%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT029-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:01 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.47s
% Output : Proof 0.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT029-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 7 12:22:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.22/0.47 % SZS status Unsatisfiable
% 0.22/0.47 % SZS output start Proof
% 0.22/0.47 tff(greater_type, type, (
% 0.22/0.47 greater: ( $i * $i ) > $o)).
% 0.22/0.47 tff(sk1_type, type, (
% 0.22/0.47 sk1: $i > $i)).
% 0.22/0.47 tff(sk3_type, type, (
% 0.22/0.47 sk3: $i)).
% 0.22/0.47 tff(sk4_type, type, (
% 0.22/0.47 sk4: $i > $i)).
% 0.22/0.47 tff(sk2_type, type, (
% 0.22/0.47 sk2: $i > $i)).
% 0.22/0.47 tff(greater_or_equal_type, type, (
% 0.22/0.47 greater_or_equal: ( $i * $i ) > $o)).
% 0.22/0.47 tff(growth_rate_type, type, (
% 0.22/0.47 growth_rate: ( $i * $i ) > $i)).
% 0.22/0.47 tff(first_movers_type, type, (
% 0.22/0.47 first_movers: $i)).
% 0.22/0.47 tff(efficient_producers_type, type, (
% 0.22/0.47 efficient_producers: $i)).
% 0.22/0.47 tff(equilibrium_type, type, (
% 0.22/0.47 equilibrium: $i > $i)).
% 0.22/0.47 tff(zero_type, type, (
% 0.22/0.47 zero: $i)).
% 0.22/0.47 tff(in_environment_type, type, (
% 0.22/0.47 in_environment: ( $i * $i ) > $o)).
% 0.22/0.47 tff(stable_type, type, (
% 0.22/0.47 stable: $i > $o)).
% 0.22/0.47 tff(environment_type, type, (
% 0.22/0.47 environment: $i > $o)).
% 0.22/0.47 tff(subpopulations_type, type, (
% 0.22/0.47 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.22/0.47 tff(1,assumption,(~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.22/0.47 tff(2,plain,
% 0.22/0.47 (^[B: $i, A: $i] : refl(((~greater(A, B)) | greater_or_equal(A, B)) <=> ((~greater(A, B)) | greater_or_equal(A, B)))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(3,plain,
% 0.22/0.47 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[2])).
% 0.22/0.47 tff(4,plain,
% 0.22/0.47 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(5,axiom,(![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_or_equal_22')).
% 0.22/0.47 tff(6,plain,
% 0.22/0.47 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.22/0.47 tff(7,plain,(
% 0.22/0.47 ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.22/0.47 inference(skolemize,[status(sab)],[6])).
% 0.22/0.47 tff(8,plain,
% 0.22/0.47 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.22/0.47 tff(9,plain,
% 0.22/0.47 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk4(sk2(sk3)), equilibrium(sk3))) | greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3)))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk4(sk2(sk3)), equilibrium(sk3))) | greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(10,plain,
% 0.22/0.47 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk4(sk2(sk3)), equilibrium(sk3))) | greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(11,plain,
% 0.22/0.47 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk4(sk2(sk3)), equilibrium(sk3))) | greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.22/0.47 tff(12,plain,
% 0.22/0.47 (~greater(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.22/0.47 tff(13,assumption,(~greater(sk4(sk2(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.22/0.47 tff(14,assumption,(greater(sk4(sk2(sk3)), sk2(sk3))), introduced(assumption)).
% 0.22/0.47 tff(15,assumption,(greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.22/0.47 tff(16,assumption,(~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))), introduced(assumption)).
% 0.22/0.47 tff(17,assumption,(growth_rate(efficient_producers, sk4(sk1(sk3))) = zero), introduced(assumption)).
% 0.22/0.47 tff(18,plain,
% 0.22/0.47 (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) <=> greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[17])).
% 0.22/0.47 tff(19,plain,
% 0.22/0.47 (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) <=> greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.22/0.47 inference(symmetry,[status(thm)],[18])).
% 0.22/0.47 tff(20,plain,
% 0.22/0.47 ((~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) <=> (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[19])).
% 0.22/0.47 tff(21,plain,
% 0.22/0.47 (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[16, 20])).
% 0.22/0.47 tff(22,plain,
% 0.22/0.47 (stable(sk3) <=> stable(sk3)),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(23,axiom,(stable(sk3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l11_37')).
% 0.22/0.47 tff(24,plain,
% 0.22/0.47 (stable(sk3)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.22/0.47 tff(25,plain,
% 0.22/0.47 (environment(sk3) <=> environment(sk3)),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(26,axiom,(environment(sk3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l11_36')).
% 0.22/0.47 tff(27,plain,
% 0.22/0.47 (environment(sk3)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.22/0.47 tff(28,plain,
% 0.22/0.47 (^[A: $i] : refl((in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A))) <=> (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(29,plain,
% 0.22/0.47 (![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A))) <=> ![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[28])).
% 0.22/0.47 tff(30,plain,
% 0.22/0.47 (![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A))) <=> ![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(31,plain,
% 0.22/0.47 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | in_environment(A, sk1(A))) <=> (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(32,plain,
% 0.22/0.47 (![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk1(A))) <=> ![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[31])).
% 0.22/0.47 tff(33,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk1(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1_32')).
% 0.22/0.47 tff(34,plain,
% 0.22/0.47 (![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.22/0.47 tff(35,plain,
% 0.22/0.47 (![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.22/0.47 tff(36,plain,(
% 0.22/0.47 ![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.47 inference(skolemize,[status(sab)],[35])).
% 0.22/0.47 tff(37,plain,
% 0.22/0.47 (![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.22/0.47 tff(38,plain,
% 0.22/0.47 (((~![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk1(sk3)))) <=> ((~![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk1(sk3)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(39,plain,
% 0.22/0.47 ((in_environment(sk3, sk1(sk3)) | (~stable(sk3)) | (~environment(sk3))) <=> ((~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk1(sk3)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(40,plain,
% 0.22/0.47 (((~![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk1(sk3)) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk1(sk3))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[39])).
% 0.22/0.47 tff(41,plain,
% 0.22/0.47 (((~![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk1(sk3)) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk1(sk3)))),
% 0.22/0.47 inference(transitivity,[status(thm)],[40, 38])).
% 0.22/0.47 tff(42,plain,
% 0.22/0.47 ((~![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk1(sk3)) | (~stable(sk3)) | (~environment(sk3)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(43,plain,
% 0.22/0.47 ((~![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk1(sk3))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.22/0.47 tff(44,plain,
% 0.22/0.47 (in_environment(sk3, sk1(sk3))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[43, 37, 27, 24])).
% 0.22/0.47 tff(45,plain,
% 0.22/0.47 (^[A: $i] : refl(((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A)) <=> ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A)))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(46,plain,
% 0.22/0.47 (![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A)) <=> ![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[45])).
% 0.22/0.47 tff(47,plain,
% 0.22/0.47 (![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A)) <=> ![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(48,axiom,(![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l11_39')).
% 0.22/0.47 tff(49,plain,
% 0.22/0.47 (![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.22/0.47 tff(50,plain,(
% 0.22/0.47 ![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))),
% 0.22/0.47 inference(skolemize,[status(sab)],[49])).
% 0.22/0.47 tff(51,plain,
% 0.22/0.47 (![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.22/0.47 tff(52,plain,
% 0.22/0.47 (((~![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))) | ((~in_environment(sk3, sk1(sk3))) | greater_or_equal(sk4(sk1(sk3)), sk1(sk3)))) <=> ((~![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))) | (~in_environment(sk3, sk1(sk3))) | greater_or_equal(sk4(sk1(sk3)), sk1(sk3)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(53,plain,
% 0.22/0.47 ((~![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))) | ((~in_environment(sk3, sk1(sk3))) | greater_or_equal(sk4(sk1(sk3)), sk1(sk3)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(54,plain,
% 0.22/0.47 ((~![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))) | (~in_environment(sk3, sk1(sk3))) | greater_or_equal(sk4(sk1(sk3)), sk1(sk3))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.22/0.47 tff(55,plain,
% 0.22/0.47 (greater_or_equal(sk4(sk1(sk3)), sk1(sk3))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[54, 51, 44])).
% 0.22/0.47 tff(56,plain,
% 0.22/0.47 (^[A: $i] : refl(((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A))) <=> ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(57,plain,
% 0.22/0.47 (![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A))) <=> ![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[56])).
