TSTP Solution File: MGT028-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT028-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 05:21:58 EDT 2022
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : MGT028-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 02:56:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(greater_or_equal_type, type, (
% 0.21/0.41 greater_or_equal: ( $i * $i ) > $o)).
% 0.21/0.41 tff(sk2_type, type, (
% 0.21/0.41 sk2: $i > $i)).
% 0.21/0.41 tff(sk4_type, type, (
% 0.21/0.41 sk4: $i)).
% 0.21/0.41 tff(sk5_type, type, (
% 0.21/0.41 sk5: $i > $i)).
% 0.21/0.41 tff(greater_type, type, (
% 0.21/0.41 greater: ( $i * $i ) > $o)).
% 0.21/0.41 tff(appear_type, type, (
% 0.21/0.41 appear: ( $i * $i ) > $i)).
% 0.21/0.41 tff(efficient_producers_type, type, (
% 0.21/0.41 efficient_producers: $i)).
% 0.21/0.41 tff(growth_rate_type, type, (
% 0.21/0.41 growth_rate: ( $i * $i ) > $i)).
% 0.21/0.41 tff(sk1_type, type, (
% 0.21/0.41 sk1: ( $i * $i ) > $i)).
% 0.21/0.41 tff(sk3_type, type, (
% 0.21/0.41 sk3: $i > $i)).
% 0.21/0.41 tff(first_movers_type, type, (
% 0.21/0.41 first_movers: $i)).
% 0.21/0.41 tff(zero_type, type, (
% 0.21/0.41 zero: $i)).
% 0.21/0.41 tff(in_environment_type, type, (
% 0.21/0.41 in_environment: ( $i * $i ) > $o)).
% 0.21/0.41 tff(stable_type, type, (
% 0.21/0.41 stable: $i > $o)).
% 0.21/0.41 tff(environment_type, type, (
% 0.21/0.41 environment: $i > $o)).
% 0.21/0.41 tff(subpopulations_type, type, (
% 0.21/0.41 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.41 tff(1,assumption,(~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))), introduced(assumption)).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (stable(sk4) <=> stable(sk4)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(3,axiom,(stable(sk4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l10_11')).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (stable(sk4)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (environment(sk4) <=> environment(sk4)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(6,axiom,(environment(sk4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l10_10')).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (environment(sk4)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (^[A: $i] : refl(((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A))) <=> ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | in_environment(A, sk3(A))) <=> ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk3(A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.41 tff(13,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk3(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l11_7')).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.21/0.41 tff(16,plain,(
% 0.21/0.41 ![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[15])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (((~![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A)))) | ((~stable(sk4)) | (~environment(sk4)) | in_environment(sk4, sk3(sk4)))) <=> ((~![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A)))) | (~stable(sk4)) | (~environment(sk4)) | in_environment(sk4, sk3(sk4)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A)))) | ((~stable(sk4)) | (~environment(sk4)) | in_environment(sk4, sk3(sk4)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | in_environment(A, sk3(A)))) | (~stable(sk4)) | (~environment(sk4)) | in_environment(sk4, sk3(sk4))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (in_environment(sk4, sk3(sk4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[20, 17, 7, 4])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (^[B: $i, A: $i] : refl((greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater_or_equal(sk1(B, A), B)))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater_or_equal(sk1(B, A), B)) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | greater(sk2(A), appear(efficient_producers, A))) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | greater(sk2(A), appear(efficient_producers, A))))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | greater(sk2(A), appear(efficient_producers, A))) <=> (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | greater(sk2(A), appear(efficient_producers, A))) <=> (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | greater(sk2(A), appear(efficient_producers, A))) <=> ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.41 tff(27,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | greater(sk2(A), appear(efficient_producers, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_first_movers_negative_growth_2')).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.41 tff(30,plain,(
% 0.21/0.41 ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.41 inference(skolemize,[status(sab)],[29])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))) <=> ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 ((greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) <=> ((~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))) <=> ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[33])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))) <=> ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[34, 32])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (greater(sk2(sk4), appear(efficient_producers, sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[37, 31, 7, 4, 21])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (greater(sk2(sk4), appear(efficient_producers, sk4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[38, 1])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (^[A: $i] : refl(((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A)) <=> ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A)) <=> ![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A)) <=> ![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(43,axiom,(![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l10_13')).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.41 tff(45,plain,(
