TSTP Solution File: MGT023-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT023-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 05:21:55 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT023-2 : TPTP v8.1.0. Released v2.4.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.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 02:37:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(subpopulations_type, type, (
% 0.19/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.19/0.40 tff(sk1_type, type, (
% 0.19/0.40 sk1: ( $i * $i ) > $i)).
% 0.19/0.40 tff(sk5_type, type, (
% 0.19/0.40 sk5: $i)).
% 0.19/0.40 tff(sk4_type, type, (
% 0.19/0.40 sk4: $i > $i)).
% 0.19/0.40 tff(efficient_producers_type, type, (
% 0.19/0.40 efficient_producers: $i)).
% 0.19/0.40 tff(first_movers_type, type, (
% 0.19/0.40 first_movers: $i)).
% 0.19/0.40 tff(greater_type, type, (
% 0.19/0.40 greater: ( $i * $i ) > $o)).
% 0.19/0.40 tff(growth_rate_type, type, (
% 0.19/0.40 growth_rate: ( $i * $i ) > $i)).
% 0.19/0.40 tff(sk2_type, type, (
% 0.19/0.40 sk2: $i > $i)).
% 0.19/0.40 tff(sk3_type, type, (
% 0.19/0.40 sk3: ( $i * $i ) > $i)).
% 0.19/0.40 tff(critical_point_type, type, (
% 0.19/0.40 critical_point: $i > $i)).
% 0.19/0.40 tff(in_environment_type, type, (
% 0.19/0.40 in_environment: ( $i * $i ) > $o)).
% 0.19/0.40 tff(stable_type, type, (
% 0.19/0.40 stable: $i > $o)).
% 0.19/0.40 tff(environment_type, type, (
% 0.19/0.40 environment: $i > $o)).
% 0.19/0.40 tff(greater_or_equal_type, type, (
% 0.19/0.40 greater_or_equal: ( $i * $i ) > $o)).
% 0.19/0.40 tff(1,assumption,(~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))), introduced(assumption)).
% 0.19/0.40 tff(2,assumption,(~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))), introduced(assumption)).
% 0.19/0.40 tff(3,assumption,(~in_environment(sk5, sk2(sk5))), introduced(assumption)).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (stable(sk5) <=> stable(sk5)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(5,axiom,(stable(sk5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l5_34')).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (stable(sk5)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (environment(sk5) <=> environment(sk5)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(8,axiom,(environment(sk5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l5_33')).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (environment(sk5)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (^[A: $i] : refl(((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A))) <=> ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A))) <=> ![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A))) <=> ![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | in_environment(A, sk4(A))) <=> ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk4(A))) <=> ![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.40 tff(15,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk4(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1_31')).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.40 tff(18,plain,(
% 0.19/0.40 ![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (((~![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A)))) | ((~environment(sk5)) | (~stable(sk5)) | in_environment(sk5, sk4(sk5)))) <=> ((~![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A)))) | (~environment(sk5)) | (~stable(sk5)) | in_environment(sk5, sk4(sk5)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 ((~![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A)))) | ((~environment(sk5)) | (~stable(sk5)) | in_environment(sk5, sk4(sk5)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 ((~![A: $i] : ((~environment(A)) | (~stable(A)) | in_environment(A, sk4(A)))) | (~environment(sk5)) | (~stable(sk5)) | in_environment(sk5, sk4(sk5))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (in_environment(sk5, sk4(sk5))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[22, 19, 9, 6])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (^[B: $i, A: $i] : refl((in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | in_environment(A, sk2(A))) <=> ((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | in_environment(A, sk2(A))))), rewrite(((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | in_environment(A, sk2(A))) <=> (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | in_environment(A, sk2(A))) <=> (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | in_environment(A, sk2(A))) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.40 tff(29,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | in_environment(A, sk2(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_19')).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.40 tff(32,plain,(
% 0.19/0.40 ![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[31])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((in_environment(sk5, sk2(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5))) <=> ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (in_environment(sk5, sk2(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (in_environment(sk5, sk2(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[36, 34])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (in_environment(sk5, sk2(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (in_environment(sk5, sk2(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[39, 33, 9, 23])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[40, 3])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (^[B: $i, A: $i] : refl((in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A))) <=> (((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A))) <=> (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A))) <=> (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A))) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.40 tff(47,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_20')).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.40 tff(50,plain,(