% 0.22/0.47 tff(58,plain,
% 0.22/0.47 (![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A))) <=> ![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(59,axiom,(![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l11_38')).
% 0.22/0.47 tff(60,plain,
% 0.22/0.47 (![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.22/0.47 tff(61,plain,(
% 0.22/0.47 ![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))),
% 0.22/0.47 inference(skolemize,[status(sab)],[60])).
% 0.22/0.47 tff(62,plain,
% 0.22/0.47 (![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.22/0.47 tff(63,plain,
% 0.22/0.47 (((~![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))) | ((~in_environment(sk3, sk1(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3))))) <=> ((~![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))) | (~in_environment(sk3, sk1(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(64,plain,
% 0.22/0.47 ((~![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))) | ((~in_environment(sk3, sk1(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(65,plain,
% 0.22/0.47 ((~![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))) | (~in_environment(sk3, sk1(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.22/0.48 tff(66,plain,
% 0.22/0.48 (subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[65, 62, 44])).
% 0.22/0.48 tff(67,plain,
% 0.22/0.48 (^[B: $i, A: $i] : refl(((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A)))) <=> ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A)))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(68,plain,
% 0.22/0.48 (![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A)))) <=> ![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[67])).
% 0.22/0.48 tff(69,plain,
% 0.22/0.48 (![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A)))) <=> ![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(70,plain,
% 0.22/0.48 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk1(A)))) <=> (((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | (~greater_or_equal(B, sk1(A)))))), rewrite((((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | (~greater_or_equal(B, sk1(A)))) <=> ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~greater_or_equal(B, sk1(A))))), (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk1(A)))) <=> ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~greater_or_equal(B, sk1(A)))))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk1(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> (((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~greater_or_equal(B, sk1(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))))), rewrite((((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (~greater_or_equal(B, sk1(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk1(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(71,plain,
% 0.22/0.48 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk1(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[70])).
% 0.22/0.48 tff(72,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk1(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1_33')).
% 0.22/0.48 tff(73,plain,
% 0.22/0.48 (![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.22/0.48 tff(74,plain,
% 0.22/0.48 (![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.22/0.48 tff(75,plain,(
% 0.22/0.48 ![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))),
% 0.22/0.48 inference(skolemize,[status(sab)],[74])).
% 0.22/0.48 tff(76,plain,
% 0.22/0.48 (![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.22/0.48 tff(77,plain,
% 0.22/0.48 (((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | ((~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | (~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(78,plain,
% 0.22/0.48 (((~stable(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3)))) <=> ((~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(79,plain,
% 0.22/0.48 (((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | ((~stable(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | ((~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3)))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[78])).
% 0.22/0.48 tff(80,plain,
% 0.22/0.48 (((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | ((~stable(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | (~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[79, 77])).
% 0.22/0.48 tff(81,plain,
% 0.22/0.48 ((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | ((~stable(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(82,plain,
% 0.22/0.48 ((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | (~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.22/0.48 tff(83,plain,
% 0.22/0.48 (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[82, 76, 27, 24, 66, 55])).
% 0.22/0.48 tff(84,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[83, 21])).
% 0.22/0.48 tff(85,plain,((~(growth_rate(efficient_producers, sk4(sk1(sk3))) = zero)) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(86,plain,
% 0.22/0.48 (~(growth_rate(efficient_producers, sk4(sk1(sk3))) = zero)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[85, 16])).
% 0.22/0.48 tff(87,assumption,(greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3))))), introduced(assumption)).
% 0.22/0.48 tff(88,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B))) <=> ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(89,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B))) <=> ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(90,plain,
% 0.22/0.48 (^[B: $i, A: $i, C: $i] : rewrite((((~greater(A, B)) | (~greater(B, C))) | greater(A, C)) <=> (greater(A, C) | (~greater(B, C)) | (~greater(A, B))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(91,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : (((~greater(A, B)) | (~greater(B, C))) | greater(A, C)) <=> ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[90])).
% 0.22/0.48 tff(92,axiom,(![B: $i, A: $i, C: $i] : (((~greater(A, B)) | (~greater(B, C))) | greater(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_transitivity_19')).
% 0.22/0.48 tff(93,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.22/0.48 tff(94,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.22/0.48 tff(95,plain,(
% 0.22/0.48 ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.22/0.48 inference(skolemize,[status(sab)],[94])).
% 0.22/0.48 tff(96,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.22/0.48 tff(97,plain,
% 0.22/0.48 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3))))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3))))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(98,plain,
% 0.22/0.48 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(99,plain,
% 0.22/0.48 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.22/0.48 tff(100,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[99, 96, 16, 83, 87])).
% 0.22/0.48 tff(101,plain,((~greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3))))) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(102,plain,
% 0.22/0.48 (~greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[101, 16])).
% 0.22/0.48 tff(103,plain,
% 0.22/0.48 (^[B: $i, A: $i] : refl((greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) <=> (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(104,plain,
% 0.22/0.48 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[103])).
% 0.22/0.48 tff(105,plain,
% 0.22/0.48 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(106,plain,
% 0.22/0.48 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) <=> ((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(efficient_producers, B) = zero)) <=> (((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | (growth_rate(efficient_producers, B) = zero)))), rewrite((((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(efficient_producers, B) = zero)) <=> ((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> (((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))))), rewrite((((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> ((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> (((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(first_movers, B))))), rewrite((((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(first_movers, B))) <=> (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(107,plain,
% 0.22/0.49 (![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[106])).
% 0.22/0.49 tff(108,axiom,(![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(efficient_producers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l6_31')).
% 0.22/0.49 tff(109,plain,
% 0.22/0.49 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.22/0.49 tff(110,plain,
% 0.22/0.49 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.22/0.49 tff(111,plain,(
% 0.22/0.49 ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.22/0.49 inference(skolemize,[status(sab)],[110])).
% 0.22/0.49 tff(112,plain,
% 0.22/0.49 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.22/0.49 tff(113,plain,
% 0.22/0.49 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(114,plain,
% 0.22/0.49 ((greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero)) <=> ((~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(115,plain,
% 0.22/0.49 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero)))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[114])).
% 0.22/0.49 tff(116,plain,
% 0.22/0.49 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero))),
% 0.22/0.49 inference(transitivity,[status(thm)],[115, 113])).
% 0.22/0.49 tff(117,plain,
% 0.22/0.49 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(118,plain,
% 0.22/0.49 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero)),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.22/0.49 tff(119,plain,
% 0.22/0.49 (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[118, 112, 27, 66])).
% 0.22/0.49 tff(120,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[119, 102, 16, 15, 86])).
% 0.22/0.49 tff(121,plain,(greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.49 tff(122,plain,
% 0.22/0.49 (greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[121, 15])).
% 0.22/0.49 tff(123,plain,
% 0.22/0.49 (^[A: $i] : refl(((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero))) <=> ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(124,plain,
% 0.22/0.49 (![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero))) <=> ![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[123])).
% 0.22/0.49 tff(125,plain,
% 0.22/0.49 (![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero))) <=> ![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(126,plain,
% 0.22/0.49 (^[A: $i] : rewrite((((~in_environment(sk3, A)) | (~greater(growth_rate(efficient_producers, sk4(A)), zero))) | (~greater(zero, growth_rate(first_movers, sk4(A))))) <=> ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(127,plain,
% 0.22/0.49 (![A: $i] : (((~in_environment(sk3, A)) | (~greater(growth_rate(efficient_producers, sk4(A)), zero))) | (~greater(zero, growth_rate(first_movers, sk4(A))))) <=> ![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[126])).
% 0.22/0.49 tff(128,axiom,(![A: $i] : (((~in_environment(sk3, A)) | (~greater(growth_rate(efficient_producers, sk4(A)), zero))) | (~greater(zero, growth_rate(first_movers, sk4(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l11_40')).
% 0.22/0.49 tff(129,plain,
% 0.22/0.49 (![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.22/0.49 tff(130,plain,
% 0.22/0.49 (![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.22/0.49 tff(131,plain,(
% 0.22/0.49 ![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))),
% 0.22/0.49 inference(skolemize,[status(sab)],[130])).