% 0.21/0.41 ![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A))),
% 0.21/0.41 inference(skolemize,[status(sab)],[44])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A))) | ((~greater(sk2(sk4), appear(efficient_producers, sk4))) | greater_or_equal(sk5(sk2(sk4)), sk2(sk4)))) <=> ((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A))) | (~greater(sk2(sk4), appear(efficient_producers, sk4))) | greater_or_equal(sk5(sk2(sk4)), sk2(sk4)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 ((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A))) | ((~greater(sk2(sk4), appear(efficient_producers, sk4))) | greater_or_equal(sk5(sk2(sk4)), sk2(sk4)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 ((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | greater_or_equal(sk5(A), A))) | (~greater(sk2(sk4), appear(efficient_producers, sk4))) | greater_or_equal(sk5(sk2(sk4)), sk2(sk4))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (greater_or_equal(sk5(sk2(sk4)), sk2(sk4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[49, 46, 39])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (^[A: $i] : refl(((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A))) <=> ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A))) <=> ![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A))) <=> ![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(54,axiom,(![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l10_12')).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.42 tff(56,plain,(
% 0.21/0.42 ![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[55])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A)))) | ((~greater(sk2(sk4), appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))))) <=> ((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A)))) | (~greater(sk2(sk4), appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 ((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A)))) | ((~greater(sk2(sk4), appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 ((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A)))) | (~greater(sk2(sk4), appear(efficient_producers, sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[60, 57, 39])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (^[A: $i] : refl(((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A))))) <=> ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A))))) <=> ![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A))))) <=> ![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(65,axiom,(![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l10_14')).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.42 tff(67,plain,(
% 0.21/0.42 ![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[66])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A)))))) | ((~greater(sk2(sk4), appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(sk2(sk4))))))) <=> ((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A)))))) | (~greater(sk2(sk4), appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(sk2(sk4))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 ((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A)))))) | ((~greater(sk2(sk4), appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(sk2(sk4))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 ((~![A: $i] : ((~greater(A, appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(A)))))) | (~greater(sk2(sk4), appear(efficient_producers, sk4))) | (~greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (~greater(zero, growth_rate(first_movers, sk5(sk2(sk4))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[71, 68, 39])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (^[B: $i, A: $i, C: $i] : refl((greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater_or_equal(sk1(B, A), B)))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater_or_equal(sk1(B, A), B)) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~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)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), ((((((~environment(A)) | (~stable(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)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))), (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) <=> (((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~greater_or_equal(C, sk2(A)))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~greater_or_equal(C, sk2(A)))) <=> ((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) <=> ((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))), ((((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C))) <=> (((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | greater(zero, growth_rate(first_movers, C))))), rewrite((((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | greater(zero, growth_rate(first_movers, C))) <=> (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), ((((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C))) <=> (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C))) <=> ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.42 tff(78,axiom,(![B: $i, A: $i, C: $i] : (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_first_movers_negative_growth_4')).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.42 tff(81,plain,(
% 0.21/0.42 ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.42 inference(skolemize,[status(sab)],[80])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 ((greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) <=> ((~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[85, 83])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[88, 82, 7, 4, 21, 1, 72, 61, 50])).
