk3, sk1(sk4, sk3))) | (~(number_of_organizations(sk3, sk1(sk4, sk3)) = zero)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~environment(sk3)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(217,plain,
% 0.13/0.41 ((~![B: $i, A: $i, C: $i] : ((cardinality_at_time(C, B) = zero) | (~subpopulation(C, A, B)) | (~(number_of_organizations(A, B) = zero)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk3)) | (cardinality_at_time(efficient_producers, sk1(sk4, sk3)) = zero) | (~in_environment(sk3, sk1(sk4, sk3))) | (~subpopulation(efficient_producers, sk3, sk1(sk4, sk3))) | (~(number_of_organizations(sk3, sk1(sk4, sk3)) = zero))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.13/0.41 tff(218,plain,
% 0.13/0.41 (~(number_of_organizations(sk3, sk1(sk4, sk3)) = zero)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[217, 211, 10, 45, 201, 190])).
% 0.13/0.41 tff(219,plain,
% 0.13/0.41 (^[B: $i, A: $i] : refl(((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B))) <=> ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(220,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[219])).
% 0.13/0.41 tff(221,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(222,plain,
% 0.13/0.41 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater(appear(an_organisation, A), B))) <=> ((~environment(A)) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(appear(an_organisation, A), B))) | (number_of_organizations(A, B) = zero)) <=> (((~environment(A)) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B))) | (number_of_organizations(A, B) = zero)))), rewrite((((~environment(A)) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B))) | (number_of_organizations(A, B) = zero)) <=> ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(appear(an_organisation, A), B))) | (number_of_organizations(A, B) = zero)) <=> ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(223,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater(appear(an_organisation, A), B))) | (number_of_organizations(A, B) = zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[222])).
% 0.13/0.41 tff(224,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater(appear(an_organisation, A), B))) | (number_of_organizations(A, B) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_start_of_organizations_32')).
% 0.13/0.41 tff(225,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.13/0.41 tff(226,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.13/0.41 tff(227,plain,(
% 0.13/0.41 ![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[226])).
% 0.13/0.41 tff(228,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.13/0.41 tff(229,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (number_of_organizations(sk3, sk1(sk4, sk3)) = zero) | (~greater(appear(an_organisation, sk3), sk1(sk4, sk3))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (number_of_organizations(sk3, sk1(sk4, sk3)) = zero) | (~greater(appear(an_organisation, sk3), sk1(sk4, sk3))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(230,plain,
% 0.13/0.41 (((~environment(sk3)) | (number_of_organizations(sk3, sk1(sk4, sk3)) = zero) | (~greater(appear(an_organisation, sk3), sk1(sk4, sk3))) | (~in_environment(sk3, sk1(sk4, sk3)))) <=> ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (number_of_organizations(sk3, sk1(sk4, sk3)) = zero) | (~greater(appear(an_organisation, sk3), sk1(sk4, sk3))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(231,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (number_of_organizations(sk3, sk1(sk4, sk3)) = zero) | (~greater(appear(an_organisation, sk3), sk1(sk4, sk3))) | (~in_environment(sk3, sk1(sk4, sk3))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (number_of_organizations(sk3, sk1(sk4, sk3)) = zero) | (~greater(appear(an_organisation, sk3), sk1(sk4, sk3)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[230])).
% 0.13/0.41 tff(232,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (number_of_organizations(sk3, sk1(sk4, sk3)) = zero) | (~greater(appear(an_organisation, sk3), sk1(sk4, sk3))) | (~in_environment(sk3, sk1(sk4, sk3))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (number_of_organizations(sk3, sk1(sk4, sk3)) = zero) | (~greater(appear(an_organisation, sk3), sk1(sk4, sk3))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[231, 229])).
