TSTP Solution File: MGT035-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT035-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 05:22:02 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT035-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 02:44:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(greater_type, type, (
% 0.20/0.44 greater: ( $i * $i ) > $o)).
% 0.20/0.44 tff(sk1_type, type, (
% 0.20/0.44 sk1: $i > $i)).
% 0.20/0.44 tff(sk3_type, type, (
% 0.20/0.44 sk3: $i)).
% 0.20/0.44 tff(sk4_type, type, (
% 0.20/0.44 sk4: $i > $i)).
% 0.20/0.44 tff(sk2_type, type, (
% 0.20/0.44 sk2: $i > $i)).
% 0.20/0.44 tff(equilibrium_type, type, (
% 0.20/0.44 equilibrium: $i > $i)).
% 0.20/0.44 tff(greater_or_equal_type, type, (
% 0.20/0.44 greater_or_equal: ( $i * $i ) > $o)).
% 0.20/0.44 tff(zero_type, type, (
% 0.20/0.44 zero: $i)).
% 0.20/0.44 tff(growth_rate_type, type, (
% 0.20/0.44 growth_rate: ( $i * $i ) > $i)).
% 0.20/0.44 tff(efficient_producers_type, type, (
% 0.20/0.44 efficient_producers: $i)).
% 0.20/0.44 tff(first_movers_type, type, (
% 0.20/0.44 first_movers: $i)).
% 0.20/0.44 tff(subpopulations_type, type, (
% 0.20/0.44 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.44 tff(in_environment_type, type, (
% 0.20/0.44 in_environment: ( $i * $i ) > $o)).
% 0.20/0.44 tff(stable_type, type, (
% 0.20/0.44 stable: $i > $o)).
% 0.20/0.44 tff(environment_type, type, (
% 0.20/0.44 environment: $i > $o)).
% 0.20/0.44 tff(outcompetes_type, type, (
% 0.20/0.44 outcompetes: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(1,assumption,(greater(sk1(sk3), equilibrium(sk3))), introduced(assumption)).
% 0.20/0.44 tff(2,assumption,(greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.20/0.44 tff(3,assumption,(~(growth_rate(first_movers, sk4(sk1(sk3))) = zero)), introduced(assumption)).
% 0.20/0.44 tff(4,assumption,(~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))), introduced(assumption)).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (stable(sk3) <=> stable(sk3)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(6,axiom,(stable(sk3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t4_43')).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (stable(sk3)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (environment(sk3) <=> environment(sk3)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(9,axiom,(environment(sk3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t4_42')).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (environment(sk3)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 (^[A: $i] : refl((in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A))) <=> (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A))) <=> ![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A))) <=> ![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | in_environment(A, sk1(A))) <=> (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk1(A))) <=> ![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.44 tff(16,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l1_38')).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 (![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.44 tff(19,plain,(
% 0.20/0.44 ![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[18])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 ((in_environment(sk3, sk1(sk3)) | (~stable(sk3)) | (~environment(sk3))) <=> ((~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk1(sk3)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[23, 21])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 ((~![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk1(sk3)) | (~stable(sk3)) | (~environment(sk3)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 ((~![A: $i] : (in_environment(A, sk1(A)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk1(sk3))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (in_environment(sk3, sk1(sk3))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[26, 20, 10, 7])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(31,axiom,(![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t4_44')).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.44 tff(33,plain,(
% 0.20/0.44 ![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[32])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 (![A: $i] : ((~in_environment(sk3, A)) | subpopulations(first_movers, efficient_producers, sk3, sk4(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 ((~![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))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[37, 34, 27])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (^[B: $i, A: $i] : refl((greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B))) <=> (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B))) <=> ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B))) <=> ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (^[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(zero, growth_rate(efficient_producers, B))) <=> (((growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | greater(zero, growth_rate(efficient_producers, B))))), rewrite((((growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) | greater(zero, growth_rate(efficient_producers, B))) <=> ((growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) <=> ((growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B))))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> (((growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))))), rewrite((((growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, equilibrium(A)))) | (growth_rate(first_movers, B) = zero)) | greater(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (![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(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.45 tff(44,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(zero, growth_rate(efficient_producers, B))) | greater(zero, growth_rate(first_movers, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l6_33')).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.45 tff(47,plain,(
% 0.20/0.45 ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[46])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | 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(first_movers, sk4(sk1(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | 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(first_movers, sk4(sk1(sk3))) = zero))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 ((greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (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)) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3))))) <=> ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | 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(first_movers, sk4(sk1(sk3))) = zero))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (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)) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | 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(first_movers, sk4(sk1(sk3))) = zero)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (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)) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | 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(first_movers, sk4(sk1(sk3))) = zero))),
% 0.20/0.45 inference(transitivity,[status(thm)],[51, 49])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (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)) | greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | 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(first_movers, sk4(sk1(sk3))) = zero)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (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(first_movers, sk4(sk1(sk3))) = zero)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[54, 48, 10, 38])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[55, 4, 2, 3])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (^[A: $i] : refl(((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A)) <=> ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A)) <=> ![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A)) <=> ![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(60,axiom,(![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t4_45')).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.45 tff(62,plain,(
% 0.20/0.45 ![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))),
% 0.20/0.45 inference(skolemize,[status(sab)],[61])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (((~![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 ((~![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)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 ((~![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))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (greater_or_equal(sk4(sk1(sk3)), sk1(sk3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[66, 63, 27])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 (^[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))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.46 tff(73,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/sandbox2/benchmark/theBenchmark.p','l1_39')).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.20/0.46 tff(76,plain,(
% 0.20/0.46 ![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))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[75])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 (((~![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))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 (((~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))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (((~![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)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (((~![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))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[80, 78])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 ((~![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))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 ((~![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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[83, 77, 10, 7, 38, 67])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.46 tff(89,axiom,(![B: $i, A: $i, C: $i] : (((~greater(A, B)) | (~greater(B, C))) | greater(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_transitivity_22')).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.46 tff(92,plain,(
% 0.20/0.46 ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[91])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (((~![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))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 ((~![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))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk1(sk3)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[96, 93, 84, 4, 56])).