% 0.21/0.43 tff(90,plain,(greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(91,assumption,(~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))), introduced(assumption)).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 (^[B: $i, A: $i] : refl((greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(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)) | (~stable(A)) | (~environment(A))))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | greater(sk2(A), appear(efficient_producers, A))) <=> ((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater(sk2(A), appear(efficient_producers, A))))), rewrite(((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater(sk2(A), appear(efficient_producers, A))) <=> (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | greater(sk2(A), appear(efficient_producers, A))) <=> (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | greater(sk2(A), appear(efficient_producers, A))) <=> ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.43 tff(97,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | greater(sk2(A), appear(efficient_producers, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_first_movers_negative_growth_1')).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.21/0.43 tff(100,plain,(
% 0.21/0.43 ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[99])).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))) <=> ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 ((greater(sk2(sk4), appear(efficient_producers, sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4))) <=> ((~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 (((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (greater(sk2(sk4), appear(efficient_producers, sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)))) <=> ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (greater(sk2(sk4), appear(efficient_producers, sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)))) <=> ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[104, 102])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (greater(sk2(sk4), appear(efficient_producers, sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 (greater(sk2(sk4), appear(efficient_producers, sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[107, 101, 7, 4, 21])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 (greater(sk2(sk4), appear(efficient_producers, sk4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[108, 91])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 (greater_or_equal(sk5(sk2(sk4)), sk2(sk4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[49, 46, 109])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 (subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[60, 57, 109])).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 (~greater(zero, growth_rate(first_movers, sk5(sk2(sk4))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[71, 68, 109])).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 (^[B: $i, A: $i, C: $i] : refl((greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(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)) | (~stable(A)) | (~environment(A))))), ((((((~environment(A)) | (~stable(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)) | (~stable(A)) | (~environment(A))) | (~subpopulations(first_movers, efficient_producers, A, C))))), rewrite(((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~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)) | (~stable(A)) | (~environment(A)))), ((((((~environment(A)) | (~stable(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)) | (~stable(A)) | (~environment(A))))), (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) <=> (((~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | (~greater_or_equal(C, sk2(A)))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | (~greater_or_equal(C, sk2(A)))) <=> ((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) <=> ((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))))), ((((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C))) <=> (((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater(zero, growth_rate(first_movers, C))))), rewrite((((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater(zero, growth_rate(first_movers, C))) <=> (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), ((((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C))) <=> (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (![B: $i, A: $i, C: $i] : (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C))) <=> ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.44 tff(118,axiom,(![B: $i, A: $i, C: $i] : (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_first_movers_negative_growth_3')).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.21/0.44 tff(121,plain,(
% 0.21/0.44 ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[120])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 ((greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4))) <=> ((~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[124])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[125, 123])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[128, 122, 7, 4, 21, 91, 112, 111, 110])).
% 0.21/0.44 tff(130,plain,(subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 (^[B: $i, A: $i] : refl(((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B))) <=> ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 (^[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_or_equal(B, sk3(A)))) <=> (((~stable(A)) | (~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))))), rewrite((((~stable(A)) | (~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) <=> ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) <=> ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B))))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) | greater(zero, growth_rate(first_movers, B))) <=> (((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, growth_rate(first_movers, B))))), rewrite((((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, growth_rate(first_movers, B))) <=> ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) | greater(zero, growth_rate(first_movers, B))) <=> ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(135,plain,
% 0.21/0.45 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) | greater(zero, growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[134])).
% 0.21/0.45 tff(136,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) | greater(zero, growth_rate(first_movers, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l11_9')).
% 0.21/0.45 tff(137,plain,
% 0.21/0.45 (![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.21/0.45 tff(138,plain,
% 0.21/0.45 (![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.21/0.45 tff(139,plain,(
% 0.21/0.45 ![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[138])).
% 0.21/0.45 tff(140,plain,
% 0.21/0.45 (![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.21/0.45 tff(141,plain,
% 0.21/0.45 (((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))) | ((~stable(sk4)) | (~environment(sk4)) | greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))) | (~stable(sk4)) | (~environment(sk4)) | greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(142,plain,
% 0.21/0.45 (((~stable(sk4)) | (~environment(sk4)) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))) | greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))) <=> ((~stable(sk4)) | (~environment(sk4)) | greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(143,plain,
% 0.21/0.45 (((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))) | ((~stable(sk4)) | (~environment(sk4)) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))) | greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))) | ((~stable(sk4)) | (~environment(sk4)) | greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[142])).
% 0.21/0.45 tff(144,plain,
% 0.21/0.45 (((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))) | ((~stable(sk4)) | (~environment(sk4)) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))) | greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))) | (~stable(sk4)) | (~environment(sk4)) | greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[143, 141])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 ((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))) | ((~stable(sk4)) | (~environment(sk4)) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))) | greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 ((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(zero, growth_rate(first_movers, B)))) | (~stable(sk4)) | (~environment(sk4)) | greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 (greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[146, 140, 7, 4, 130])).
% 0.21/0.45 tff(148,plain,
% 0.21/0.45 (greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[147, 90])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 (^[B: $i, A: $i] : refl((greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(150,plain,
% 0.21/0.45 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[149])).