% 0.13/0.41 tff(233,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))) | ((~environment(sk3)) | (number_of_organizations(sk3, sk1(sk4, sk3)) = zero) | (~greater(appear(an_organisation, sk3), sk1(sk4, sk3))) | (~in_environment(sk3, sk1(sk4, sk3))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(234,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | (number_of_organizations(A, B) = zero) | (~greater(appear(an_organisation, A), B)) | (~in_environment(A, B)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (number_of_organizations(sk3, sk1(sk4, sk3)) = zero) | (~greater(appear(an_organisation, sk3), sk1(sk4, sk3)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.13/0.41 tff(235,plain,
% 0.13/0.41 ((number_of_organizations(sk3, sk1(sk4, sk3)) = zero) | (~greater(appear(an_organisation, sk3), sk1(sk4, sk3)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[234, 228, 10, 45])).
% 0.13/0.41 tff(236,plain,
% 0.13/0.41 (~greater(appear(an_organisation, sk3), sk1(sk4, sk3))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[235, 218])).
% 0.13/0.41 tff(237,plain,
% 0.13/0.41 (^[B: $i, A: $i] : refl(((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A))) <=> ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(238,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A))) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[237])).
% 0.13/0.41 tff(239,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A))) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(240,plain,
% 0.13/0.41 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(B, appear(an_organisation, A))) <=> ((~environment(A)) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(B, appear(an_organisation, A))) | greater(appear(an_organisation, A), B)) <=> (((~environment(A)) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A))) | greater(appear(an_organisation, A), B)))), rewrite((((~environment(A)) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A))) | greater(appear(an_organisation, A), B)) <=> ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(B, appear(an_organisation, A))) | greater(appear(an_organisation, A), B)) <=> ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(241,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(B, appear(an_organisation, A))) | greater(appear(an_organisation, A), B)) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[240])).
% 0.13/0.41 tff(242,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(B, appear(an_organisation, A))) | greater(appear(an_organisation, A), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_environment_inequality_42')).
% 0.13/0.41 tff(243,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.13/0.41 tff(244,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.13/0.41 tff(245,plain,(
% 0.13/0.41 ![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[244])).
% 0.13/0.41 tff(246,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[245, 238])).
% 0.13/0.41 tff(247,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3)) | greater(appear(an_organisation, sk3), sk1(sk4, sk3)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3)) | greater(appear(an_organisation, sk3), sk1(sk4, sk3)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(248,plain,
% 0.13/0.41 (((~environment(sk3)) | greater(appear(an_organisation, sk3), sk1(sk4, sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3))) <=> ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3)) | greater(appear(an_organisation, sk3), sk1(sk4, sk3)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(249,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))) | ((~environment(sk3)) | greater(appear(an_organisation, sk3), sk1(sk4, sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3)) | greater(appear(an_organisation, sk3), sk1(sk4, sk3))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[248])).
% 0.13/0.41 tff(250,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))) | ((~environment(sk3)) | greater(appear(an_organisation, sk3), sk1(sk4, sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3)) | greater(appear(an_organisation, sk3), sk1(sk4, sk3)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[249, 247])).
% 0.13/0.41 tff(251,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))) | ((~environment(sk3)) | greater(appear(an_organisation, sk3), sk1(sk4, sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(252,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | greater(appear(an_organisation, A), B) | (~in_environment(A, B)) | greater_or_equal(B, appear(an_organisation, A)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3)) | greater(appear(an_organisation, sk3), sk1(sk4, sk3))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.13/0.41 tff(253,plain,
% 0.13/0.41 (greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3)) | greater(appear(an_organisation, sk3), sk1(sk4, sk3))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[252, 246, 10, 45])).
% 0.13/0.41 tff(254,plain,
% 0.13/0.41 (greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[253, 236])).
% 0.13/0.41 tff(255,plain,
% 0.13/0.41 (^[B: $i, A: $i] : refl(((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero)) <=> ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(256,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[255])).