% 0.20/0.46 tff(98,plain,(greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (growth_rate(first_movers, sk4(sk1(sk3))) = zero)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[98, 3, 2])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (^[A: $i] : refl(((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A)))) <=> ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A)))) <=> ![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A)))) <=> ![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(103,axiom,(![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t4_46')).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.46 tff(105,plain,(
% 0.20/0.46 ![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[104])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 (![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (((~![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))) | ((~in_environment(sk3, sk1(sk3))) | (~outcompetes(efficient_producers, first_movers, sk4(sk1(sk3)))))) <=> ((~![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))) | (~in_environment(sk3, sk1(sk3))) | (~outcompetes(efficient_producers, first_movers, sk4(sk1(sk3)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 ((~![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))) | ((~in_environment(sk3, sk1(sk3))) | (~outcompetes(efficient_producers, first_movers, sk4(sk1(sk3)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 ((~![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))) | (~in_environment(sk3, sk1(sk3))) | (~outcompetes(efficient_producers, first_movers, sk4(sk1(sk3))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 (~outcompetes(efficient_producers, first_movers, sk4(sk1(sk3)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[109, 106, 27])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (^[B: $i, D: $i, A: $i, C: $i] : refl((outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> ![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 (![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> ![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater_or_equal(growth_rate(C, D), zero))) <=> ((~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater_or_equal(growth_rate(C, D), zero))) | (~greater(zero, growth_rate(B, D)))) <=> (((~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A))) | (~greater(zero, growth_rate(B, D)))))), rewrite((((~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A))) | (~greater(zero, growth_rate(B, D)))) <=> ((~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater_or_equal(growth_rate(C, D), zero))) | (~greater(zero, growth_rate(B, D)))) <=> ((~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A))))), ((((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater_or_equal(growth_rate(C, D), zero))) | (~greater(zero, growth_rate(B, D)))) | outcompetes(C, B, D)) <=> (((~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A))) | outcompetes(C, B, D)))), rewrite((((~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A))) | outcompetes(C, B, D)) <=> (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))), ((((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater_or_equal(growth_rate(C, D), zero))) | (~greater(zero, growth_rate(B, D)))) | outcompetes(C, B, D)) <=> (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (![B: $i, D: $i, A: $i, C: $i] : (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater_or_equal(growth_rate(C, D), zero))) | (~greater(zero, growth_rate(B, D)))) | outcompetes(C, B, D)) <=> ![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.46 tff(116,axiom,(![B: $i, D: $i, A: $i, C: $i] : (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater_or_equal(growth_rate(C, D), zero))) | (~greater(zero, growth_rate(B, D)))) | outcompetes(C, B, D))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_27')).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 (![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.20/0.46 tff(119,plain,(
% 0.20/0.46 ![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[118])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | ((~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk1(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk1(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 ((outcompetes(efficient_producers, first_movers, sk4(sk1(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3))) <=> ((~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk1(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (outcompetes(efficient_producers, first_movers, sk4(sk1(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | ((~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk1(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[122])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (outcompetes(efficient_producers, first_movers, sk4(sk1(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk1(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[123, 121])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 ((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (outcompetes(efficient_producers, first_movers, sk4(sk1(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~environment(sk3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 ((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk1(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 ((~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[126, 120, 10, 110, 38])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 (~greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[127, 99])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (^[B: $i, A: $i] : refl(((~greater(A, B)) | greater_or_equal(A, B)) <=> ((~greater(A, B)) | greater_or_equal(A, B)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(132,axiom,(![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_or_equal_25')).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.46 tff(134,plain,(
% 0.20/0.46 ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.20/0.46 inference(skolemize,[status(sab)],[133])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[138, 135, 128])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[143])).
% 0.20/0.47 tff(145,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/sandbox2/benchmark/theBenchmark.p','l6_30')).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.20/0.47 tff(148,plain,(
% 0.20/0.47 ![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)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[147])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 (((~![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)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | 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))) <=> ((~![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)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | 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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 ((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)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | 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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (((~![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)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | 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)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 (((~![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)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | 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))),
% 0.20/0.47 inference(transitivity,[status(thm)],[152, 150])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 ((~![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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 ((~![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)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | 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)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 ((~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | 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)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[155, 149, 10, 38])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[156, 139, 2, 3])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 ((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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (((~![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))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[159])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[160, 158])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 ((~![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))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[163, 93, 84, 139, 157])).
% 0.20/0.47 tff(165,plain,((growth_rate(first_movers, sk4(sk1(sk3))) = zero) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 (growth_rate(first_movers, sk4(sk1(sk3))) = zero),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[165, 2])).
% 0.20/0.47 tff(167,plain,
% 0.20/0.47 (zero = growth_rate(first_movers, sk4(sk1(sk3)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[166])).
% 0.20/0.47 tff(168,plain,
% 0.20/0.47 (greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) <=> greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[166])).
% 0.20/0.47 tff(169,plain,
% 0.20/0.47 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(171,plain,
% 0.20/0.47 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))) | greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.20/0.47 tff(172,plain,
% 0.20/0.47 (greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[171, 135, 84])).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 (greater_or_equal(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 (~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[127, 173])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 (greater(growth_rate(first_movers, sk4(sk1(sk3))), zero) <=> greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[166, 167])).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) <=> greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)),
% 0.20/0.47 inference(symmetry,[status(thm)],[175])).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 ((~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) <=> (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[176])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 (~greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[174, 177])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 (^[B: $i, A: $i] : refl((greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~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(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[179])).
% 0.20/0.47 tff(181,plain,
% 0.20/0.47 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 (^[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(growth_rate(first_movers, B), zero)) <=> (((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, 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(growth_rate(first_movers, B), zero)) <=> (greater(growth_rate(first_movers, 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(growth_rate(first_movers, B), zero)) <=> (greater(growth_rate(first_movers, 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(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B))) <=> ((greater(growth_rate(first_movers, B), zero) | (~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(first_movers, B))))), rewrite(((greater(growth_rate(first_movers, B), zero) | (~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(first_movers, B))) <=> (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, 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(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B))) <=> (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (![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(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[182])).
% 0.20/0.48 tff(184,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(growth_rate(first_movers, B), zero)) | greater(zero, growth_rate(first_movers, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l6_35')).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.20/0.48 tff(187,plain,(
% 0.20/0.48 ![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.48 inference(skolemize,[status(sab)],[186])).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 (![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.20/0.48 tff(189,plain,
% 0.20/0.48 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 ((greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | greater(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)) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero)) <=> ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~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(first_movers, sk4(sk1(sk3)))) | greater(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)) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[190])).
% 0.20/0.48 tff(192,plain,
% 0.20/0.48 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~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(first_movers, sk4(sk1(sk3)))) | greater(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)) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero))),
% 0.20/0.48 inference(transitivity,[status(thm)],[191, 189])).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~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(first_movers, sk4(sk1(sk3)))) | greater(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)) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(194,plain,
% 0.20/0.48 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk1(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) | (~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk1(sk3))), zero)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[194, 188, 10, 38])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 (growth_rate(efficient_producers, sk4(sk1(sk3))) = zero),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[195, 178, 2, 174])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero) <=> greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[196, 167])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 (greater(zero, growth_rate(first_movers, sk4(sk1(sk3)))) <=> greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)),
% 0.20/0.48 inference(symmetry,[status(thm)],[197])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 ((~greater(zero, growth_rate(first_movers, sk4(sk1(sk3))))) <=> (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[198])).
% 0.20/0.48 tff(200,plain,
% 0.20/0.48 (~greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[174, 199])).
% 0.20/0.48 tff(201,plain,
% 0.20/0.48 (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), growth_rate(first_movers, sk4(sk1(sk3)))) <=> greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[166])).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 (greater(growth_rate(efficient_producers, sk4(sk1(sk3))), zero)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[84, 201])).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[202, 200])).
% 0.20/0.48 tff(204,plain,(~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 ((~![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)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 ((~![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))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.20/0.48 tff(208,plain,
% 0.20/0.48 (~greater(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[207, 135, 204])).
% 0.20/0.48 tff(209,assumption,(~greater(sk4(sk1(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.20/0.48 tff(210,assumption,(greater(sk4(sk1(sk3)), sk1(sk3))), introduced(assumption)).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | ((~greater(sk1(sk3), equilibrium(sk3))) | greater(sk4(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(sk1(sk3), equilibrium(sk3))) | greater(sk4(sk1(sk3)), equilibrium(sk3)) | (~greater(sk4(sk1(sk3)), sk1(sk3))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 ((greater(sk4(sk1(sk3)), equilibrium(sk3)) | (~greater(sk1(sk3), equilibrium(sk3))) | (~greater(sk4(sk1(sk3)), sk1(sk3)))) <=> ((~greater(sk1(sk3), equilibrium(sk3))) | greater(sk4(sk1(sk3)), equilibrium(sk3)) | (~greater(sk4(sk1(sk3)), sk1(sk3))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 (((~![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(sk1(sk3), equilibrium(sk3))) | greater(sk4(sk1(sk3)), equilibrium(sk3)) | (~greater(sk4(sk1(sk3)), sk1(sk3)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[212])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 (((~![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(sk1(sk3), equilibrium(sk3))) | greater(sk4(sk1(sk3)), equilibrium(sk3)) | (~greater(sk4(sk1(sk3)), sk1(sk3))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[213, 211])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 ((~![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))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (~greater(sk1(sk3), equilibrium(sk3))) | greater(sk4(sk1(sk3)), equilibrium(sk3)) | (~greater(sk4(sk1(sk3)), sk1(sk3)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.20/0.48 tff(217,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[216, 93, 210, 1, 209])).