% 0.21/0.45 tff(151,plain,
% 0.21/0.45 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(152,plain,
% 0.21/0.45 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | greater(sk2(A), appear(efficient_producers, A))) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | greater(sk2(A), appear(efficient_producers, A))))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | greater(sk2(A), appear(efficient_producers, A))) <=> (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | greater(sk2(A), appear(efficient_producers, A))) <=> (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(153,plain,
% 0.21/0.45 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | greater(sk2(A), appear(efficient_producers, A))) <=> ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.45 tff(154,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | greater(sk2(A), appear(efficient_producers, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_first_movers_negative_growth_5')).
% 0.21/0.45 tff(155,plain,
% 0.21/0.45 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.21/0.45 tff(156,plain,
% 0.21/0.45 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.21/0.45 tff(157,plain,(
% 0.21/0.45 ![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[156])).
% 0.21/0.45 tff(158,plain,
% 0.21/0.45 (![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.21/0.45 tff(159,plain,
% 0.21/0.45 (((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | ((~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))))) <=> ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(160,plain,
% 0.21/0.46 ((greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))))) <=> ((~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 (((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))))) <=> ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | ((~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[160])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 (((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))))) <=> ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[161, 159])).
% 0.21/0.46 tff(163,plain,
% 0.21/0.46 ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(164,plain,
% 0.21/0.46 ((~![B: $i, A: $i] : (greater(sk2(A), appear(efficient_producers, A)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (~stable(sk4)) | (~environment(sk4)) | greater(sk2(sk4), appear(efficient_producers, sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 (greater(sk2(sk4), appear(efficient_producers, sk4)) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[164, 158, 7, 4, 21])).
% 0.21/0.46 tff(166,plain,
% 0.21/0.46 (greater(sk2(sk4), appear(efficient_producers, sk4))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[165, 148])).
% 0.21/0.46 tff(167,plain,
% 0.21/0.46 (greater_or_equal(sk5(sk2(sk4)), sk2(sk4))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[49, 46, 166])).
% 0.21/0.46 tff(168,plain,
% 0.21/0.46 (subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[60, 57, 166])).
% 0.21/0.46 tff(169,plain,
% 0.21/0.46 (~greater(zero, growth_rate(first_movers, sk5(sk2(sk4))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[71, 68, 166])).
% 0.21/0.46 tff(170,plain,
% 0.21/0.46 (^[B: $i, A: $i, C: $i] : refl((greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(171,plain,
% 0.21/0.46 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[170])).
% 0.21/0.46 tff(172,plain,
% 0.21/0.46 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(173,plain,
% 0.21/0.46 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, 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)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, 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)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))))), (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) <=> (((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | (~greater_or_equal(C, sk2(A)))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | (~greater_or_equal(C, sk2(A)))) <=> ((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))), (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) <=> ((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))))), ((((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C))) <=> (((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | greater(zero, growth_rate(first_movers, C))))), rewrite((((~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | greater(zero, growth_rate(first_movers, C))) <=> (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))), ((((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C))) <=> (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(174,plain,
% 0.21/0.46 (![B: $i, A: $i, C: $i] : (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C))) <=> ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.46 tff(175,axiom,(![B: $i, A: $i, C: $i] : (((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(C, sk2(A)))) | greater(zero, growth_rate(first_movers, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_first_movers_negative_growth_6')).
% 0.21/0.46 tff(176,plain,
% 0.21/0.46 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.21/0.46 tff(177,plain,
% 0.21/0.46 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.21/0.46 tff(178,plain,(
% 0.21/0.46 ![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[177])).
% 0.21/0.46 tff(179,plain,
% 0.21/0.46 (![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.21/0.46 tff(180,plain,
% 0.21/0.46 (((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | ((~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(181,plain,
% 0.21/0.46 ((greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4))))) <=> ((~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(182,plain,
% 0.21/0.46 (((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | ((~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[181])).
% 0.21/0.47 tff(183,plain,
% 0.21/0.47 (((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[182, 180])).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~stable(sk4)) | (~environment(sk4)) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 ((~![B: $i, A: $i, C: $i] : (greater(zero, growth_rate(first_movers, C)) | (~greater_or_equal(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (~stable(sk4)) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(zero, growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(zero, growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater_or_equal(sk5(sk2(sk4)), sk2(sk4)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.47 tff(186,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[185, 179, 7, 4, 21, 148, 169, 168, 167])).
% 0.21/0.47 % SZS output end Proof
%------------------------------------------------------------------------------