% 0.19/0.40 ![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.19/0.40 inference(skolemize,[status(sab)],[49])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((in_environment(sk5, sk2(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))) <=> ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (in_environment(sk5, sk2(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (in_environment(sk5, sk2(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (in_environment(sk5, sk2(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | in_environment(sk5, sk2(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (in_environment(sk5, sk2(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[57, 51, 9, 23])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[58, 3])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (^[B: $i, A: $i] : refl(((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~environment(A)) | (~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk4(A)))) <=> (((~environment(A)) | (~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk4(A)))))), rewrite((((~environment(A)) | (~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk4(A)))) <=> ((~environment(A)) | (~stable(A)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk4(A)))) <=> ((~environment(A)) | (~stable(A)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B))))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk4(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> (((~environment(A)) | (~stable(A)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))))), rewrite((((~environment(A)) | (~stable(A)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk4(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk4(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.41 tff(65,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk4(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1_32')).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.41 tff(68,plain,(
% 0.19/0.41 ![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[67])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk5)) | (~stable(sk5)) | greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5))) | (~greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk5)) | (~stable(sk5)) | greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5))) | (~greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk5)) | (~stable(sk5)) | greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5))) | (~greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk4(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk5)) | (~stable(sk5)) | greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5))) | (~greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[72, 69, 9, 6, 2, 59, 41])).
% 0.19/0.41 tff(74,plain,(in_environment(sk5, sk2(sk5)) | greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (in_environment(sk5, sk2(sk5))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[74, 2])).
% 0.19/0.41 tff(76,assumption,(sk2(sk5) = critical_point(sk5)), introduced(assumption)).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (in_environment(sk5, sk2(sk5)) <=> in_environment(sk5, critical_point(sk5))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[76])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (in_environment(sk5, critical_point(sk5)) <=> in_environment(sk5, sk2(sk5))),
% 0.19/0.41 inference(symmetry,[status(thm)],[77])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 ((~in_environment(sk5, critical_point(sk5))) <=> (~in_environment(sk5, sk2(sk5)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 ((~in_environment(sk5, critical_point(sk5))) <=> (~in_environment(sk5, critical_point(sk5)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(81,axiom,(~in_environment(sk5, critical_point(sk5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l5_35')).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (~in_environment(sk5, critical_point(sk5))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (~in_environment(sk5, sk2(sk5))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[82, 79])).
% 0.19/0.41 tff(84,assumption,(in_environment(sk5, sk2(sk5))), introduced(assumption)).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.41 tff(86,plain,((~(sk2(sk5) = critical_point(sk5))) | (~in_environment(sk5, sk2(sk5)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (~(sk2(sk5) = critical_point(sk5))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[86, 75])).
% 0.19/0.41 tff(88,assumption,(~(sk2(sk5) = critical_point(sk5))), introduced(assumption)).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (^[B: $i, A: $i] : refl(((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) <=> (((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) | (B = critical_point(A))) <=> (((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) | (B = critical_point(A))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) | (B = critical_point(A))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) | (B = critical_point(A))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (![B: $i, A: $i] : (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) | (B = critical_point(A))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.42 tff(94,axiom,(![B: $i, A: $i] : (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk3(B, A))) | (B = critical_point(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_28')).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.19/0.42 tff(97,plain,(
% 0.19/0.42 ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[96])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))) | ((~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) <=> ((~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))) | ((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))) | ((~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[100])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))) | ((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[101, 99])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))) | ((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | subpopulations(first_movers, efficient_producers, A, sk3(B, A)))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 ((sk2(sk5) = critical_point(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[104, 98, 9, 1, 84])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[105, 88])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (^[B: $i, A: $i] : refl(((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B)) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B)) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B)) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk3(B, A), B)) <=> (((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | greater(sk3(B, A), B)))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | greater(sk3(B, A), B)) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk3(B, A), B)) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B)))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk3(B, A), B)) | (B = critical_point(A))) <=> (((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B)) | (B = critical_point(A))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B)) | (B = critical_point(A))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk3(B, A), B)) | (B = critical_point(A))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (![B: $i, A: $i] : (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk3(B, A), B)) | (B = critical_point(A))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.42 tff(112,axiom,(![B: $i, A: $i] : (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk3(B, A), B)) | (B = critical_point(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_29')).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.20/0.42 tff(115,plain,(