% 0.20/0.48 tff(218,plain,((~greater(sk1(sk3), equilibrium(sk3))) | (~greater(sk4(sk1(sk3)), sk1(sk3))) | greater(sk4(sk1(sk3)), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(219,plain,
% 0.20/0.48 ((~greater(sk1(sk3), equilibrium(sk3))) | (~greater(sk4(sk1(sk3)), sk1(sk3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[218, 208])).
% 0.20/0.48 tff(220,plain,
% 0.20/0.48 (~greater(sk4(sk1(sk3)), sk1(sk3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[219, 1])).
% 0.20/0.48 tff(221,plain,
% 0.20/0.48 (^[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))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(222,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[221])).
% 0.20/0.48 tff(223,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 (^[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))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(225,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[224])).
% 0.20/0.48 tff(226,axiom,(![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_or_equal_24')).
% 0.20/0.48 tff(227,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.20/0.48 tff(228,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[227, 223])).
% 0.20/0.48 tff(229,plain,(
% 0.20/0.48 ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[228])).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[229, 222])).
% 0.20/0.48 tff(231,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(232,plain,
% 0.20/0.48 (((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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 (((~![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))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[232])).
% 0.20/0.48 tff(234,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[233, 231])).
% 0.20/0.48 tff(235,plain,
% 0.20/0.48 ((~![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))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))) | (sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.48 tff(237,plain,
% 0.20/0.48 ((sk4(sk1(sk3)) = sk1(sk3)) | greater(sk4(sk1(sk3)), sk1(sk3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[236, 230, 67])).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 (sk4(sk1(sk3)) = sk1(sk3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[237, 220])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 (greater(sk4(sk1(sk3)), equilibrium(sk3)) <=> greater(sk1(sk3), equilibrium(sk3))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[238])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 (greater(sk1(sk3), equilibrium(sk3)) <=> greater(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.20/0.48 inference(symmetry,[status(thm)],[239])).
% 0.20/0.48 tff(241,plain,
% 0.20/0.48 (greater(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[1, 240])).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[208, 241])).
% 0.20/0.48 tff(243,plain,(~greater(sk1(sk3), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(244,assumption,(~greater(sk2(sk3), sk1(sk3))), introduced(assumption)).
% 0.20/0.48 tff(245,assumption,(~greater(sk1(sk3), equilibrium(sk3))), introduced(assumption)).
% 0.20/0.48 tff(246,assumption,(sk2(sk3) = equilibrium(sk3)), introduced(assumption)).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (in_environment(sk3, sk2(sk3)) <=> in_environment(sk3, equilibrium(sk3))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[246])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 (in_environment(sk3, equilibrium(sk3)) <=> in_environment(sk3, sk2(sk3))),
% 0.20/0.48 inference(symmetry,[status(thm)],[247])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 ((~in_environment(sk3, equilibrium(sk3))) <=> (~in_environment(sk3, sk2(sk3)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.48 tff(250,assumption,(~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.20/0.48 tff(251,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(252,plain,
% 0.20/0.48 ((~![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)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(253,plain,
% 0.20/0.48 ((~![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))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.20/0.48 tff(254,plain,
% 0.20/0.48 (~greater(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[253, 135, 250])).
% 0.20/0.48 tff(255,plain,
% 0.20/0.48 (greater_or_equal(sk4(sk2(sk3)), sk2(sk3)) <=> greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[246])).
% 0.20/0.48 tff(256,plain,
% 0.20/0.48 (greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3)) <=> greater_or_equal(sk4(sk2(sk3)), sk2(sk3))),
% 0.20/0.48 inference(symmetry,[status(thm)],[255])).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 ((~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) <=> (~greater_or_equal(sk4(sk2(sk3)), sk2(sk3)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[256])).
% 0.20/0.48 tff(258,plain,
% 0.20/0.48 (~greater_or_equal(sk4(sk2(sk3)), sk2(sk3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[250, 257])).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 (^[A: $i] : refl((in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A))) <=> (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 (![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A))) <=> ![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[259])).
% 0.20/0.48 tff(261,plain,
% 0.20/0.48 (![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A))) <=> ![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(262,plain,
% 0.20/0.48 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | in_environment(A, sk2(A))) <=> (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(263,plain,
% 0.20/0.48 (![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk2(A))) <=> ![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[262])).
% 0.20/0.49 tff(264,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk2(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a4_40')).
% 0.20/0.49 tff(265,plain,
% 0.20/0.49 (![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.20/0.49 tff(266,plain,
% 0.20/0.49 (![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[265, 261])).
% 0.20/0.49 tff(267,plain,(
% 0.20/0.49 ![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[266])).
% 0.20/0.49 tff(268,plain,
% 0.20/0.49 (![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[267, 260])).
% 0.20/0.49 tff(269,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(270,plain,
% 0.20/0.49 ((in_environment(sk3, sk2(sk3)) | (~stable(sk3)) | (~environment(sk3))) <=> ((~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(271,plain,
% 0.20/0.49 (((~![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))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[270])).
% 0.20/0.49 tff(272,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[271, 269])).
% 0.20/0.49 tff(273,plain,
% 0.20/0.49 ((~![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk2(sk3)) | (~stable(sk3)) | (~environment(sk3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(274,plain,
% 0.20/0.49 ((~![A: $i] : (in_environment(A, sk2(A)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.49 tff(275,plain,
% 0.20/0.49 (in_environment(sk3, sk2(sk3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[274, 268, 10, 7])).
% 0.20/0.49 tff(276,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(277,plain,
% 0.20/0.49 ((~![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)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(278,plain,
% 0.20/0.49 ((~![A: $i] : ((~in_environment(sk3, A)) | greater_or_equal(sk4(A), A))) | (~in_environment(sk3, sk2(sk3))) | greater_or_equal(sk4(sk2(sk3)), sk2(sk3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.20/0.49 tff(279,plain,
% 0.20/0.49 (greater_or_equal(sk4(sk2(sk3)), sk2(sk3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[278, 63, 275])).
% 0.20/0.49 tff(280,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[279, 258])).
% 0.20/0.49 tff(281,plain,((~(sk2(sk3) = equilibrium(sk3))) | greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(282,plain,
% 0.20/0.49 (~(sk2(sk3) = equilibrium(sk3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[281, 250])).
% 0.20/0.49 tff(283,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(284,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[283])).
% 0.20/0.49 tff(285,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(286,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(287,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[286])).
% 0.20/0.49 tff(288,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | greater_or_equal(sk2(A), equilibrium(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a4_41')).
% 0.20/0.49 tff(289,plain,
% 0.20/0.49 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.20/0.49 tff(290,plain,
% 0.20/0.49 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[289, 285])).
% 0.20/0.49 tff(291,plain,(
% 0.20/0.49 ![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[290])).