% 0.13/0.41 tff(257,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(258,plain,
% 0.13/0.41 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(B, appear(an_organisation, A)))) <=> ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(B, appear(an_organisation, A)))) | greater(number_of_organizations(A, B), zero)) <=> (((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A)))) | greater(number_of_organizations(A, B), zero)))), rewrite((((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A)))) | greater(number_of_organizations(A, B), zero)) <=> ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(B, appear(an_organisation, A)))) | greater(number_of_organizations(A, B), zero)) <=> ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(259,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(B, appear(an_organisation, A)))) | greater(number_of_organizations(A, B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[258])).
% 0.13/0.41 tff(260,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(B, appear(an_organisation, A)))) | greater(number_of_organizations(A, B), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a1_45')).
% 0.13/0.41 tff(261,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.13/0.41 tff(262,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[261, 257])).
% 0.13/0.41 tff(263,plain,(
% 0.13/0.41 ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.41 inference(skolemize,[status(sab)],[262])).
% 0.13/0.41 tff(264,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[263, 256])).
% 0.13/0.41 tff(265,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3))) | greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3))) | greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(266,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3))) | greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(267,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | (~greater_or_equal(B, appear(an_organisation, A))) | greater(number_of_organizations(A, B), zero))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | (~greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3))) | greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.13/0.41 tff(268,plain,
% 0.13/0.41 ((~greater_or_equal(sk1(sk4, sk3), appear(an_organisation, sk3))) | greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[267, 264, 10, 45])).
% 0.13/0.41 tff(269,plain,
% 0.13/0.41 (greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[268, 254])).
% 0.13/0.41 tff(270,plain,
% 0.13/0.41 (^[B: $i, A: $i] : refl(((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero))) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(271,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[270])).
% 0.13/0.41 tff(272,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(273,plain,
% 0.13/0.41 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) <=> ((~environment(A)) | (~in_environment(A, B)) | (~greater(number_of_organizations(A, B), zero)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | (~greater(equilibrium(A), B))) <=> (((~environment(A)) | (~in_environment(A, B)) | (~greater(number_of_organizations(A, B), zero))) | (~greater(equilibrium(A), B))))), rewrite((((~environment(A)) | (~in_environment(A, B)) | (~greater(number_of_organizations(A, B), zero))) | (~greater(equilibrium(A), B))) <=> ((~environment(A)) | (~in_environment(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | (~greater(equilibrium(A), B))) <=> ((~environment(A)) | (~in_environment(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | (~greater(equilibrium(A), B))) | decreases(resources(A, B))) <=> (((~environment(A)) | (~in_environment(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero))) | decreases(resources(A, B))))), rewrite((((~environment(A)) | (~in_environment(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero))) | decreases(resources(A, B))) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | (~greater(equilibrium(A), B))) | decreases(resources(A, B))) <=> ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(274,plain,
% 0.13/0.42 (![B: $i, A: $i] : (((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | (~greater(equilibrium(A), B))) | decreases(resources(A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[273])).
% 0.13/0.42 tff(275,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | (~greater(equilibrium(A), B))) | decreases(resources(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a3_43')).
% 0.13/0.42 tff(276,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.13/0.42 tff(277,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[276, 272])).
% 0.13/0.42 tff(278,plain,(
% 0.13/0.42 ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(skolemize,[status(sab)],[277])).
% 0.13/0.42 tff(279,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[278, 271])).
% 0.13/0.42 tff(280,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)) | (~greater(equilibrium(sk3), sk1(sk4, sk3))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)) | (~greater(equilibrium(sk3), sk1(sk4, sk3))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(281,plain,
% 0.13/0.42 (((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(equilibrium(sk3), sk1(sk4, sk3))) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero))) <=> ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)) | (~greater(equilibrium(sk3), sk1(sk4, sk3))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(282,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(equilibrium(sk3), sk1(sk4, sk3))) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)) | (~greater(equilibrium(sk3), sk1(sk4, sk3)))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[281])).