% 0.22/0.49 tff(132,plain,
% 0.22/0.49 (![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.22/0.49 tff(133,plain,
% 0.22/0.49 (((~![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))) | ((~in_environment(sk3, sk1(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)))) <=> ((~![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))) | (~in_environment(sk3, sk1(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(134,plain,
% 0.22/0.49 ((~![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))) | ((~in_environment(sk3, sk1(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(135,plain,
% 0.22/0.49 ((~![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))) | (~in_environment(sk3, sk1(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.22/0.49 tff(136,plain,
% 0.22/0.49 ((~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[135, 132, 44])).
% 0.22/0.50 tff(137,plain,
% 0.22/0.50 (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[136, 122])).
% 0.22/0.50 tff(138,assumption,(greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)), introduced(assumption)).
% 0.22/0.50 tff(139,assumption,(~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)), introduced(assumption)).
% 0.22/0.50 tff(140,plain,
% 0.22/0.50 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(141,plain,
% 0.22/0.50 ((greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))))) <=> (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(142,plain,
% 0.22/0.50 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[141])).
% 0.22/0.50 tff(143,plain,
% 0.22/0.50 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[142, 140])).
% 0.22/0.50 tff(144,plain,
% 0.22/0.50 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(145,plain,
% 0.22/0.50 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.22/0.50 tff(146,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[145, 96, 139, 83, 138])).
% 0.22/0.50 tff(147,plain,((~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(148,plain,
% 0.22/0.50 (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[147, 137])).
% 0.22/0.50 tff(149,plain,
% 0.22/0.50 (^[B: $i, A: $i] : refl((greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(150,plain,
% 0.22/0.50 (![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[149])).
% 0.22/0.50 tff(151,plain,
% 0.22/0.50 (![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(152,plain,
% 0.22/0.50 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) <=> ((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(first_movers, B) = zero)) <=> (((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | (growth_rate(first_movers, B) = zero)))), rewrite((((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | (growth_rate(first_movers, B) = zero)) <=> ((growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(first_movers, B) = zero)) <=> ((growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> (((growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | greater(growth_rate(first_movers, B), zero)))), rewrite((((growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | greater(growth_rate(first_movers, B), zero)) <=> (greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) <=> (greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> ((greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | greater(growth_rate(efficient_producers, B), zero)))), rewrite(((greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | greater(growth_rate(efficient_producers, B), zero)) <=> (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(153,plain,
% 0.22/0.50 (![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[152])).
% 0.22/0.50 tff(154,axiom,(![B: $i, A: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(first_movers, B) = zero)) | greater(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l6_24')).
% 0.22/0.50 tff(155,plain,
% 0.22/0.50 (![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.22/0.50 tff(156,plain,
% 0.22/0.50 (![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.22/0.50 tff(157,plain,(
% 0.22/0.50 ![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.22/0.50 inference(skolemize,[status(sab)],[156])).
% 0.22/0.50 tff(158,plain,
% 0.22/0.50 (![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.22/0.50 tff(159,plain,
% 0.22/0.50 (((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(160,plain,
% 0.22/0.50 ((greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3))) <=> ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(161,plain,
% 0.22/0.50 (((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)))) <=> ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero)))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[160])).
% 0.22/0.50 tff(162,plain,
% 0.22/0.50 (((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)))) <=> ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero))),
% 0.22/0.51 inference(transitivity,[status(thm)],[161, 159])).
% 0.22/0.51 tff(163,plain,
% 0.22/0.51 ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(164,plain,
% 0.22/0.51 ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.22/0.51 tff(165,plain,
% 0.22/0.51 (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[164, 158, 27, 66])).
% 0.22/0.51 tff(166,plain,
% 0.22/0.51 (growth_rate(first_movers, sk4(sk1(sk3))) = zero),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[165, 148, 15, 137])).
% 0.22/0.51 tff(167,plain,
% 0.22/0.51 (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) <=> greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[166])).
% 0.22/0.51 tff(168,plain,
% 0.22/0.51 (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) <=> greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.22/0.51 inference(symmetry,[status(thm)],[167])).
% 0.22/0.51 tff(169,plain,
% 0.22/0.51 ((~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)) <=> (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[168])).
% 0.22/0.51 tff(170,plain,
% 0.22/0.51 (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[137, 169])).
% 0.22/0.51 tff(171,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[83, 170])).
% 0.22/0.51 tff(172,plain,(~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(173,assumption,(sk2(sk3) = equilibrium(sk3)), introduced(assumption)).
% 0.22/0.51 tff(174,plain,
% 0.22/0.51 (greater_or_equal(sk4(sk2(sk3)), sk2(sk3)) <=> greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[173])).
% 0.22/0.51 tff(175,plain,
% 0.22/0.51 (^[A: $i] : refl((in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A))) <=> (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(176,plain,
% 0.22/0.51 (![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A))) <=> ![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[175])).
% 0.22/0.51 tff(177,plain,
% 0.22/0.51 (![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A))) <=> ![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(178,plain,
% 0.22/0.51 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | in_environment(A, sk2(A))) <=> (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(179,plain,
% 0.22/0.51 (![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk2(A))) <=> ![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[178])).
% 0.22/0.51 tff(180,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk2(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a4_34')).
% 0.22/0.51 tff(181,plain,
% 0.22/0.51 (![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.22/0.51 tff(182,plain,
% 0.22/0.51 (![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.22/0.51 tff(183,plain,(
% 0.22/0.51 ![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.51 inference(skolemize,[status(sab)],[182])).
% 0.22/0.51 tff(184,plain,
% 0.22/0.51 (![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.22/0.51 tff(185,plain,
% 0.22/0.51 (((~![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3)))) <=> ((~![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(186,plain,
% 0.22/0.51 ((in_environment(sk3, sk2(sk3)) | (~stable(sk3)) | (~environment(sk3))) <=> ((~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(187,plain,
% 0.22/0.51 (((~![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk2(sk3)) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[186])).
% 0.22/0.51 tff(188,plain,
% 0.22/0.51 (((~![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk2(sk3)) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[187, 185])).
% 0.22/0.51 tff(189,plain,
% 0.22/0.51 ((~![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk2(sk3)) | (~stable(sk3)) | (~environment(sk3)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(190,plain,
% 0.22/0.51 ((~![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.22/0.51 tff(191,plain,
% 0.22/0.51 (in_environment(sk3, sk2(sk3))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[190, 184, 27, 24])).
% 0.22/0.51 tff(192,plain,
% 0.22/0.51 (((~![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))) | ((~in_environment(sk3, sk2(sk3))) | greater_or_equal(sk4(sk2(sk3)), sk2(sk3)))) <=> ((~![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))) | (~in_environment(sk3, sk2(sk3))) | greater_or_equal(sk4(sk2(sk3)), sk2(sk3)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(193,plain,
% 0.22/0.51 ((~![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))) | ((~in_environment(sk3, sk2(sk3))) | greater_or_equal(sk4(sk2(sk3)), sk2(sk3)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(194,plain,
% 0.22/0.51 ((~![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))) | (~in_environment(sk3, sk2(sk3))) | greater_or_equal(sk4(sk2(sk3)), sk2(sk3))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.22/0.51 tff(195,plain,
% 0.22/0.51 (greater_or_equal(sk4(sk2(sk3)), sk2(sk3))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[194, 51, 191])).
% 0.22/0.51 tff(196,plain,
% 0.22/0.51 (greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[195, 174])).
% 0.22/0.51 tff(197,assumption,(greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.22/0.51 tff(198,assumption,(greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))), introduced(assumption)).
% 0.22/0.51 tff(199,assumption,(~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)), introduced(assumption)).
% 0.22/0.51 tff(200,assumption,(greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)), introduced(assumption)).
% 0.22/0.51 tff(201,plain,
% 0.22/0.51 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(202,plain,
% 0.22/0.51 ((greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))))) <=> (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(203,plain,
% 0.22/0.51 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[202])).
% 0.22/0.51 tff(204,plain,
% 0.22/0.51 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[203, 201])).
% 0.22/0.51 tff(205,plain,
% 0.22/0.51 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(206,plain,
% 0.22/0.51 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.22/0.51 tff(207,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[206, 96, 199, 198, 200])).
% 0.22/0.51 tff(208,plain,((~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(209,plain,
% 0.22/0.51 (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[208, 199, 198])).