% 0.20/0.49 tff(292,plain,
% 0.20/0.49 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[291, 284])).
% 0.20/0.49 tff(293,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(294,plain,
% 0.20/0.49 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))) | ((~stable(sk3)) | (~environment(sk3)) | greater_or_equal(sk2(sk3), equilibrium(sk3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(295,plain,
% 0.20/0.49 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | greater_or_equal(sk2(A), equilibrium(A)))) | (~stable(sk3)) | (~environment(sk3)) | greater_or_equal(sk2(sk3), equilibrium(sk3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.20/0.49 tff(296,plain,
% 0.20/0.49 (greater_or_equal(sk2(sk3), equilibrium(sk3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[295, 292, 10, 7])).
% 0.20/0.49 tff(297,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(298,plain,
% 0.20/0.49 (((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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(299,plain,
% 0.20/0.49 (((~![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))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[298])).
% 0.20/0.49 tff(300,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[299, 297])).
% 0.20/0.49 tff(301,plain,
% 0.20/0.49 ((~![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))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(302,plain,
% 0.20/0.49 ((~![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))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.20/0.49 tff(303,plain,
% 0.20/0.49 ((sk2(sk3) = equilibrium(sk3)) | greater(sk2(sk3), equilibrium(sk3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[302, 230, 296])).
% 0.20/0.49 tff(304,plain,
% 0.20/0.49 (greater(sk2(sk3), equilibrium(sk3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[303, 282])).
% 0.20/0.49 tff(305,assumption,(~greater(sk4(sk2(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.20/0.49 tff(306,assumption,(greater(sk4(sk2(sk3)), sk2(sk3))), introduced(assumption)).
% 0.20/0.49 tff(307,assumption,(greater(sk2(sk3), equilibrium(sk3))), introduced(assumption)).
% 0.20/0.49 tff(308,plain,
% 0.20/0.49 (((~![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))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(309,plain,
% 0.20/0.49 ((~![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))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(310,plain,
% 0.20/0.49 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk2(sk3)), equilibrium(sk3)) | (~greater(sk2(sk3), equilibrium(sk3))) | (~greater(sk4(sk2(sk3)), sk2(sk3)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.20/0.49 tff(311,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[310, 93, 307, 306, 305])).
% 0.20/0.49 tff(312,plain,((~greater(sk4(sk2(sk3)), sk2(sk3))) | (~greater(sk2(sk3), equilibrium(sk3))) | greater(sk4(sk2(sk3)), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(313,plain,
% 0.20/0.49 (~greater(sk4(sk2(sk3)), sk2(sk3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[312, 304, 254])).
% 0.20/0.49 tff(314,plain,
% 0.20/0.49 (((~![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))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(315,plain,
% 0.20/0.49 ((~![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))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(316,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (sk4(sk2(sk3)) = sk2(sk3)) | greater(sk4(sk2(sk3)), sk2(sk3)) | (~greater_or_equal(sk4(sk2(sk3)), sk2(sk3)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.20/0.49 tff(317,plain,
% 0.20/0.49 ((sk4(sk2(sk3)) = sk2(sk3)) | greater(sk4(sk2(sk3)), sk2(sk3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[316, 230, 279])).
% 0.20/0.49 tff(318,plain,
% 0.20/0.49 (sk4(sk2(sk3)) = sk2(sk3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[317, 313])).
% 0.20/0.49 tff(319,plain,
% 0.20/0.49 (greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3)) <=> greater_or_equal(sk2(sk3), equilibrium(sk3))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[318])).
% 0.20/0.49 tff(320,plain,
% 0.20/0.49 (greater_or_equal(sk2(sk3), equilibrium(sk3)) <=> greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.20/0.49 inference(symmetry,[status(thm)],[319])).
% 0.20/0.49 tff(321,plain,
% 0.20/0.49 (greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[296, 320])).
% 0.20/0.49 tff(322,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[250, 321])).
% 0.20/0.49 tff(323,plain,(greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(324,assumption,(greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))), introduced(assumption)).
% 0.20/0.49 tff(325,assumption,(~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)), introduced(assumption)).
% 0.20/0.49 tff(326,plain,
% 0.20/0.49 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(327,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(328,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.20/0.49 tff(329,plain,
% 0.20/0.49 (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[328, 135, 325])).
% 0.20/0.49 tff(330,plain,
% 0.20/0.49 (^[B: $i, A: $i] : refl(((~(A = B)) | greater_or_equal(A, B)) <=> ((~(A = B)) | greater_or_equal(A, B)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(331,plain,
% 0.20/0.49 (![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[330])).
% 0.20/0.49 tff(332,plain,
% 0.20/0.49 (![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(333,axiom,(![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_or_equal_26')).
% 0.20/0.49 tff(334,plain,
% 0.20/0.49 (![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.20/0.49 tff(335,plain,(
% 0.20/0.49 ![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))),
% 0.20/0.49 inference(skolemize,[status(sab)],[334])).
% 0.20/0.49 tff(336,plain,
% 0.20/0.49 (![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[335, 331])).
% 0.20/0.49 tff(337,plain,
% 0.20/0.49 (((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | ((~(growth_rate(efficient_producers, sk4(sk2(sk3))) = zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))) <=> ((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | (~(growth_rate(efficient_producers, sk4(sk2(sk3))) = zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(338,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | ((~(growth_rate(efficient_producers, sk4(sk2(sk3))) = zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(339,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | (~(growth_rate(efficient_producers, sk4(sk2(sk3))) = zero)) | greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.20/0.49 tff(340,plain,
% 0.20/0.49 (~(growth_rate(efficient_producers, sk4(sk2(sk3))) = zero)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[339, 336, 325])).
% 0.20/0.49 tff(341,plain,
% 0.20/0.49 (((~![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))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(342,plain,
% 0.20/0.49 ((~![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))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(343,plain,
% 0.20/0.49 ((~![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)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.20/0.49 tff(344,plain,
% 0.20/0.49 (subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[343, 34, 275])).
% 0.20/0.49 tff(345,plain,
% 0.20/0.49 (^[B: $i, A: $i] : refl((greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)) <=> (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(346,plain,
% 0.20/0.49 (![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[345])).
% 0.20/0.49 tff(347,plain,
% 0.20/0.49 (![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)) <=> ![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(348,plain,
% 0.20/0.49 (^[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(growth_rate(first_movers, B), zero)) <=> (((~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(first_movers, 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(growth_rate(first_movers, B), zero)) <=> (greater(growth_rate(first_movers, 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(growth_rate(first_movers, B), zero)) <=> (greater(growth_rate(first_movers, 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(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> ((greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(efficient_producers, B), zero)))), rewrite(((greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero)) | greater(growth_rate(efficient_producers, B), zero)) <=> (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, 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(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) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(349,plain,
% 0.20/0.49 (![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(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) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[348])).
% 0.20/0.49 tff(350,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(growth_rate(first_movers, B), zero)) | greater(growth_rate(efficient_producers, B), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l6_34')).
% 0.20/0.49 tff(351,plain,
% 0.20/0.49 (![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.20/0.49 tff(352,plain,
% 0.20/0.49 (![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[351, 347])).
% 0.20/0.49 tff(353,plain,(
% 0.20/0.49 ![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.49 inference(skolemize,[status(sab)],[352])).
% 0.20/0.49 tff(354,plain,
% 0.20/0.49 (![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[353, 346])).
% 0.20/0.49 tff(355,plain,
% 0.20/0.49 (((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(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) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(356,plain,
% 0.20/0.49 ((greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(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)) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero)) <=> ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(357,plain,
% 0.20/0.50 (((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(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)) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[356])).
