TSTP Solution File: MGT023-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT023-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT023-1 : 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 : n013.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 02:36:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35 Usage: tptp [options] [-file:]file
% 0.19/0.35 -h, -? prints this message.
% 0.19/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.35 -m, -model generate model.
% 0.19/0.35 -p, -proof generate proof.
% 0.19/0.35 -c, -core generate unsat core of named formulas.
% 0.19/0.35 -st, -statistics display statistics.
% 0.19/0.35 -t:timeout set timeout (in second).
% 0.19/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35 -<param>:<value> configuration parameter and value.
% 0.19/0.35 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(in_environment_type, type, (
% 0.19/0.39 in_environment: ( $i * $i ) > $o)).
% 0.19/0.39 tff(sk2_type, type, (
% 0.19/0.39 sk2: $i > $i)).
% 0.19/0.39 tff(sk3_type, type, (
% 0.19/0.39 sk3: $i)).
% 0.19/0.39 tff(critical_point_type, type, (
% 0.19/0.39 critical_point: $i > $i)).
% 0.19/0.39 tff(greater_type, type, (
% 0.19/0.39 greater: ( $i * $i ) > $o)).
% 0.19/0.39 tff(sk1_type, type, (
% 0.19/0.39 sk1: ( $i * $i ) > $i)).
% 0.19/0.39 tff(growth_rate_type, type, (
% 0.19/0.39 growth_rate: ( $i * $i ) > $i)).
% 0.19/0.39 tff(first_movers_type, type, (
% 0.19/0.39 first_movers: $i)).
% 0.19/0.39 tff(efficient_producers_type, type, (
% 0.19/0.39 efficient_producers: $i)).
% 0.19/0.39 tff(stable_type, type, (
% 0.19/0.39 stable: $i > $o)).
% 0.19/0.39 tff(environment_type, type, (
% 0.19/0.39 environment: $i > $o)).
% 0.19/0.39 tff(subpopulations_type, type, (
% 0.19/0.39 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.19/0.39 tff(1,assumption,(~(sk2(sk3) = critical_point(sk3))), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (stable(sk3) <=> stable(sk3)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,axiom,(stable(sk3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l5_24')).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (stable(sk3)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (environment(sk3) <=> environment(sk3)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(6,axiom,(environment(sk3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l5_23')).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (environment(sk3)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (^[A: $i] : refl(((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![A: $i] : (((~environment(A)) | (~stable(A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.39 tff(13,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l12_21')).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.39 tff(16,plain,(
% 0.19/0.39 ![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[15])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (((~![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~stable(sk3)) | (~environment(sk3)) | (~greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3)))))) <=> ((~![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~stable(sk3)) | (~environment(sk3)) | (~greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~stable(sk3)) | (~environment(sk3)) | (~greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~stable(sk3)) | (~environment(sk3)) | (~greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (~greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[20, 17, 7, 4])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (^[A: $i] : refl(((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A))) <=> ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | in_environment(A, sk2(A))) <=> ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk2(A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.39 tff(27,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk2(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l12_20')).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.39 tff(30,plain,(
% 0.19/0.39 ![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (((~![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A)))) | ((~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3)))) <=> ((~![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A)))) | (~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A)))) | ((~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk2(A)))) | (~stable(sk3)) | (~environment(sk3)) | in_environment(sk3, sk2(sk3))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (in_environment(sk3, sk2(sk3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[34, 31, 7, 4])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (^[B: $i, A: $i] : refl(((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B)) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B)) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B)) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (^[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)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk1(B, A), B)) <=> (((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))) | greater(sk1(B, A), B)))), rewrite((((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))) | greater(sk1(B, A), B)) <=> ((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk1(B, A), B)) <=> ((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B)))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk1(B, A), B)) | (B = critical_point(A))) <=> (((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B)) | (B = critical_point(A))))), rewrite((((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B)) | (B = critical_point(A))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk1(B, A), B)) | (B = critical_point(A))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (![B: $i, A: $i] : (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk1(B, A), B)) | (B = critical_point(A))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.40 tff(41,axiom,(![B: $i, A: $i] : (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | greater(sk1(B, A), B)) | (B = critical_point(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_18')).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.40 tff(44,plain,(
% 0.19/0.40 ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))),
% 0.19/0.40 inference(skolemize,[status(sab)],[43])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))) | ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(sk1(sk2(sk3), sk3), sk2(sk3)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(sk1(sk2(sk3), sk3), sk2(sk3)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (((sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3))) <=> ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(sk1(sk2(sk3), sk3), sk2(sk3)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))) | ((sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))) | ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(sk1(sk2(sk3), sk3), sk2(sk3))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))) | ((sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(sk1(sk2(sk3), sk3), sk2(sk3)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))) | ((sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | greater(sk1(B, A), B))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(sk1(sk2(sk3), sk3), sk2(sk3))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 ((sk2(sk3) = critical_point(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[51, 45, 7, 35, 21])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (greater(sk1(sk2(sk3), sk3), sk2(sk3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[52, 1])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (^[B: $i, A: $i] : refl(((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))) <=> ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (^[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)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))))), rewrite((((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~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)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (B = critical_point(A))) <=> ((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))) | (B = critical_point(A))))), rewrite(((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))) | (B = critical_point(A))) <=> ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (B = critical_point(A))) <=> ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![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, sk1(B, A))) | (B = critical_point(A))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.40 tff(59,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, sk1(B, A))) | (B = critical_point(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_17')).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.40 tff(62,plain,(