% 0.22/0.51 tff(210,plain,
% 0.22/0.51 (((~![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))) | ((~in_environment(sk3, sk2(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3))))) <=> ((~![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))) | (~in_environment(sk3, sk2(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(211,plain,
% 0.22/0.51 ((~![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))) | ((~in_environment(sk3, sk2(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(212,plain,
% 0.22/0.51 ((~![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))) | (~in_environment(sk3, sk2(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.22/0.51 tff(213,plain,
% 0.22/0.51 (subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[212, 62, 191])).
% 0.22/0.51 tff(214,plain,
% 0.22/0.51 (((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(215,plain,
% 0.22/0.51 ((greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3))) <=> ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(216,plain,
% 0.22/0.52 (((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)))) <=> ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero)))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[215])).
% 0.22/0.52 tff(217,plain,
% 0.22/0.52 (((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)))) <=> ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero))),
% 0.22/0.52 inference(transitivity,[status(thm)],[216, 214])).
% 0.22/0.52 tff(218,plain,
% 0.22/0.52 ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(219,plain,
% 0.22/0.52 ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero)),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.22/0.52 tff(220,plain,
% 0.22/0.52 (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[219, 158, 27, 213])).
% 0.22/0.52 tff(221,plain,
% 0.22/0.52 (growth_rate(first_movers, sk4(sk2(sk3))) = zero),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[220, 209, 197, 199])).
% 0.22/0.52 tff(222,plain,
% 0.22/0.52 (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) <=> greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)),
% 0.22/0.52 inference(monotonicity,[status(thm)],[221])).
% 0.22/0.52 tff(223,plain,
% 0.22/0.52 (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) <=> greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))),
% 0.22/0.52 inference(symmetry,[status(thm)],[222])).
% 0.22/0.52 tff(224,plain,
% 0.22/0.52 ((~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)) <=> (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[223])).
% 0.22/0.52 tff(225,plain,
% 0.22/0.52 (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[199, 224])).
% 0.22/0.52 tff(226,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[198, 225])).
% 0.22/0.52 tff(227,plain,(greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.52 tff(228,plain,
% 0.22/0.52 (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[227, 198, 197])).
% 0.22/0.52 tff(229,plain,
% 0.22/0.52 (((~![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))) | ((~in_environment(sk3, sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)))) <=> ((~![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))) | (~in_environment(sk3, sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(230,plain,
% 0.22/0.52 ((~![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))) | ((~in_environment(sk3, sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(231,plain,
% 0.22/0.52 ((~![A: $i] : ((~in_environment(sk3, A)) | (~greater(zero, growth_rate(first_movers, sk4(A)))) | (~greater(growth_rate(efficient_producers, sk4(A)), zero)))) | (~in_environment(sk3, sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.22/0.52 tff(232,plain,
% 0.22/0.52 ((~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[231, 132, 191])).
% 0.22/0.52 tff(233,plain,
% 0.22/0.52 (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[232, 228])).
% 0.22/0.52 tff(234,assumption,(greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))), introduced(assumption)).
% 0.22/0.52 tff(235,assumption,(~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))), introduced(assumption)).
% 0.22/0.52 tff(236,plain,
% 0.22/0.52 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(237,plain,
% 0.22/0.52 ((greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))))) <=> (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(238,plain,
% 0.22/0.52 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[237])).
% 0.22/0.52 tff(239,plain,
% 0.22/0.52 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))))),
% 0.22/0.52 inference(transitivity,[status(thm)],[238, 236])).
% 0.22/0.52 tff(240,plain,
% 0.22/0.52 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(241,plain,
% 0.22/0.52 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.22/0.52 tff(242,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[241, 96, 235, 198, 234])).
% 0.22/0.52 tff(243,plain,((~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.52 tff(244,plain,
% 0.22/0.52 (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[243, 233, 198])).
% 0.22/0.52 tff(245,plain,
% 0.22/0.52 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(246,plain,
% 0.22/0.53 ((greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero)) <=> ((~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(247,plain,
% 0.22/0.53 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | ((~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero)))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[246])).
% 0.22/0.53 tff(248,plain,
% 0.22/0.53 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))),
% 0.22/0.53 inference(transitivity,[status(thm)],[247, 245])).
% 0.22/0.53 tff(249,plain,
% 0.22/0.53 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))),
% 0.22/0.53 inference(quant_inst,[status(thm)],[])).
% 0.22/0.53 tff(250,plain,
% 0.22/0.53 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero)),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.22/0.53 tff(251,plain,
% 0.22/0.53 (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero)),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[250, 112, 27, 213])).
% 0.22/0.53 tff(252,plain,
% 0.22/0.53 (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[251, 244, 197, 233])).
% 0.22/0.53 tff(253,plain,
% 0.22/0.53 (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) <=> greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[252])).
% 0.22/0.53 tff(254,plain,
% 0.22/0.53 (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) <=> greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))),
% 0.22/0.53 inference(symmetry,[status(thm)],[253])).
% 0.22/0.53 tff(255,plain,
% 0.22/0.53 ((~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) <=> (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[254])).
% 0.22/0.53 tff(256,plain,
% 0.22/0.53 (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[233, 255])).
% 0.22/0.53 tff(257,plain,
% 0.22/0.53 ($false),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[198, 256])).
% 0.22/0.53 tff(258,plain,((~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.53 tff(259,plain,
% 0.22/0.53 (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[258, 196])).
% 0.22/0.53 tff(260,plain,
% 0.22/0.53 (((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | ((~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | (~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(261,plain,
% 0.22/0.53 (((~stable(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3)))) <=> ((~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(262,plain,
% 0.22/0.53 (((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | ((~stable(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | ((~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3)))))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[261])).
% 0.22/0.53 tff(263,plain,
% 0.22/0.53 (((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | ((~stable(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | (~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3))))),
% 0.22/0.53 inference(transitivity,[status(thm)],[262, 260])).
% 0.22/0.53 tff(264,plain,
% 0.22/0.53 ((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | ((~stable(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3))))),
% 0.22/0.53 inference(quant_inst,[status(thm)],[])).
% 0.22/0.53 tff(265,plain,
% 0.22/0.53 ((~![B: $i, A: $i] : ((~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk1(A))))) | (~stable(sk3)) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.22/0.54 tff(266,plain,
% 0.22/0.54 (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[265, 76, 27, 24, 213])).
% 0.22/0.54 tff(267,plain,
% 0.22/0.54 (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[266, 259])).
% 0.22/0.54 tff(268,plain,
% 0.22/0.54 (equilibrium(sk3) = sk2(sk3)),
% 0.22/0.54 inference(symmetry,[status(thm)],[173])).
% 0.22/0.54 tff(269,assumption,(greater(sk2(sk3), sk1(sk3))), introduced(assumption)).
% 0.22/0.54 tff(270,assumption,(~greater_or_equal(sk4(sk2(sk3)), sk1(sk3))), introduced(assumption)).
% 0.22/0.54 tff(271,plain,
% 0.22/0.54 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk4(sk2(sk3)), sk1(sk3))) | greater_or_equal(sk4(sk2(sk3)), sk1(sk3)))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk4(sk2(sk3)), sk1(sk3))) | greater_or_equal(sk4(sk2(sk3)), sk1(sk3)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(272,plain,
% 0.22/0.54 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk4(sk2(sk3)), sk1(sk3))) | greater_or_equal(sk4(sk2(sk3)), sk1(sk3)))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(273,plain,
% 0.22/0.54 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk4(sk2(sk3)), sk1(sk3))) | greater_or_equal(sk4(sk2(sk3)), sk1(sk3))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.22/0.54 tff(274,plain,
% 0.22/0.54 (~greater(sk4(sk2(sk3)), sk1(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[273, 8, 270])).
% 0.22/0.54 tff(275,plain,
% 0.22/0.54 (greater(equilibrium(sk3), sk1(sk3)) <=> greater(sk2(sk3), sk1(sk3))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[268])).
% 0.22/0.54 tff(276,plain,
% 0.22/0.54 (greater(sk2(sk3), sk1(sk3)) <=> greater(equilibrium(sk3), sk1(sk3))),
% 0.22/0.54 inference(symmetry,[status(thm)],[275])).
% 0.22/0.54 tff(277,plain,
% 0.22/0.54 (greater(equilibrium(sk3), sk1(sk3))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[269, 276])).
% 0.22/0.54 tff(278,assumption,(~greater(sk4(sk2(sk3)), sk1(sk3))), introduced(assumption)).