% 0.20/0.50 tff(358,plain,
% 0.20/0.50 (((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(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)) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero))),
% 0.20/0.50 inference(transitivity,[status(thm)],[357, 355])).
% 0.20/0.50 tff(359,plain,
% 0.20/0.50 ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(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)) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(360,plain,
% 0.20/0.50 ((~![B: $i, A: $i] : (greater(growth_rate(efficient_producers, B), zero) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.20/0.50 tff(361,plain,
% 0.20/0.50 ((~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[360, 354, 10, 344])).
% 0.20/0.50 tff(362,plain,
% 0.20/0.50 (greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[361, 340, 323, 329])).
% 0.20/0.50 tff(363,plain,
% 0.20/0.50 (((~![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(first_movers, sk4(sk2(sk3))), zero)) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(364,plain,
% 0.20/0.50 ((~![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))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(365,plain,
% 0.20/0.50 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.20/0.50 tff(366,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[365, 93, 324, 329, 362])).
% 0.20/0.50 tff(367,plain,(greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(368,plain,
% 0.20/0.50 (greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[367, 324])).
% 0.20/0.50 tff(369,plain,
% 0.20/0.50 (((~![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))) | ((~in_environment(sk3, sk2(sk3))) | (~outcompetes(efficient_producers, first_movers, sk4(sk2(sk3)))))) <=> ((~![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))) | (~in_environment(sk3, sk2(sk3))) | (~outcompetes(efficient_producers, first_movers, sk4(sk2(sk3)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(370,plain,
% 0.20/0.50 ((~![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))) | ((~in_environment(sk3, sk2(sk3))) | (~outcompetes(efficient_producers, first_movers, sk4(sk2(sk3)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(371,plain,
% 0.20/0.50 ((~![A: $i] : ((~in_environment(sk3, A)) | (~outcompetes(efficient_producers, first_movers, sk4(A))))) | (~in_environment(sk3, sk2(sk3))) | (~outcompetes(efficient_producers, first_movers, sk4(sk2(sk3))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.20/0.50 tff(372,plain,
% 0.20/0.50 (~outcompetes(efficient_producers, first_movers, sk4(sk2(sk3)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[371, 106, 275])).
% 0.20/0.50 tff(373,plain,
% 0.20/0.50 (((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | ((~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(374,plain,
% 0.20/0.50 ((outcompetes(efficient_producers, first_movers, sk4(sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3))) <=> ((~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(375,plain,
% 0.20/0.50 (((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (outcompetes(efficient_producers, first_movers, sk4(sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | ((~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[374])).
% 0.20/0.50 tff(376,plain,
% 0.20/0.50 (((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (outcompetes(efficient_producers, first_movers, sk4(sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[375, 373])).
% 0.20/0.50 tff(377,plain,
% 0.20/0.50 ((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (outcompetes(efficient_producers, first_movers, sk4(sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~environment(sk3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(378,plain,
% 0.20/0.50 ((~![B: $i, D: $i, A: $i, C: $i] : (outcompetes(C, B, D) | (~greater(zero, growth_rate(B, D))) | (~greater_or_equal(growth_rate(C, D), zero)) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (~environment(sk3)) | outcompetes(efficient_producers, first_movers, sk4(sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.20/0.50 tff(379,plain,
% 0.20/0.50 ((~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) | (~greater_or_equal(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[378, 120, 10, 372, 344])).
% 0.20/0.50 tff(380,plain,
% 0.20/0.50 (~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[379, 368])).
% 0.20/0.50 tff(381,assumption,(~(growth_rate(first_movers, sk4(sk2(sk3))) = zero)), introduced(assumption)).
% 0.20/0.50 tff(382,assumption,(~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))), introduced(assumption)).
% 0.20/0.50 tff(383,plain,
% 0.20/0.50 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | 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(first_movers, sk4(sk2(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | 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(first_movers, sk4(sk2(sk3))) = zero))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(384,plain,
% 0.20/0.50 ((greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (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)) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))) <=> ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | 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(first_movers, sk4(sk2(sk3))) = zero))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(385,plain,
% 0.20/0.50 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (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)) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | 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(first_movers, sk4(sk2(sk3))) = zero)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[384])).
% 0.20/0.50 tff(386,plain,
% 0.20/0.50 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (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)) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | 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(first_movers, sk4(sk2(sk3))) = zero))),
% 0.20/0.50 inference(transitivity,[status(thm)],[385, 383])).
% 0.20/0.50 tff(387,plain,
% 0.20/0.50 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (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)) | greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(388,plain,
% 0.20/0.50 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | (growth_rate(first_movers, B) = zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, growth_rate(efficient_producers, B)))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | 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(first_movers, sk4(sk2(sk3))) = zero)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[387, 386])).
% 0.20/0.50 tff(389,plain,
% 0.20/0.50 (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(first_movers, sk4(sk2(sk3))) = zero)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[388, 48, 10, 344])).
% 0.20/0.50 tff(390,plain,
% 0.20/0.50 (greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[389, 382, 323, 381])).
% 0.20/0.50 tff(391,plain,
% 0.20/0.50 (((~![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))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(392,plain,
% 0.20/0.51 ((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))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(393,plain,
% 0.20/0.51 (((~![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)))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[392])).
% 0.20/0.51 tff(394,plain,
% 0.20/0.51 (((~![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))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[393, 391])).
% 0.20/0.51 tff(395,plain,
% 0.20/0.51 ((~![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))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(396,plain,
% 0.20/0.51 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(zero, growth_rate(efficient_producers, sk4(sk2(sk3))))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.20/0.51 tff(397,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[396, 93, 324, 382, 390])).
% 0.20/0.51 tff(398,plain,(greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))) | (growth_rate(first_movers, sk4(sk2(sk3))) = zero)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(399,plain,
% 0.20/0.51 (growth_rate(first_movers, sk4(sk2(sk3))) = zero),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[398, 380, 324])).
% 0.20/0.51 tff(400,plain,
% 0.20/0.51 (zero = growth_rate(first_movers, sk4(sk2(sk3)))),
% 0.20/0.51 inference(symmetry,[status(thm)],[399])).
% 0.20/0.51 tff(401,plain,
% 0.20/0.51 (greater(growth_rate(first_movers, sk4(sk2(sk3))), zero) <=> greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[399, 400])).
% 0.20/0.51 tff(402,plain,
% 0.20/0.51 (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) <=> greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)),
% 0.20/0.51 inference(symmetry,[status(thm)],[401])).
% 0.20/0.51 tff(403,plain,
% 0.20/0.51 ((~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) <=> (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[402])).
% 0.20/0.51 tff(404,plain,
% 0.20/0.51 (~greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[380, 403])).
% 0.20/0.51 tff(405,plain,
% 0.20/0.51 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(406,plain,
% 0.20/0.51 ((greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | greater(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)) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero)) <=> ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(407,plain,
% 0.20/0.51 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~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(first_movers, sk4(sk2(sk3)))) | greater(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)) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | ((~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[406])).
% 0.20/0.51 tff(408,plain,
% 0.20/0.51 (((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~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(first_movers, sk4(sk2(sk3)))) | greater(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)) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))) <=> ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero))),
% 0.20/0.51 inference(transitivity,[status(thm)],[407, 405])).