% 0.20/0.42 ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))),
% 0.20/0.42 inference(skolemize,[status(sab)],[114])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))) | ((~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | greater(sk3(sk2(sk5), sk5), sk2(sk5)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | greater(sk3(sk2(sk5), sk5), sk2(sk5)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | greater(sk3(sk2(sk5), sk5), sk2(sk5))) <=> ((~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | greater(sk3(sk2(sk5), sk5), sk2(sk5)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))) | ((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | greater(sk3(sk2(sk5), sk5), sk2(sk5)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))) | ((~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | greater(sk3(sk2(sk5), sk5), sk2(sk5))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[118])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))) | ((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | greater(sk3(sk2(sk5), sk5), sk2(sk5)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | greater(sk3(sk2(sk5), sk5), sk2(sk5)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[119, 117])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))) | ((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | greater(sk3(sk2(sk5), sk5), sk2(sk5)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | greater(sk3(B, A), B))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | greater(sk3(sk2(sk5), sk5), sk2(sk5))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 ((sk2(sk5) = critical_point(sk5)) | greater(sk3(sk2(sk5), sk5), sk2(sk5))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[122, 116, 9, 1, 84])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (greater(sk3(sk2(sk5), sk5), sk2(sk5))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[123, 88])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (^[B: $i, A: $i] : refl(((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) <=> (((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) | (B = critical_point(A))) <=> (((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) | (B = critical_point(A))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) | (B = critical_point(A))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) | (B = critical_point(A))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (![B: $i, A: $i] : (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) | (B = critical_point(A))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.43 tff(130,axiom,(![B: $i, A: $i] : (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A))))) | (B = critical_point(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_30')).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.20/0.43 tff(133,plain,(
% 0.20/0.43 ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[132])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))) | ((~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5)))))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))))) <=> ((~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))) | ((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5)))))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))) | ((~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))) | ((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5)))))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5)))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))) | ((sk2(sk5) = critical_point(sk5)) | (~in_environment(sk5, sk2(sk5))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | (~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater(growth_rate(efficient_producers, sk3(B, A)), growth_rate(first_movers, sk3(B, A)))))) | (~environment(sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5))) | (sk2(sk5) = critical_point(sk5)) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 ((sk2(sk5) = critical_point(sk5)) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[140, 134, 9, 1, 84])).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[141, 88])).
% 0.20/0.43 tff(143,assumption,(~subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))), introduced(assumption)).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 (^[B: $i, A: $i, C: $i] : refl((greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[144])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~subpopulations(first_movers, efficient_producers, A, C))))), rewrite(((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))))), ((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> (((~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~greater(C, sk2(A)))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), ((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))))), (((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))))), rewrite((((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.44 tff(149,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_22')).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.20/0.44 tff(152,plain,(
% 0.20/0.44 ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[151])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 ((greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5))) <=> ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[155])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[156, 154])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[159, 153, 9, 23, 143, 142, 124, 106])).
% 0.20/0.45 tff(161,plain,((sk2(sk5) = critical_point(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))) | (~in_environment(sk5, sk2(sk5)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[161, 87, 1, 75])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 ((sk2(sk5) = critical_point(sk5)) | subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[104, 98, 9, 1, 75])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 (subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[163, 87])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 ((sk2(sk5) = critical_point(sk5)) | greater(sk3(sk2(sk5), sk5), sk2(sk5))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[122, 116, 9, 1, 75])).
% 0.20/0.45 tff(166,plain,
% 0.20/0.45 (greater(sk3(sk2(sk5), sk5), sk2(sk5))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[165, 87])).
% 0.20/0.45 tff(167,plain,
% 0.20/0.45 ((sk2(sk5) = critical_point(sk5)) | (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[140, 134, 9, 1, 75])).
% 0.20/0.45 tff(168,plain,
% 0.20/0.45 (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[167, 87])).
% 0.20/0.45 tff(169,plain,
% 0.20/0.45 (^[B: $i, A: $i, C: $i] : refl((greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(170,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[169])).