% 0.22/0.54 tff(279,assumption,(greater(sk4(sk2(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.22/0.54 tff(280,plain,
% 0.22/0.54 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(equilibrium(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), equilibrium(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(equilibrium(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), equilibrium(sk3))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(281,plain,
% 0.22/0.54 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(equilibrium(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), equilibrium(sk3))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(282,plain,
% 0.22/0.54 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(equilibrium(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), equilibrium(sk3)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.22/0.54 tff(283,plain,
% 0.22/0.54 (~greater(equilibrium(sk3), sk1(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[282, 96, 279, 278])).
% 0.22/0.54 tff(284,plain,
% 0.22/0.54 ($false),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[283, 277])).
% 0.22/0.54 tff(285,plain,((~greater(sk2(sk3), sk1(sk3))) | (~(sk2(sk3) = equilibrium(sk3))) | (~greater(sk4(sk2(sk3)), equilibrium(sk3))) | greater(sk4(sk2(sk3)), sk1(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.54 tff(286,plain,
% 0.22/0.54 (~greater(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[285, 274, 269, 173])).
% 0.22/0.54 tff(287,plain,
% 0.22/0.54 (^[B: $i, A: $i] : refl(((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ((A = B) | greater(A, B) | (~greater_or_equal(A, B))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(288,plain,
% 0.22/0.54 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[287])).
% 0.22/0.54 tff(289,plain,
% 0.22/0.54 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(290,plain,
% 0.22/0.54 (^[B: $i, A: $i] : rewrite((((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> ((A = B) | greater(A, B) | (~greater_or_equal(A, B))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(291,plain,
% 0.22/0.54 (![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[290])).
% 0.22/0.54 tff(292,axiom,(![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_or_equal_21')).
% 0.22/0.54 tff(293,plain,
% 0.22/0.54 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.22/0.54 tff(294,plain,
% 0.22/0.54 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.22/0.54 tff(295,plain,(
% 0.22/0.54 ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.22/0.54 inference(skolemize,[status(sab)],[294])).
% 0.22/0.54 tff(296,plain,
% 0.22/0.54 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.22/0.54 tff(297,plain,
% 0.22/0.54 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3)))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(298,plain,
% 0.22/0.54 (((sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3)) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3)))) <=> ((~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(299,plain,
% 0.22/0.54 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3)) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3))))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[298])).
% 0.22/0.54 tff(300,plain,
% 0.22/0.54 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3)) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3)))),
% 0.22/0.54 inference(transitivity,[status(thm)],[299, 297])).
% 0.22/0.54 tff(301,plain,
% 0.22/0.54 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3)) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(302,plain,
% 0.22/0.54 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.22/0.54 tff(303,plain,
% 0.22/0.54 ((sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[302, 296, 196])).
% 0.22/0.54 tff(304,plain,
% 0.22/0.54 (sk4(sk2(sk3)) = equilibrium(sk3)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[303, 286])).
% 0.22/0.54 tff(305,plain,
% 0.22/0.54 (sk4(sk2(sk3)) = sk2(sk3)),
% 0.22/0.54 inference(transitivity,[status(thm)],[304, 268])).
% 0.22/0.54 tff(306,plain,
% 0.22/0.54 (greater_or_equal(sk4(sk2(sk3)), sk1(sk3)) <=> greater_or_equal(sk2(sk3), sk1(sk3))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[305])).
% 0.22/0.54 tff(307,plain,
% 0.22/0.54 (greater_or_equal(sk2(sk3), sk1(sk3)) <=> greater_or_equal(sk4(sk2(sk3)), sk1(sk3))),
% 0.22/0.54 inference(symmetry,[status(thm)],[306])).
% 0.22/0.54 tff(308,plain,
% 0.22/0.54 (greater_or_equal(equilibrium(sk3), sk1(sk3)) <=> greater_or_equal(sk2(sk3), sk1(sk3))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[268])).
% 0.22/0.54 tff(309,plain,
% 0.22/0.54 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(equilibrium(sk3), sk1(sk3))) | greater_or_equal(equilibrium(sk3), sk1(sk3)))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(equilibrium(sk3), sk1(sk3))) | greater_or_equal(equilibrium(sk3), sk1(sk3)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(310,plain,
% 0.22/0.54 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(equilibrium(sk3), sk1(sk3))) | greater_or_equal(equilibrium(sk3), sk1(sk3)))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(311,plain,
% 0.22/0.54 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(equilibrium(sk3), sk1(sk3))) | greater_or_equal(equilibrium(sk3), sk1(sk3))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.22/0.54 tff(312,plain,
% 0.22/0.54 ((~greater(equilibrium(sk3), sk1(sk3))) | greater_or_equal(equilibrium(sk3), sk1(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[311, 8])).
% 0.22/0.54 tff(313,plain,
% 0.22/0.54 (greater_or_equal(equilibrium(sk3), sk1(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[312, 277])).
% 0.22/0.54 tff(314,plain,
% 0.22/0.54 (greater_or_equal(sk2(sk3), sk1(sk3))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[313, 308])).
% 0.22/0.54 tff(315,plain,
% 0.22/0.54 (greater_or_equal(sk4(sk2(sk3)), sk1(sk3))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[314, 307])).
% 0.22/0.54 tff(316,plain,
% 0.22/0.54 ($false),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[270, 315])).
% 0.22/0.54 tff(317,plain,(greater_or_equal(sk4(sk2(sk3)), sk1(sk3)) | (~(sk2(sk3) = equilibrium(sk3))) | (~greater(sk2(sk3), sk1(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.54 tff(318,plain,
% 0.22/0.54 (~greater(sk2(sk3), sk1(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[317, 267, 173])).
% 0.22/0.54 tff(319,assumption,(~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.22/0.54 tff(320,assumption,(sk1(sk3) = sk2(sk3)), introduced(assumption)).
% 0.22/0.54 tff(321,plain,
% 0.22/0.54 (sk1(sk3) = equilibrium(sk3)),
% 0.22/0.54 inference(transitivity,[status(thm)],[320, 173])).
% 0.22/0.54 tff(322,plain,
% 0.22/0.54 (greater_or_equal(sk4(sk1(sk3)), sk1(sk3)) <=> greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[321])).
% 0.22/0.54 tff(323,plain,
% 0.22/0.54 (greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)) <=> greater_or_equal(sk4(sk1(sk3)), sk1(sk3))),
% 0.22/0.54 inference(symmetry,[status(thm)],[322])).
% 0.22/0.54 tff(324,plain,
% 0.22/0.54 ((~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) <=> (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3)))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[323])).
% 0.22/0.54 tff(325,plain,
% 0.22/0.54 (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[319, 324])).
% 0.22/0.54 tff(326,plain,
% 0.22/0.54 ($false),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[55, 325])).
% 0.22/0.54 tff(327,plain,((~(sk1(sk3) = sk2(sk3))) | greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)) | (~(sk2(sk3) = equilibrium(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.54 tff(328,plain,
% 0.22/0.54 (~(sk1(sk3) = sk2(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[327, 319, 173])).
% 0.22/0.54 tff(329,plain,
% 0.22/0.54 (^[B: $i, A: $i, C: $i] : refl((greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B))) <=> (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(330,plain,
% 0.22/0.54 (![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B))) <=> ![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[329])).
% 0.22/0.54 tff(331,plain,
% 0.22/0.54 (![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B))) <=> ![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(332,plain,
% 0.22/0.54 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~in_environment(A, B)) | (~in_environment(A, C))) <=> ((~in_environment(A, C)) | (~in_environment(A, B)))), ((((~in_environment(A, B)) | (~in_environment(A, C))) | greater(C, B)) <=> (((~in_environment(A, C)) | (~in_environment(A, B))) | greater(C, B)))), rewrite((((~in_environment(A, C)) | (~in_environment(A, B))) | greater(C, B)) <=> (greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))), ((((~in_environment(A, B)) | (~in_environment(A, C))) | greater(C, B)) <=> (greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B))))), (((((~in_environment(A, B)) | (~in_environment(A, C))) | greater(C, B)) | (C = B)) <=> ((greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B))) | (C = B)))), rewrite(((greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B))) | (C = B)) <=> ((C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))), (((((~in_environment(A, B)) | (~in_environment(A, C))) | greater(C, B)) | (C = B)) <=> ((C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B))))), ((((((~in_environment(A, B)) | (~in_environment(A, C))) | greater(C, B)) | (C = B)) | greater(B, C)) <=> (((C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B))) | greater(B, C)))), rewrite((((C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B))) | greater(B, C)) <=> (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))), ((((((~in_environment(A, B)) | (~in_environment(A, C))) | greater(C, B)) | (C = B)) | greater(B, C)) <=> (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(333,plain,
% 0.22/0.54 (![B: $i, A: $i, C: $i] : (((((~in_environment(A, B)) | (~in_environment(A, C))) | greater(C, B)) | (C = B)) | greater(B, C)) <=> ![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[332])).