% 0.13/0.42 tff(283,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(equilibrium(sk3), sk1(sk4, sk3))) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)) | (~greater(equilibrium(sk3), sk1(sk4, sk3))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[282, 280])).
% 0.13/0.42 tff(284,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(equilibrium(sk3), sk1(sk4, sk3))) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(285,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | decreases(resources(A, B)) | (~greater(equilibrium(A), B)) | (~greater(number_of_organizations(A, B), zero)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)) | (~greater(equilibrium(sk3), sk1(sk4, sk3)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.13/0.42 tff(286,plain,
% 0.13/0.42 (decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)) | (~greater(equilibrium(sk3), sk1(sk4, sk3)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[285, 279, 10, 45])).
% 0.13/0.42 tff(287,plain,
% 0.13/0.42 (decreases(resources(sk3, sk1(sk4, sk3))) | (~greater(equilibrium(sk3), sk1(sk4, sk3)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[286, 269])).
% 0.13/0.42 tff(288,plain,
% 0.13/0.42 (~greater(equilibrium(sk3), sk1(sk4, sk3))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[287, 173])).
% 0.13/0.42 tff(289,plain,
% 0.13/0.42 (^[B: $i, A: $i] : refl(((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero))) <=> ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(290,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[289])).
% 0.13/0.42 tff(291,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(292,plain,
% 0.13/0.42 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) <=> ((~environment(A)) | (~in_environment(A, B)) | (~greater(number_of_organizations(A, B), zero)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)) <=> (((~environment(A)) | (~in_environment(A, B)) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)))), rewrite((((~environment(A)) | (~in_environment(A, B)) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)) <=> ((~environment(A)) | (~in_environment(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)) <=> ((~environment(A)) | (~in_environment(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)) | constant(resources(A, B))) <=> (((~environment(A)) | (~in_environment(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero))) | constant(resources(A, B))))), rewrite((((~environment(A)) | (~in_environment(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero))) | constant(resources(A, B))) <=> ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(number_of_organizations(A, B), zero))) | greater(equilibrium(A), B)) | constant(resources(A, B))) <=> ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(293,plain,
% 0.13/0.42 (![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)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[292])).
% 0.13/0.42 tff(294,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_44')).
% 0.13/0.42 tff(295,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.13/0.42 tff(296,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[295, 291])).
% 0.13/0.42 tff(297,plain,(
% 0.13/0.42 ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(skolemize,[status(sab)],[296])).
% 0.13/0.42 tff(298,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[297, 290])).
% 0.13/0.42 tff(299,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | constant(resources(sk3, sk1(sk4, sk3))) | greater(equilibrium(sk3), sk1(sk4, sk3)) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | constant(resources(sk3, sk1(sk4, sk3))) | greater(equilibrium(sk3), sk1(sk4, sk3)) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(300,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | constant(resources(sk3, sk1(sk4, sk3))) | greater(equilibrium(sk3), sk1(sk4, sk3)) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero)))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(301,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(resources(A, B)) | greater(equilibrium(A), B) | (~greater(number_of_organizations(A, B), zero)))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | constant(resources(sk3, sk1(sk4, sk3))) | greater(equilibrium(sk3), sk1(sk4, sk3)) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.13/0.42 tff(302,plain,
% 0.13/0.42 (constant(resources(sk3, sk1(sk4, sk3))) | greater(equilibrium(sk3), sk1(sk4, sk3)) | (~greater(number_of_organizations(sk3, sk1(sk4, sk3)), zero))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[301, 298, 10, 45])).
% 0.13/0.42 tff(303,plain,
% 0.13/0.42 (constant(resources(sk3, sk1(sk4, sk3))) | greater(equilibrium(sk3), sk1(sk4, sk3))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[302, 269])).
% 0.13/0.42 tff(304,plain,
% 0.13/0.42 (constant(resources(sk3, sk1(sk4, sk3)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[303, 288])).