% 0.20/0.45 tff(171,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(172,plain,
% 0.20/0.45 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> (((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))), ((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> (((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~greater(C, sk2(A)))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), ((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))), (((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))))), rewrite((((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(173,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[172])).
% 0.20/0.45 tff(174,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_24')).
% 0.20/0.45 tff(175,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.45 tff(176,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.20/0.45 tff(177,plain,(
% 0.20/0.45 ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.20/0.45 inference(skolemize,[status(sab)],[176])).
% 0.20/0.45 tff(178,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.20/0.45 tff(179,plain,
% 0.20/0.45 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(180,plain,
% 0.20/0.45 ((greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))) <=> ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[180])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[181, 179])).
% 0.20/0.45 tff(183,plain,
% 0.20/0.45 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 (greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[184, 178, 9, 23, 168, 166, 164])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[72, 69, 9, 6, 2, 185, 162])).
% 0.20/0.46 tff(187,plain,(greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5))) | greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[187, 1])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 (^[B: $i, A: $i] : refl(((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | in_environment(A, sk2(A))) <=> (((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A))) | in_environment(A, sk2(A))))), rewrite((((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A))) | in_environment(A, sk2(A))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | in_environment(A, sk2(A))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | in_environment(A, sk2(A))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[192])).
% 0.20/0.46 tff(194,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | in_environment(A, sk2(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_25')).
% 0.20/0.46 tff(195,plain,
% 0.20/0.46 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.20/0.46 tff(196,plain,
% 0.20/0.46 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.20/0.46 tff(197,plain,(
% 0.20/0.46 ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[196])).
% 0.20/0.46 tff(198,plain,
% 0.20/0.46 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.20/0.46 tff(199,plain,
% 0.20/0.46 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | in_environment(sk5, sk2(sk5)))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | in_environment(sk5, sk2(sk5)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(200,plain,
% 0.20/0.46 (((~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | in_environment(sk5, sk2(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5))) <=> ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | in_environment(sk5, sk2(sk5)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(201,plain,
% 0.20/0.46 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | in_environment(sk5, sk2(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | in_environment(sk5, sk2(sk5))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[200])).
% 0.20/0.46 tff(202,plain,
% 0.20/0.46 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | in_environment(sk5, sk2(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | in_environment(sk5, sk2(sk5)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[201, 199])).
% 0.20/0.46 tff(203,plain,
% 0.20/0.46 ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | in_environment(sk5, sk2(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(204,plain,
% 0.20/0.46 ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | in_environment(sk5, sk2(sk5))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.46 tff(205,plain,
% 0.20/0.46 ((~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | in_environment(sk5, sk2(sk5))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[204, 198, 9, 23])).
% 0.20/0.46 tff(206,plain,
% 0.20/0.46 (in_environment(sk5, sk2(sk5))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[205, 188])).
% 0.20/0.46 tff(207,plain,
% 0.20/0.46 (~(sk2(sk5) = critical_point(sk5))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[86, 206])).
% 0.20/0.46 tff(208,plain,
% 0.20/0.46 (subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[104, 98, 9, 1, 206, 207])).
% 0.20/0.46 tff(209,plain,
% 0.20/0.46 (greater(sk3(sk2(sk5), sk5), sk2(sk5))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[122, 116, 9, 1, 206, 207])).
% 0.20/0.46 tff(210,plain,
% 0.20/0.46 (~greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[140, 134, 9, 1, 206, 207])).
% 0.20/0.46 tff(211,plain,
% 0.20/0.46 (^[B: $i, A: $i, C: $i] : refl((greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(212,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[211])).
% 0.20/0.46 tff(213,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(214,plain,
% 0.20/0.46 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ((~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> (((~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> (((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(C, sk2(A)))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))))), rewrite((((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(215,plain,
% 0.20/0.47 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[214])).
% 0.20/0.47 tff(216,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_27')).
% 0.20/0.47 tff(217,plain,
% 0.20/0.47 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.20/0.47 tff(218,plain,
% 0.20/0.47 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.20/0.47 tff(219,plain,(
% 0.20/0.47 ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[218])).
% 0.20/0.47 tff(220,plain,
% 0.20/0.47 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.20/0.47 tff(221,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 ((greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5))))) <=> ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(223,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[222])).