% 0.20/0.51 tff(409,plain,
% 0.20/0.51 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~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(first_movers, sk4(sk2(sk3)))) | greater(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)) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(410,plain,
% 0.20/0.51 ((~![B: $i, A: $i] : (greater(zero, growth_rate(first_movers, B)) | greater(growth_rate(first_movers, B), zero) | (~greater_or_equal(B, equilibrium(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | (growth_rate(efficient_producers, B) = zero))) | (~environment(sk3)) | (~subpopulations(first_movers, efficient_producers, sk3, sk4(sk2(sk3)))) | greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.20/0.51 tff(411,plain,
% 0.20/0.51 (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero) | greater(growth_rate(first_movers, sk4(sk2(sk3))), zero)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[410, 188, 10, 344])).
% 0.20/0.51 tff(412,plain,
% 0.20/0.51 (growth_rate(efficient_producers, sk4(sk2(sk3))) = zero),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[411, 404, 323, 380])).
% 0.20/0.51 tff(413,plain,
% 0.20/0.51 (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero) <=> greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[412, 400])).
% 0.20/0.51 tff(414,plain,
% 0.20/0.51 (greater(zero, growth_rate(first_movers, sk4(sk2(sk3)))) <=> greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)),
% 0.20/0.51 inference(symmetry,[status(thm)],[413])).
% 0.20/0.51 tff(415,plain,
% 0.20/0.51 ((~greater(zero, growth_rate(first_movers, sk4(sk2(sk3))))) <=> (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[414])).
% 0.20/0.51 tff(416,plain,
% 0.20/0.51 (~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[380, 415])).
% 0.20/0.51 tff(417,plain,
% 0.20/0.51 (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) <=> greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[399])).
% 0.20/0.51 tff(418,plain,
% 0.20/0.51 (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), zero)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[324, 417])).
% 0.20/0.51 tff(419,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[418, 416])).
% 0.20/0.51 tff(420,plain,(~greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(421,plain,
% 0.20/0.51 (((~![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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(422,plain,
% 0.20/0.51 (((~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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(423,plain,
% 0.20/0.51 (((~![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)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[422])).
% 0.20/0.51 tff(424,plain,
% 0.20/0.51 (((~![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))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[423, 421])).
% 0.20/0.51 tff(425,plain,
% 0.20/0.51 ((~![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))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(426,plain,
% 0.20/0.51 ((~![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)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.20/0.51 tff(427,plain,
% 0.20/0.51 (greater(growth_rate(efficient_producers, sk4(sk2(sk3))), growth_rate(first_movers, sk4(sk2(sk3)))) | (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[426, 77, 10, 7, 344])).
% 0.20/0.51 tff(428,plain,
% 0.20/0.51 (~greater_or_equal(sk4(sk2(sk3)), sk1(sk3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[427, 420])).
% 0.20/0.51 tff(429,plain,
% 0.20/0.51 (((~![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(430,plain,
% 0.20/0.51 ((~![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)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(431,plain,
% 0.20/0.51 ((~![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))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.20/0.51 tff(432,plain,
% 0.20/0.51 (~greater(sk4(sk2(sk3)), sk1(sk3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[431, 135, 428])).
% 0.20/0.51 tff(433,assumption,(~greater(sk4(sk2(sk3)), sk1(sk3))), introduced(assumption)).
% 0.20/0.51 tff(434,assumption,(greater(equilibrium(sk3), sk1(sk3))), introduced(assumption)).
% 0.20/0.51 tff(435,assumption,(greater(sk4(sk2(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.20/0.51 tff(436,plain,
% 0.20/0.51 (((~![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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(437,plain,
% 0.20/0.51 ((~![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))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(438,plain,
% 0.20/0.51 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(equilibrium(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), equilibrium(sk3)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.20/0.51 tff(439,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[438, 93, 435, 433, 434])).
% 0.20/0.51 tff(440,plain,((~greater(equilibrium(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), equilibrium(sk3))) | greater(sk4(sk2(sk3)), sk1(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(441,plain,
% 0.20/0.51 (~greater(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[440, 434, 433])).
% 0.20/0.51 tff(442,assumption,(greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.20/0.51 tff(443,plain,
% 0.20/0.51 (((~![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(444,plain,
% 0.20/0.51 (((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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(445,plain,
% 0.20/0.51 (((~![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))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[444])).
% 0.20/0.51 tff(446,plain,
% 0.20/0.51 (((~![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)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[445, 443])).
% 0.20/0.51 tff(447,plain,
% 0.20/0.51 ((~![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))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(448,plain,
% 0.20/0.51 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3))) | (sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.20/0.51 tff(449,plain,
% 0.20/0.51 ((sk4(sk2(sk3)) = equilibrium(sk3)) | greater(sk4(sk2(sk3)), equilibrium(sk3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[448, 230, 442])).
% 0.20/0.51 tff(450,plain,
% 0.20/0.51 (sk4(sk2(sk3)) = equilibrium(sk3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[449, 441])).
% 0.20/0.51 tff(451,plain,
% 0.20/0.51 (greater(sk4(sk2(sk3)), sk1(sk3)) <=> greater(equilibrium(sk3), sk1(sk3))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[450])).
% 0.20/0.51 tff(452,plain,
% 0.20/0.51 (greater(equilibrium(sk3), sk1(sk3)) <=> greater(sk4(sk2(sk3)), sk1(sk3))),
% 0.20/0.51 inference(symmetry,[status(thm)],[451])).
% 0.20/0.51 tff(453,plain,
% 0.20/0.51 (greater(sk4(sk2(sk3)), sk1(sk3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[434, 452])).
% 0.20/0.51 tff(454,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[433, 453])).
% 0.20/0.51 tff(455,plain,((~greater(equilibrium(sk3), sk1(sk3))) | greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater_or_equal(sk4(sk2(sk3)), equilibrium(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(456,plain,
% 0.20/0.51 (~greater(equilibrium(sk3), sk1(sk3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[455, 432, 323])).
% 0.20/0.51 tff(457,assumption,(in_environment(sk3, equilibrium(sk3))), introduced(assumption)).
% 0.20/0.51 tff(458,assumption,(~greater(equilibrium(sk3), sk1(sk3))), introduced(assumption)).
% 0.20/0.51 tff(459,assumption,(~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))), introduced(assumption)).
% 0.20/0.51 tff(460,plain,
% 0.20/0.51 (~greater(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[207, 135, 459])).
% 0.20/0.51 tff(461,plain,
% 0.20/0.51 (~greater(sk1(sk3), equilibrium(sk3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[218, 460, 210])).
% 0.20/0.51 tff(462,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(463,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[462])).
% 0.20/0.51 tff(464,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(465,plain,
% 0.20/0.51 (^[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)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(466,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[465])).
% 0.20/0.51 tff(467,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/sandbox2/benchmark/theBenchmark.p','mp_times_in_environment_23')).
% 0.20/0.51 tff(468,plain,
% 0.20/0.51 (![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.20/0.51 tff(469,plain,
% 0.20/0.51 (![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[468, 464])).
% 0.20/0.51 tff(470,plain,(
% 0.20/0.51 ![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[469])).
% 0.20/0.51 tff(471,plain,
% 0.20/0.51 (![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[470, 463])).