% 0.19/0.40 ![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[61])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))) | ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (((sk2(sk3) = critical_point(sk3)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3))) <=> ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))) | ((sk2(sk3) = critical_point(sk3)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))) | ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[65])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))) | ((sk2(sk3) = critical_point(sk3)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3)))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[66, 64])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))) | ((sk2(sk3) = critical_point(sk3)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((B = critical_point(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 ((sk2(sk3) = critical_point(sk3)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[69, 63, 7, 35, 21])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[70, 1])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (^[B: $i, A: $i] : refl(((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(75,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)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> (((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))))), rewrite((((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))), (((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (B = critical_point(A))) <=> (((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (B = critical_point(A))))), rewrite((((~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (B = critical_point(A))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))), ((((((~environment(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (B = critical_point(A))) <=> ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (![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, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (B = critical_point(A))) <=> ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.41 tff(77,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, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (B = critical_point(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_19')).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.42 tff(80,plain,(
% 0.19/0.42 ![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[79])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3)))))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (((sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3)) | (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))))) <=> ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | ((sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3)) | (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3)))))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | ((~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | ((sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3)) | (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3)))))) <=> ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | ((sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (~environment(sk3)) | (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((B = critical_point(A)) | (~in_environment(A, B)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk2(sk3)), growth_rate(first_movers, sk2(sk3))) | (sk2(sk3) = critical_point(sk3)) | (~in_environment(sk3, sk2(sk3))) | (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 ((sk2(sk3) = critical_point(sk3)) | (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[87, 81, 7, 35, 21])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (~greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[88, 1])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (^[B: $i, A: $i] : refl(((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~stable(A)) | (~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater(B, sk2(A)))) <=> (((~stable(A)) | (~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater(B, sk2(A)))))), rewrite((((~stable(A)) | (~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater(B, sk2(A)))) <=> ((~stable(A)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater(B, sk2(A)))) <=> ((~stable(A)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater(B, sk2(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> (((~stable(A)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))))), rewrite((((~stable(A)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater(B, sk2(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater(B, sk2(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.42 tff(95,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater(B, sk2(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l12_22')).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.42 tff(98,plain,(
% 0.19/0.42 ![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[97])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~stable(sk3)) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~stable(sk3)) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (((~stable(sk3)) | greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)))) <=> ((~stable(sk3)) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~stable(sk3)) | greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~stable(sk3)) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~stable(sk3)) | greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~stable(sk3)) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[102, 100])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~stable(sk3)) | greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~environment(A)) | (~greater(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~stable(sk3)) | (~environment(sk3)) | greater(growth_rate(efficient_producers, sk1(sk2(sk3), sk3)), growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[105, 99, 7, 4, 89, 71, 53])).
% 0.19/0.43 tff(107,plain,(sk2(sk3) = critical_point(sk3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (in_environment(sk3, sk2(sk3)) <=> in_environment(sk3, critical_point(sk3))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (in_environment(sk3, critical_point(sk3)) <=> in_environment(sk3, sk2(sk3))),
% 0.19/0.43 inference(symmetry,[status(thm)],[108])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 ((~in_environment(sk3, critical_point(sk3))) <=> (~in_environment(sk3, sk2(sk3)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 ((~in_environment(sk3, critical_point(sk3))) <=> (~in_environment(sk3, critical_point(sk3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(112,axiom,(~in_environment(sk3, critical_point(sk3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l5_25')).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 (~in_environment(sk3, critical_point(sk3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (~in_environment(sk3, sk2(sk3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[35, 114])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------