% 0.13/0.42 tff(305,plain,
% 0.13/0.42 (^[B: $i, A: $i] : refl(((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B)))) <=> ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(306,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[305])).
% 0.13/0.42 tff(307,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(308,plain,
% 0.13/0.42 (^[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))) <=> ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(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(number_of_organizations(A, B)) | (~constant(resources(A, B))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(309,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~constant(resources(A, B)))) | constant(number_of_organizations(A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[308])).
% 0.13/0.42 tff(310,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_47')).
% 0.13/0.42 tff(311,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.13/0.42 tff(312,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[311, 307])).
% 0.13/0.42 tff(313,plain,(
% 0.13/0.42 ![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[312])).
% 0.13/0.42 tff(314,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[313, 306])).
% 0.13/0.42 tff(315,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B))))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | constant(number_of_organizations(sk3, sk1(sk4, sk3))) | (~constant(resources(sk3, sk1(sk4, sk3)))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B))))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | constant(number_of_organizations(sk3, sk1(sk4, sk3))) | (~constant(resources(sk3, sk1(sk4, sk3)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(316,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B))))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | constant(number_of_organizations(sk3, sk1(sk4, sk3))) | (~constant(resources(sk3, sk1(sk4, sk3)))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(317,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~environment(A)) | (~in_environment(A, B)) | constant(number_of_organizations(A, B)) | (~constant(resources(A, B))))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk4, sk3))) | constant(number_of_organizations(sk3, sk1(sk4, sk3))) | (~constant(resources(sk3, sk1(sk4, sk3))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.13/0.42 tff(318,plain,
% 0.13/0.42 (constant(number_of_organizations(sk3, sk1(sk4, sk3))) | (~constant(resources(sk3, sk1(sk4, sk3))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[317, 314, 10, 45])).
% 0.13/0.42 tff(319,plain,
% 0.13/0.42 (constant(number_of_organizations(sk3, sk1(sk4, sk3)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[318, 304])).
% 0.13/0.42 tff(320,plain,
% 0.13/0.42 (^[A: $i] : refl(((~constant(A)) | (~decreases(A))) <=> ((~constant(A)) | (~decreases(A))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(321,plain,
% 0.13/0.42 (![A: $i] : ((~constant(A)) | (~decreases(A))) <=> ![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[320])).
% 0.13/0.42 tff(322,plain,
% 0.13/0.42 (![A: $i] : ((~constant(A)) | (~decreases(A))) <=> ![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(323,axiom,(![A: $i] : ((~constant(A)) | (~decreases(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_constant_not_decrease_41')).
% 0.13/0.42 tff(324,plain,
% 0.13/0.42 (![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.13/0.42 tff(325,plain,(
% 0.13/0.42 ![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.13/0.42 inference(skolemize,[status(sab)],[324])).
% 0.13/0.42 tff(326,plain,
% 0.13/0.42 (![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[325, 321])).
% 0.13/0.42 tff(327,plain,
% 0.13/0.42 (((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | ((~constant(number_of_organizations(sk3, sk1(sk4, sk3)))) | (~decreases(number_of_organizations(sk3, sk1(sk4, sk3)))))) <=> ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | (~constant(number_of_organizations(sk3, sk1(sk4, sk3)))) | (~decreases(number_of_organizations(sk3, sk1(sk4, sk3)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(328,plain,
% 0.13/0.42 ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | ((~constant(number_of_organizations(sk3, sk1(sk4, sk3)))) | (~decreases(number_of_organizations(sk3, sk1(sk4, sk3)))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(329,plain,
% 0.13/0.42 ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | (~constant(number_of_organizations(sk3, sk1(sk4, sk3)))) | (~decreases(number_of_organizations(sk3, sk1(sk4, sk3))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.13/0.42 tff(330,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[329, 326, 319, 158])).
% 0.13/0.42 % SZS output end Proof
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------