% 0.20/0.47 tff(224,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[223, 221])).
% 0.20/0.47 tff(225,plain,
% 0.20/0.47 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(226,plain,
% 0.20/0.47 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | greater(growth_rate(efficient_producers, sk3(sk2(sk5), sk5)), growth_rate(first_movers, sk3(sk2(sk5), sk5))) | (~greater(sk3(sk2(sk5), sk5), sk2(sk5))) | (~subpopulations(first_movers, efficient_producers, sk5, sk3(sk2(sk5), sk5)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.20/0.47 tff(227,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[226, 220, 9, 23, 188, 210, 209, 208])).
% 0.20/0.47 tff(228,plain,(greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(229,plain,
% 0.20/0.47 (^[B: $i, A: $i] : refl((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(230,plain,
% 0.20/0.47 (![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[229])).
% 0.20/0.47 tff(231,plain,
% 0.20/0.47 (![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(232,plain,
% 0.20/0.47 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))), rewrite(((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(233,plain,
% 0.20/0.47 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[232])).
% 0.20/0.47 tff(234,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_21')).
% 0.20/0.47 tff(235,plain,
% 0.20/0.47 (![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 (![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[235, 231])).
% 0.20/0.48 tff(237,plain,(
% 0.20/0.48 ![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[236])).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 (![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 (((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)))) <=> ((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 ((subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))))) <=> ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(241,plain,
% 0.20/0.48 (((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))) <=> ((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[240])).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 (((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))) <=> ((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[241, 239])).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 ((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5)) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 ((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 ((~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[244, 238, 9, 23])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 (subpopulations(first_movers, efficient_producers, sk5, sk1(sk4(sk5), sk5))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[245, 228])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (^[B: $i, A: $i] : refl(((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[247])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> (((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(251,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[250])).
% 0.20/0.48 tff(252,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_23')).
% 0.20/0.48 tff(253,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.20/0.48 tff(254,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.20/0.48 tff(255,plain,(
% 0.20/0.48 ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[254])).
% 0.20/0.48 tff(256,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[255, 248])).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(258,plain,
% 0.20/0.48 (((~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))))) <=> ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[258])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[259, 257])).
% 0.20/0.48 tff(261,plain,
% 0.20/0.48 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(262,plain,
% 0.20/0.48 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.20/0.48 tff(263,plain,
% 0.20/0.48 ((~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))) | greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[262, 256, 9, 23])).
% 0.20/0.48 tff(264,plain,
% 0.20/0.48 (greater_or_equal(sk1(sk4(sk5), sk5), sk4(sk5))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[263, 228])).
% 0.20/0.48 tff(265,plain,
% 0.20/0.48 (^[B: $i, A: $i] : refl(((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[265])).
% 0.20/0.48 tff(267,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(268,plain,
% 0.20/0.48 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> (((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))), rewrite((((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[268])).
% 0.20/0.48 tff(270,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_26')).
% 0.20/0.48 tff(271,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.20/0.48 tff(272,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[271, 267])).
% 0.20/0.48 tff(273,plain,(
% 0.20/0.48 ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[272])).
% 0.20/0.48 tff(274,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[273, 266])).
% 0.20/0.49 tff(275,plain,
% 0.20/0.49 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(276,plain,
% 0.20/0.49 (((~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))))) <=> ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(277,plain,
% 0.20/0.49 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[276])).
% 0.20/0.49 tff(278,plain,
% 0.20/0.49 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[277, 275])).
% 0.20/0.49 tff(279,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | (~in_environment(sk5, sk4(sk5))) | (~environment(sk5)) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(280,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk5)) | (~in_environment(sk5, sk4(sk5))) | (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.20/0.49 tff(281,plain,
% 0.20/0.49 ((~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))) | (~greater(growth_rate(efficient_producers, sk2(sk5)), growth_rate(first_movers, sk2(sk5))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[280, 274, 9, 23])).
% 0.20/0.49 tff(282,plain,
% 0.20/0.49 (~greater(growth_rate(efficient_producers, sk1(sk4(sk5), sk5)), growth_rate(first_movers, sk1(sk4(sk5), sk5)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[281, 228])).
% 0.20/0.49 tff(283,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[72, 69, 9, 6, 282, 264, 246])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------