% 0.22/0.54 tff(334,axiom,(![B: $i, A: $i, C: $i] : (((((~in_environment(A, B)) | (~in_environment(A, C))) | greater(C, B)) | (C = B)) | greater(B, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_times_in_environment_20')).
% 0.22/0.54 tff(335,plain,
% 0.22/0.54 (![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.22/0.54 tff(336,plain,
% 0.22/0.54 (![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[335, 331])).
% 0.22/0.54 tff(337,plain,(
% 0.22/0.54 ![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))),
% 0.22/0.54 inference(skolemize,[status(sab)],[336])).
% 0.22/0.54 tff(338,plain,
% 0.22/0.54 (![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[337, 330])).
% 0.22/0.54 tff(339,plain,
% 0.22/0.54 (((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | ((~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3))) | greater(sk2(sk3), sk1(sk3)) | greater(sk1(sk3), sk2(sk3)) | (sk1(sk3) = sk2(sk3)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3))) | greater(sk2(sk3), sk1(sk3)) | greater(sk1(sk3), sk2(sk3)) | (sk1(sk3) = sk2(sk3)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(340,plain,
% 0.22/0.54 ((greater(sk2(sk3), sk1(sk3)) | (sk1(sk3) = sk2(sk3)) | greater(sk1(sk3), sk2(sk3)) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3)))) <=> ((~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3))) | greater(sk2(sk3), sk1(sk3)) | greater(sk1(sk3), sk2(sk3)) | (sk1(sk3) = sk2(sk3)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(341,plain,
% 0.22/0.54 (((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (greater(sk2(sk3), sk1(sk3)) | (sk1(sk3) = sk2(sk3)) | greater(sk1(sk3), sk2(sk3)) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | ((~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3))) | greater(sk2(sk3), sk1(sk3)) | greater(sk1(sk3), sk2(sk3)) | (sk1(sk3) = sk2(sk3))))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[340])).
% 0.22/0.54 tff(342,plain,
% 0.22/0.54 (((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (greater(sk2(sk3), sk1(sk3)) | (sk1(sk3) = sk2(sk3)) | greater(sk1(sk3), sk2(sk3)) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3))) | greater(sk2(sk3), sk1(sk3)) | greater(sk1(sk3), sk2(sk3)) | (sk1(sk3) = sk2(sk3)))),
% 0.22/0.54 inference(transitivity,[status(thm)],[341, 339])).
% 0.22/0.54 tff(343,plain,
% 0.22/0.54 ((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (greater(sk2(sk3), sk1(sk3)) | (sk1(sk3) = sk2(sk3)) | greater(sk1(sk3), sk2(sk3)) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(344,plain,
% 0.22/0.54 ((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3))) | greater(sk2(sk3), sk1(sk3)) | greater(sk1(sk3), sk2(sk3)) | (sk1(sk3) = sk2(sk3))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.22/0.54 tff(345,plain,
% 0.22/0.54 (greater(sk2(sk3), sk1(sk3)) | greater(sk1(sk3), sk2(sk3)) | (sk1(sk3) = sk2(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[344, 338, 44, 191])).
% 0.22/0.54 tff(346,plain,
% 0.22/0.54 (greater(sk1(sk3), sk2(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[345, 328, 318])).
% 0.22/0.54 tff(347,plain,
% 0.22/0.54 (greater(sk1(sk3), equilibrium(sk3)) <=> greater(sk1(sk3), sk2(sk3))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[268])).
% 0.22/0.54 tff(348,plain,
% 0.22/0.54 (greater(sk1(sk3), sk2(sk3)) <=> greater(sk1(sk3), equilibrium(sk3))),
% 0.22/0.54 inference(symmetry,[status(thm)],[347])).
% 0.22/0.54 tff(349,assumption,(greater(sk1(sk3), sk2(sk3))), introduced(assumption)).
% 0.22/0.54 tff(350,plain,
% 0.22/0.54 (greater(sk1(sk3), equilibrium(sk3))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.22/0.54 tff(351,assumption,(~greater(sk1(sk3), equilibrium(sk3))), introduced(assumption)).
% 0.22/0.54 tff(352,plain,
% 0.22/0.54 ($false),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[351, 350])).
% 0.22/0.54 tff(353,plain,((~greater(sk1(sk3), sk2(sk3))) | greater(sk1(sk3), equilibrium(sk3)) | (~(sk2(sk3) = equilibrium(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.54 tff(354,plain,
% 0.22/0.54 (greater(sk1(sk3), equilibrium(sk3))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[353, 346, 173])).
% 0.22/0.54 tff(355,plain,
% 0.22/0.54 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk4(sk1(sk3)), equilibrium(sk3))) | greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk4(sk1(sk3)), equilibrium(sk3))) | greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(356,plain,
% 0.22/0.55 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk4(sk1(sk3)), equilibrium(sk3))) | greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(357,plain,
% 0.22/0.55 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk4(sk1(sk3)), equilibrium(sk3))) | greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.22/0.55 tff(358,plain,
% 0.22/0.55 (~greater(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[357, 8, 319])).
% 0.22/0.55 tff(359,assumption,(~greater(sk4(sk1(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.22/0.55 tff(360,assumption,(greater(sk1(sk3), equilibrium(sk3))), introduced(assumption)).
% 0.22/0.55 tff(361,assumption,(greater(sk4(sk1(sk3)), sk1(sk3))), introduced(assumption)).
% 0.22/0.55 tff(362,plain,
% 0.22/0.55 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk4(sk1(sk3)), equilibrium(sk3)) | (~greater(sk1(sk3), equilibrium(sk3))) | (~greater(sk4(sk1(sk3)), sk1(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk1(sk3)), equilibrium(sk3)) | (~greater(sk1(sk3), equilibrium(sk3))) | (~greater(sk4(sk1(sk3)), sk1(sk3))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(363,plain,
% 0.22/0.55 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk4(sk1(sk3)), equilibrium(sk3)) | (~greater(sk1(sk3), equilibrium(sk3))) | (~greater(sk4(sk1(sk3)), sk1(sk3))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(364,plain,
% 0.22/0.55 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk1(sk3)), equilibrium(sk3)) | (~greater(sk1(sk3), equilibrium(sk3))) | (~greater(sk4(sk1(sk3)), sk1(sk3)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.22/0.55 tff(365,plain,
% 0.22/0.55 ($false),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[364, 96, 361, 360, 359])).
% 0.22/0.55 tff(366,plain,((~greater(sk4(sk1(sk3)), sk1(sk3))) | (~greater(sk1(sk3), equilibrium(sk3))) | greater(sk4(sk1(sk3)), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.55 tff(367,plain,
% 0.22/0.55 (~greater(sk4(sk1(sk3)), sk1(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[366, 358, 354])).
% 0.22/0.55 tff(368,plain,
% 0.22/0.55 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))) | (sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3)))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))) | (sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(369,plain,
% 0.22/0.55 (((sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3)) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3)))) <=> ((~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))) | (sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(370,plain,
% 0.22/0.55 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3)) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))) | (sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[369])).
% 0.22/0.55 tff(371,plain,
% 0.22/0.55 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3)) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))) | (sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3)))),
% 0.22/0.55 inference(transitivity,[status(thm)],[370, 368])).
% 0.22/0.55 tff(372,plain,
% 0.22/0.55 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3)) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(373,plain,
% 0.22/0.55 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))) | (sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.22/0.55 tff(374,plain,
% 0.22/0.55 ((sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[373, 296, 55])).
% 0.22/0.55 tff(375,plain,
% 0.22/0.55 (sk4(sk1(sk3)) = sk1(sk3)),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[374, 367])).
% 0.22/0.55 tff(376,plain,
% 0.22/0.55 (greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)) <=> greater_or_equal(sk1(sk3), equilibrium(sk3))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[375])).
% 0.22/0.55 tff(377,plain,
% 0.22/0.55 (greater_or_equal(sk1(sk3), equilibrium(sk3)) <=> greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.22/0.55 inference(symmetry,[status(thm)],[376])).