% 0.20/0.51 tff(472,plain,
% 0.20/0.51 (((~![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))) | (sk1(sk3) = equilibrium(sk3)) | greater(sk1(sk3), equilibrium(sk3)) | greater(equilibrium(sk3), sk1(sk3)) | (~in_environment(sk3, equilibrium(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))) | (sk1(sk3) = equilibrium(sk3)) | greater(sk1(sk3), equilibrium(sk3)) | greater(equilibrium(sk3), sk1(sk3)) | (~in_environment(sk3, equilibrium(sk3))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(473,plain,
% 0.20/0.52 ((greater(equilibrium(sk3), sk1(sk3)) | (sk1(sk3) = equilibrium(sk3)) | greater(sk1(sk3), equilibrium(sk3)) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, equilibrium(sk3)))) <=> ((~in_environment(sk3, sk1(sk3))) | (sk1(sk3) = equilibrium(sk3)) | greater(sk1(sk3), equilibrium(sk3)) | greater(equilibrium(sk3), sk1(sk3)) | (~in_environment(sk3, equilibrium(sk3))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(474,plain,
% 0.20/0.52 (((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (greater(equilibrium(sk3), sk1(sk3)) | (sk1(sk3) = equilibrium(sk3)) | greater(sk1(sk3), equilibrium(sk3)) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, equilibrium(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))) | (sk1(sk3) = equilibrium(sk3)) | greater(sk1(sk3), equilibrium(sk3)) | greater(equilibrium(sk3), sk1(sk3)) | (~in_environment(sk3, equilibrium(sk3)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[473])).
% 0.20/0.52 tff(475,plain,
% 0.20/0.52 (((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (greater(equilibrium(sk3), sk1(sk3)) | (sk1(sk3) = equilibrium(sk3)) | greater(sk1(sk3), equilibrium(sk3)) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, equilibrium(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))) | (sk1(sk3) = equilibrium(sk3)) | greater(sk1(sk3), equilibrium(sk3)) | greater(equilibrium(sk3), sk1(sk3)) | (~in_environment(sk3, equilibrium(sk3))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[474, 472])).
% 0.20/0.52 tff(476,plain,
% 0.20/0.52 ((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (greater(equilibrium(sk3), sk1(sk3)) | (sk1(sk3) = equilibrium(sk3)) | greater(sk1(sk3), equilibrium(sk3)) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, equilibrium(sk3))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(477,plain,
% 0.20/0.52 ((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (~in_environment(sk3, sk1(sk3))) | (sk1(sk3) = equilibrium(sk3)) | greater(sk1(sk3), equilibrium(sk3)) | greater(equilibrium(sk3), sk1(sk3)) | (~in_environment(sk3, equilibrium(sk3)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.20/0.52 tff(478,plain,
% 0.20/0.52 ((sk1(sk3) = equilibrium(sk3)) | greater(sk1(sk3), equilibrium(sk3)) | (~in_environment(sk3, equilibrium(sk3)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[477, 471, 27, 458])).
% 0.20/0.52 tff(479,plain,
% 0.20/0.52 (sk1(sk3) = equilibrium(sk3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[478, 461, 457])).
% 0.20/0.52 tff(480,plain,
% 0.20/0.52 (greater_or_equal(sk4(sk1(sk3)), sk1(sk3)) <=> greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[479])).
% 0.20/0.52 tff(481,plain,
% 0.20/0.52 (greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)) <=> greater_or_equal(sk4(sk1(sk3)), sk1(sk3))),
% 0.20/0.52 inference(symmetry,[status(thm)],[480])).
% 0.20/0.52 tff(482,plain,
% 0.20/0.52 ((~greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))) <=> (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[481])).
% 0.20/0.52 tff(483,plain,
% 0.20/0.52 (~greater_or_equal(sk4(sk1(sk3)), sk1(sk3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[459, 482])).
% 0.20/0.52 tff(484,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[67, 483])).
% 0.20/0.52 tff(485,plain,(greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)) | (~in_environment(sk3, equilibrium(sk3))) | greater(equilibrium(sk3), sk1(sk3)) | (~greater(sk4(sk1(sk3)), sk1(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(486,plain,
% 0.20/0.52 (~greater(sk4(sk1(sk3)), sk1(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[485, 459, 458, 457])).
% 0.20/0.52 tff(487,plain,
% 0.20/0.52 (sk4(sk1(sk3)) = sk1(sk3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[237, 486])).
% 0.20/0.52 tff(488,plain,
% 0.20/0.52 (greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)) <=> greater_or_equal(sk1(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[487])).
% 0.20/0.52 tff(489,plain,
% 0.20/0.52 (greater_or_equal(sk1(sk3), equilibrium(sk3)) <=> greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.20/0.52 inference(symmetry,[status(thm)],[488])).
% 0.20/0.52 tff(490,assumption,(~greater_or_equal(sk1(sk3), equilibrium(sk3))), introduced(assumption)).
% 0.20/0.52 tff(491,plain,
% 0.20/0.52 (((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | ((~(sk1(sk3) = equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3)))) <=> ((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | (~(sk1(sk3) = equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(492,plain,
% 0.20/0.52 ((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | ((~(sk1(sk3) = equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(493,plain,
% 0.20/0.52 ((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | (~(sk1(sk3) = equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.20/0.52 tff(494,plain,
% 0.20/0.52 ((~(sk1(sk3) = equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[493, 336])).
% 0.20/0.52 tff(495,plain,
% 0.20/0.52 (~(sk1(sk3) = equilibrium(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[494, 490])).
% 0.20/0.52 tff(496,plain,
% 0.20/0.52 (((~![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)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(497,plain,
% 0.20/0.52 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk1(sk3), equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(498,plain,
% 0.20/0.52 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk1(sk3), equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.20/0.52 tff(499,plain,
% 0.20/0.52 ((~greater(sk1(sk3), equilibrium(sk3))) | greater_or_equal(sk1(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[498, 135])).
% 0.20/0.52 tff(500,plain,
% 0.20/0.52 (~greater(sk1(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[499, 490])).
% 0.20/0.52 tff(501,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[478, 500, 495, 457])).
% 0.20/0.52 tff(502,plain,(greater_or_equal(sk1(sk3), equilibrium(sk3)) | (~in_environment(sk3, equilibrium(sk3))) | greater(equilibrium(sk3), sk1(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(503,plain,
% 0.20/0.52 (greater_or_equal(sk1(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[502, 458, 457])).
% 0.20/0.52 tff(504,plain,
% 0.20/0.52 (greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[503, 489])).
% 0.20/0.52 tff(505,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[459, 504])).
% 0.20/0.52 tff(506,plain,(greater_or_equal(sk4(sk1(sk3)), equilibrium(sk3)) | greater(equilibrium(sk3), sk1(sk3)) | (~in_environment(sk3, equilibrium(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(507,plain,
% 0.20/0.52 (greater(equilibrium(sk3), sk1(sk3)) | (~in_environment(sk3, equilibrium(sk3)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[506, 204])).
% 0.20/0.52 tff(508,plain,
% 0.20/0.52 (~in_environment(sk3, equilibrium(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[507, 456])).
% 0.20/0.52 tff(509,plain,
% 0.20/0.52 (~in_environment(sk3, sk2(sk3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[508, 249])).
% 0.20/0.52 tff(510,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[275, 509])).
% 0.20/0.52 tff(511,plain,(~(sk2(sk3) = equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(512,plain,
% 0.20/0.52 (greater(sk2(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[303, 511])).
% 0.20/0.52 tff(513,assumption,(greater(sk1(sk3), sk2(sk3))), introduced(assumption)).
% 0.20/0.52 tff(514,plain,
% 0.20/0.52 (((~![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(sk1(sk3), equilibrium(sk3)) | (~greater(sk2(sk3), equilibrium(sk3))) | (~greater(sk1(sk3), sk2(sk3))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(515,plain,
% 0.20/0.52 ((~![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))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(516,plain,
% 0.20/0.52 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk1(sk3), equilibrium(sk3)) | (~greater(sk2(sk3), equilibrium(sk3))) | (~greater(sk1(sk3), sk2(sk3)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.20/0.52 tff(517,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[516, 93, 307, 245, 513])).