% 0.22/0.55 tff(378,plain,
% 0.22/0.55 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk1(sk3), equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3)))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk1(sk3), equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(379,plain,
% 0.22/0.55 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk1(sk3), equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3)))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(380,plain,
% 0.22/0.55 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk1(sk3), equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.22/0.55 tff(381,plain,
% 0.22/0.55 (greater_or_equal(sk1(sk3), equilibrium(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[380, 8, 354])).
% 0.22/0.55 tff(382,plain,
% 0.22/0.55 (greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[381, 377])).
% 0.22/0.55 tff(383,plain,
% 0.22/0.55 ($false),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[319, 382])).
% 0.22/0.55 tff(384,plain,(greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)) | (~(sk2(sk3) = equilibrium(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.55 tff(385,plain,
% 0.22/0.55 (~(sk2(sk3) = equilibrium(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[384, 172])).
% 0.22/0.55 tff(386,plain,
% 0.22/0.55 (^[A: $i] : refl(((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A))) <=> ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(387,plain,
% 0.22/0.55 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[386])).
% 0.22/0.55 tff(388,plain,
% 0.22/0.55 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(389,plain,
% 0.22/0.55 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | greater_or_equal(sk2(A), equilibrium(A))) <=> ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(390,plain,
% 0.22/0.55 (![A: $i] : (((~environment(A)) | (~stable(A))) | greater_or_equal(sk2(A), equilibrium(A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[389])).
% 0.22/0.55 tff(391,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | greater_or_equal(sk2(A), equilibrium(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a4_35')).
% 0.22/0.55 tff(392,plain,
% 0.22/0.55 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.22/0.55 tff(393,plain,
% 0.22/0.55 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[392, 388])).
% 0.22/0.55 tff(394,plain,(
% 0.22/0.55 ![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))),
% 0.22/0.55 inference(skolemize,[status(sab)],[393])).
% 0.22/0.55 tff(395,plain,
% 0.22/0.55 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[394, 387])).
% 0.22/0.55 tff(396,plain,
% 0.22/0.55 (((~![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))) | ((~stable(sk3)) | (~environment(sk3)) | greater_or_equal(sk2(sk3), equilibrium(sk3)))) <=> ((~![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))) | (~stable(sk3)) | (~environment(sk3)) | greater_or_equal(sk2(sk3), equilibrium(sk3)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(397,plain,
% 0.22/0.55 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))) | ((~stable(sk3)) | (~environment(sk3)) | greater_or_equal(sk2(sk3), equilibrium(sk3)))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(398,plain,
% 0.22/0.55 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))) | (~stable(sk3)) | (~environment(sk3)) | greater_or_equal(sk2(sk3), equilibrium(sk3))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.22/0.55 tff(399,plain,
% 0.22/0.55 (greater_or_equal(sk2(sk3), equilibrium(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[398, 395, 27, 24])).
% 0.22/0.55 tff(400,plain,
% 0.22/0.55 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((~greater_or_equal(sk2(sk3), equilibrium(sk3))) | (sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3)))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk2(sk3), equilibrium(sk3))) | (sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(401,plain,
% 0.22/0.55 (((sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3)) | (~greater_or_equal(sk2(sk3), equilibrium(sk3)))) <=> ((~greater_or_equal(sk2(sk3), equilibrium(sk3))) | (sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(402,plain,
% 0.22/0.55 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3)) | (~greater_or_equal(sk2(sk3), equilibrium(sk3))))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((~greater_or_equal(sk2(sk3), equilibrium(sk3))) | (sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[401])).
% 0.22/0.55 tff(403,plain,
% 0.22/0.55 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3)) | (~greater_or_equal(sk2(sk3), equilibrium(sk3))))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk2(sk3), equilibrium(sk3))) | (sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3)))),
% 0.22/0.55 inference(transitivity,[status(thm)],[402, 400])).
% 0.22/0.55 tff(404,plain,
% 0.22/0.55 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3)) | (~greater_or_equal(sk2(sk3), equilibrium(sk3))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(405,plain,
% 0.22/0.55 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk2(sk3), equilibrium(sk3))) | (sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.22/0.55 tff(406,plain,
% 0.22/0.55 ((sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[405, 296, 399])).
% 0.22/0.55 tff(407,plain,
% 0.22/0.55 (greater(sk2(sk3), equilibrium(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[406, 385])).
% 0.22/0.55 tff(408,plain,
% 0.22/0.55 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk4(sk2(sk3)), equilibrium(sk3)) | (~greater(sk2(sk3), equilibrium(sk3))) | (~greater(sk4(sk2(sk3)), sk2(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk2(sk3)), equilibrium(sk3)) | (~greater(sk2(sk3), equilibrium(sk3))) | (~greater(sk4(sk2(sk3)), sk2(sk3))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(409,plain,
% 0.22/0.55 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk4(sk2(sk3)), equilibrium(sk3)) | (~greater(sk2(sk3), equilibrium(sk3))) | (~greater(sk4(sk2(sk3)), sk2(sk3))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(410,plain,
% 0.22/0.55 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk2(sk3)), equilibrium(sk3)) | (~greater(sk2(sk3), equilibrium(sk3))) | (~greater(sk4(sk2(sk3)), sk2(sk3)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.22/0.55 tff(411,plain,
% 0.22/0.55 ($false),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[410, 96, 407, 14, 13])).
% 0.22/0.55 tff(412,plain,((~greater(sk4(sk2(sk3)), sk2(sk3))) | greater(sk4(sk2(sk3)), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.55 tff(413,plain,
% 0.22/0.55 (~greater(sk4(sk2(sk3)), sk2(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[412, 12])).
% 0.22/0.55 tff(414,plain,
% 0.22/0.55 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk4(sk2(sk3)) = sk2(sk3)) | greater(sk4(sk2(sk3)), sk2(sk3)) | (~greater_or_equal(sk4(sk2(sk3)), sk2(sk3))))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (sk4(sk2(sk3)) = sk2(sk3)) | greater(sk4(sk2(sk3)), sk2(sk3)) | (~greater_or_equal(sk4(sk2(sk3)), sk2(sk3))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(415,plain,
% 0.22/0.55 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk4(sk2(sk3)) = sk2(sk3)) | greater(sk4(sk2(sk3)), sk2(sk3)) | (~greater_or_equal(sk4(sk2(sk3)), sk2(sk3))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(416,plain,
% 0.22/0.55 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (sk4(sk2(sk3)) = sk2(sk3)) | greater(sk4(sk2(sk3)), sk2(sk3)) | (~greater_or_equal(sk4(sk2(sk3)), sk2(sk3)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.22/0.55 tff(417,plain,
% 0.22/0.55 ((sk4(sk2(sk3)) = sk2(sk3)) | greater(sk4(sk2(sk3)), sk2(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[416, 296, 195])).
% 0.22/0.55 tff(418,plain,
% 0.22/0.55 (sk4(sk2(sk3)) = sk2(sk3)),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[417, 413])).
% 0.22/0.55 tff(419,plain,
% 0.22/0.55 (greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3)) <=> greater_or_equal(sk2(sk3), equilibrium(sk3))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[418])).
% 0.22/0.55 tff(420,plain,
% 0.22/0.55 (greater_or_equal(sk2(sk3), equilibrium(sk3)) <=> greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.22/0.55 inference(symmetry,[status(thm)],[419])).
% 0.22/0.55 tff(421,plain,
% 0.22/0.55 (greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[399, 420])).
% 0.22/0.55 tff(422,plain,
% 0.22/0.55 ($false),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[1, 421])).
% 0.22/0.55 tff(423,plain,(greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.55 tff(424,plain,
% 0.22/0.55 (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[258, 423])).
% 0.22/0.55 tff(425,plain,
% 0.22/0.55 (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[266, 424])).
% 0.22/0.55 tff(426,plain,
% 0.22/0.55 (~greater(sk4(sk2(sk3)), sk1(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[273, 8, 425])).
% 0.22/0.55 tff(427,plain,
% 0.22/0.55 (~greater(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[357, 8, 172])).
% 0.22/0.55 tff(428,plain,
% 0.22/0.55 ((~greater(sk4(sk1(sk3)), sk1(sk3))) | (~greater(sk1(sk3), equilibrium(sk3)))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[366, 427])).
% 0.22/0.55 tff(429,plain,
% 0.32/0.56 (~greater(sk4(sk1(sk3)), sk1(sk3))),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[428, 360])).
% 0.32/0.56 tff(430,plain,
% 0.32/0.56 (sk4(sk1(sk3)) = sk1(sk3)),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[374, 429])).
% 0.32/0.56 tff(431,plain,
% 0.32/0.56 (greater(sk4(sk1(sk3)), equilibrium(sk3)) <=> greater(sk1(sk3), equilibrium(sk3))),
% 0.32/0.56 inference(monotonicity,[status(thm)],[430])).
% 0.32/0.56 tff(432,plain,
% 0.32/0.56 (greater(sk1(sk3), equilibrium(sk3)) <=> greater(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.32/0.56 inference(symmetry,[status(thm)],[431])).
% 0.32/0.56 tff(433,plain,
% 0.32/0.56 (greater(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.32/0.56 inference(modus_ponens,[status(thm)],[360, 432])).
% 0.32/0.56 tff(434,plain,
% 0.32/0.56 ($false),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[427, 433])).
% 0.32/0.56 tff(435,plain,(~greater(sk1(sk3), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.32/0.56 tff(436,plain,
% 0.32/0.56 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | ((~greater(sk2(sk3), equilibrium(sk3))) | greater(sk1(sk3), equilibrium(sk3)) | (~greater(sk1(sk3), sk2(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (~greater(sk2(sk3), equilibrium(sk3))) | greater(sk1(sk3), equilibrium(sk3)) | (~greater(sk1(sk3), sk2(sk3))))),
% 0.32/0.56 inference(rewrite,[status(thm)],[])).
% 0.32/0.56 tff(437,plain,
% 0.32/0.56 ((greater(sk1(sk3), equilibrium(sk3)) | (~greater(sk2(sk3), equilibrium(sk3))) | (~greater(sk1(sk3), sk2(sk3)))) <=> ((~greater(sk2(sk3), equilibrium(sk3))) | greater(sk1(sk3), equilibrium(sk3)) | (~greater(sk1(sk3), sk2(sk3))))),
% 0.32/0.56 inference(rewrite,[status(thm)],[])).
% 0.32/0.56 tff(438,plain,
% 0.32/0.56 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk1(sk3), equilibrium(sk3)) | (~greater(sk2(sk3), equilibrium(sk3))) | (~greater(sk1(sk3), sk2(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | ((~greater(sk2(sk3), equilibrium(sk3))) | greater(sk1(sk3), equilibrium(sk3)) | (~greater(sk1(sk3), sk2(sk3)))))),
% 0.32/0.56 inference(monotonicity,[status(thm)],[437])).
% 0.32/0.56 tff(439,plain,
% 0.32/0.56 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk1(sk3), equilibrium(sk3)) | (~greater(sk2(sk3), equilibrium(sk3))) | (~greater(sk1(sk3), sk2(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (~greater(sk2(sk3), equilibrium(sk3))) | greater(sk1(sk3), equilibrium(sk3)) | (~greater(sk1(sk3), sk2(sk3))))),
% 0.32/0.56 inference(transitivity,[status(thm)],[438, 436])).
% 0.32/0.56 tff(440,plain,
% 0.32/0.56 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk1(sk3), equilibrium(sk3)) | (~greater(sk2(sk3), equilibrium(sk3))) | (~greater(sk1(sk3), sk2(sk3))))),
% 0.32/0.56 inference(quant_inst,[status(thm)],[])).
% 0.32/0.56 tff(441,plain,
% 0.32/0.56 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (~greater(sk2(sk3), equilibrium(sk3))) | greater(sk1(sk3), equilibrium(sk3)) | (~greater(sk1(sk3), sk2(sk3)))),
% 0.32/0.56 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.32/0.56 tff(442,plain,
% 0.32/0.56 ($false),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[441, 96, 407, 349, 435])).
% 0.32/0.56 tff(443,plain,(~greater(sk1(sk3), sk2(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.32/0.56 tff(444,plain,
% 0.32/0.56 (greater_or_equal(sk4(sk2(sk3)), sk1(sk3)) <=> greater_or_equal(sk4(sk2(sk3)), sk2(sk3))),
% 0.32/0.56 inference(monotonicity,[status(thm)],[320])).
% 0.32/0.56 tff(445,plain,
% 0.32/0.56 (greater_or_equal(sk4(sk2(sk3)), sk2(sk3)) <=> greater_or_equal(sk4(sk2(sk3)), sk1(sk3))),
% 0.32/0.56 inference(symmetry,[status(thm)],[444])).
% 0.32/0.56 tff(446,plain,
% 0.32/0.56 (greater_or_equal(sk4(sk2(sk3)), sk1(sk3))),
% 0.32/0.56 inference(modus_ponens,[status(thm)],[195, 445])).
% 0.32/0.56 tff(447,plain,
% 0.32/0.56 ($false),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[270, 446])).
% 0.32/0.56 tff(448,plain,((~(sk1(sk3) = sk2(sk3))) | greater_or_equal(sk4(sk2(sk3)), sk1(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.32/0.56 tff(449,plain,
% 0.32/0.56 (~(sk1(sk3) = sk2(sk3))),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[448, 425])).
% 0.32/0.56 tff(450,plain,
% 0.32/0.56 (greater(sk2(sk3), sk1(sk3))),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[345, 449, 443])).
% 0.32/0.56 tff(451,assumption,(sk4(sk2(sk3)) = sk2(sk3)), introduced(assumption)).
% 0.32/0.56 tff(452,plain,
% 0.32/0.56 (greater_or_equal(sk4(sk2(sk3)), sk1(sk3)) <=> greater_or_equal(sk2(sk3), sk1(sk3))),
% 0.32/0.56 inference(monotonicity,[status(thm)],[451])).
% 0.32/0.56 tff(453,plain,
% 0.32/0.56 (greater_or_equal(sk2(sk3), sk1(sk3)) <=> greater_or_equal(sk4(sk2(sk3)), sk1(sk3))),
% 0.32/0.56 inference(symmetry,[status(thm)],[452])).
% 0.32/0.56 tff(454,plain,
% 0.32/0.56 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk2(sk3), sk1(sk3))) | greater_or_equal(sk2(sk3), sk1(sk3)))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk2(sk3), sk1(sk3))) | greater_or_equal(sk2(sk3), sk1(sk3)))),
% 0.32/0.56 inference(rewrite,[status(thm)],[])).
% 0.32/0.56 tff(455,plain,
% 0.32/0.56 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk2(sk3), sk1(sk3))) | greater_or_equal(sk2(sk3), sk1(sk3)))),
% 0.32/0.56 inference(quant_inst,[status(thm)],[])).
% 0.32/0.56 tff(456,plain,
% 0.32/0.56 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk2(sk3), sk1(sk3))) | greater_or_equal(sk2(sk3), sk1(sk3))),
% 0.32/0.56 inference(modus_ponens,[status(thm)],[455, 454])).
% 0.32/0.56 tff(457,plain,
% 0.32/0.56 (greater_or_equal(sk2(sk3), sk1(sk3))),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[456, 8, 450])).
% 0.32/0.56 tff(458,plain,
% 0.32/0.56 (greater_or_equal(sk4(sk2(sk3)), sk1(sk3))),
% 0.32/0.56 inference(modus_ponens,[status(thm)],[457, 453])).
% 0.32/0.56 tff(459,plain,
% 0.32/0.56 ($false),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[425, 458])).
% 0.32/0.56 tff(460,plain,(~(sk4(sk2(sk3)) = sk2(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.32/0.56 tff(461,plain,
% 0.32/0.56 (greater(sk4(sk2(sk3)), sk2(sk3))),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[417, 460])).
% 0.32/0.56 tff(462,plain,
% 0.32/0.56 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(sk2(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), sk2(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(sk2(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), sk2(sk3))))),
% 0.32/0.56 inference(rewrite,[status(thm)],[])).
% 0.32/0.56 tff(463,plain,
% 0.32/0.56 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(sk2(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), sk2(sk3))))),
% 0.32/0.56 inference(quant_inst,[status(thm)],[])).
% 0.32/0.56 tff(464,plain,
% 0.32/0.56 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(sk2(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), sk2(sk3)))),
% 0.32/0.56 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.32/0.56 tff(465,plain,
% 0.32/0.56 ($false),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[464, 96, 461, 450, 426])).
% 0.32/0.56 % SZS output end Proof
% 0.32/0.56 % E exiting
%------------------------------------------------------------------------------