% 0.20/0.52 tff(518,plain,((~greater(sk1(sk3), sk2(sk3))) | (~greater(sk2(sk3), equilibrium(sk3))) | greater(sk1(sk3), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(519,plain,
% 0.20/0.52 ((~greater(sk1(sk3), sk2(sk3))) | greater(sk1(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[518, 512])).
% 0.20/0.52 tff(520,plain,
% 0.20/0.52 (~greater(sk1(sk3), sk2(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[519, 245])).
% 0.20/0.52 tff(521,assumption,(sk2(sk3) = sk1(sk3)), introduced(assumption)).
% 0.20/0.52 tff(522,plain,
% 0.20/0.52 (greater(sk2(sk3), equilibrium(sk3)) <=> greater(sk1(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[521])).
% 0.20/0.52 tff(523,plain,
% 0.20/0.52 (greater(sk1(sk3), equilibrium(sk3)) <=> greater(sk2(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(symmetry,[status(thm)],[522])).
% 0.20/0.52 tff(524,plain,
% 0.20/0.52 ((~greater(sk1(sk3), equilibrium(sk3))) <=> (~greater(sk2(sk3), equilibrium(sk3)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[523])).
% 0.20/0.52 tff(525,plain,
% 0.20/0.52 (~greater(sk2(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[245, 524])).
% 0.20/0.52 tff(526,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[307, 525])).
% 0.20/0.52 tff(527,plain,((~(sk2(sk3) = sk1(sk3))) | (~greater(sk2(sk3), equilibrium(sk3))) | greater(sk1(sk3), equilibrium(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(528,plain,
% 0.20/0.52 ((~(sk2(sk3) = sk1(sk3))) | greater(sk1(sk3), equilibrium(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[527, 512])).
% 0.20/0.52 tff(529,plain,
% 0.20/0.52 (~(sk2(sk3) = sk1(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[528, 245])).
% 0.20/0.52 tff(530,plain,
% 0.20/0.52 (((~![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)) | (sk2(sk3) = sk1(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)) | (sk2(sk3) = sk1(sk3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(531,plain,
% 0.20/0.52 ((greater(sk1(sk3), sk2(sk3)) | (sk2(sk3) = sk1(sk3)) | greater(sk2(sk3), sk1(sk3)) | (~in_environment(sk3, sk2(sk3))) | (~in_environment(sk3, sk1(sk3)))) <=> ((~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3))) | greater(sk2(sk3), sk1(sk3)) | greater(sk1(sk3), sk2(sk3)) | (sk2(sk3) = sk1(sk3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(532,plain,
% 0.20/0.52 (((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (greater(sk1(sk3), sk2(sk3)) | (sk2(sk3) = sk1(sk3)) | greater(sk2(sk3), sk1(sk3)) | (~in_environment(sk3, sk2(sk3))) | (~in_environment(sk3, sk1(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)) | (sk2(sk3) = sk1(sk3))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[531])).
% 0.20/0.52 tff(533,plain,
% 0.20/0.52 (((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (greater(sk1(sk3), sk2(sk3)) | (sk2(sk3) = sk1(sk3)) | greater(sk2(sk3), sk1(sk3)) | (~in_environment(sk3, sk2(sk3))) | (~in_environment(sk3, sk1(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)) | (sk2(sk3) = sk1(sk3)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[532, 530])).
% 0.20/0.52 tff(534,plain,
% 0.20/0.52 ((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (greater(sk1(sk3), sk2(sk3)) | (sk2(sk3) = sk1(sk3)) | greater(sk2(sk3), sk1(sk3)) | (~in_environment(sk3, sk2(sk3))) | (~in_environment(sk3, sk1(sk3))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(535,plain,
% 0.20/0.52 ((~![B: $i, A: $i, C: $i] : (greater(B, C) | (C = B) | greater(C, B) | (~in_environment(A, C)) | (~in_environment(A, B)))) | (~in_environment(sk3, sk1(sk3))) | (~in_environment(sk3, sk2(sk3))) | greater(sk2(sk3), sk1(sk3)) | greater(sk1(sk3), sk2(sk3)) | (sk2(sk3) = sk1(sk3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[534, 533])).
% 0.20/0.52 tff(536,plain,
% 0.20/0.52 (greater(sk2(sk3), sk1(sk3)) | greater(sk1(sk3), sk2(sk3)) | (sk2(sk3) = sk1(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[535, 471, 27, 275])).
% 0.20/0.52 tff(537,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[536, 529, 520, 244])).
% 0.20/0.52 tff(538,plain,(greater(sk1(sk3), equilibrium(sk3)) | greater(sk2(sk3), sk1(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(539,plain,
% 0.20/0.52 (greater(sk2(sk3), sk1(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[538, 243])).
% 0.20/0.52 tff(540,assumption,(greater(sk2(sk3), sk1(sk3))), introduced(assumption)).
% 0.20/0.52 tff(541,plain,
% 0.20/0.52 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(sk4(sk2(sk3)), sk2(sk3))) | (~greater(sk2(sk3), sk1(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(sk4(sk2(sk3)), sk2(sk3))) | (~greater(sk2(sk3), sk1(sk3))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(542,plain,
% 0.20/0.52 ((greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(sk2(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), sk2(sk3)))) <=> (greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(sk4(sk2(sk3)), sk2(sk3))) | (~greater(sk2(sk3), sk1(sk3))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(543,plain,
% 0.20/0.52 (((~![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(sk4(sk2(sk3)), sk2(sk3))) | (~greater(sk2(sk3), sk1(sk3)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[542])).
% 0.20/0.52 tff(544,plain,
% 0.20/0.52 (((~![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(sk4(sk2(sk3)), sk2(sk3))) | (~greater(sk2(sk3), sk1(sk3))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[543, 541])).
% 0.20/0.52 tff(545,plain,
% 0.20/0.52 ((~![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))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(546,plain,
% 0.20/0.52 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | greater(sk4(sk2(sk3)), sk1(sk3)) | (~greater(sk4(sk2(sk3)), sk2(sk3))) | (~greater(sk2(sk3), sk1(sk3)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.20/0.52 tff(547,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[546, 93, 306, 432, 540])).
% 0.20/0.52 tff(548,plain,((~greater(sk2(sk3), sk1(sk3))) | (~greater(sk4(sk2(sk3)), sk2(sk3)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(549,plain,
% 0.20/0.52 (~greater(sk4(sk2(sk3)), sk2(sk3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[548, 539])).
% 0.20/0.52 tff(550,plain,
% 0.20/0.52 (sk4(sk2(sk3)) = sk2(sk3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[317, 549])).
% 0.20/0.52 tff(551,plain,
% 0.20/0.52 (greater(sk4(sk2(sk3)), sk1(sk3)) <=> greater(sk2(sk3), sk1(sk3))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[550])).
% 0.20/0.52 tff(552,plain,
% 0.20/0.52 (greater(sk2(sk3), sk1(sk3)) <=> greater(sk4(sk2(sk3)), sk1(sk3))),
% 0.20/0.52 inference(symmetry,[status(thm)],[551])).
% 0.20/0.52 tff(553,plain,
% 0.20/0.52 (greater(sk4(sk2(sk3)), sk1(sk3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[539, 552])).
% 0.20/0.52 tff(554,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[432, 553])).
% 0.20/0.52 % SZS output end Proof
%------------------------------------------------------------------------------