TSTP Solution File: MGT025-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT025-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 05:21:56 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT025-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 02:42:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(zero_type, type, (
% 0.20/0.40 zero: $i)).
% 0.20/0.40 tff(growth_rate_type, type, (
% 0.20/0.40 growth_rate: ( $i * $i ) > $i)).
% 0.20/0.40 tff(sk2_type, type, (
% 0.20/0.40 sk2: $i)).
% 0.20/0.40 tff(efficient_producers_type, type, (
% 0.20/0.40 efficient_producers: $i)).
% 0.20/0.40 tff(constant_type, type, (
% 0.20/0.40 constant: $i > $o)).
% 0.20/0.40 tff(cardinality_at_time_type, type, (
% 0.20/0.40 cardinality_at_time: ( $i * $i ) > $i)).
% 0.20/0.40 tff(increases_type, type, (
% 0.20/0.40 increases: $i > $o)).
% 0.20/0.40 tff(greater_type, type, (
% 0.20/0.40 greater: ( $i * $i ) > $o)).
% 0.20/0.40 tff(first_movers_type, type, (
% 0.20/0.40 first_movers: $i)).
% 0.20/0.40 tff(decreases_type, type, (
% 0.20/0.40 decreases: $i > $o)).
% 0.20/0.40 tff(sum_type, type, (
% 0.20/0.40 sum: ( $i * $i ) > $i)).
% 0.20/0.40 tff(number_of_organizations_type, type, (
% 0.20/0.40 number_of_organizations: ( $i * $i ) > $i)).
% 0.20/0.40 tff(sk1_type, type, (
% 0.20/0.40 sk1: $i)).
% 0.20/0.40 tff(subpopulation_type, type, (
% 0.20/0.40 subpopulation: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(in_environment_type, type, (
% 0.20/0.40 in_environment: ( $i * $i ) > $o)).
% 0.20/0.40 tff(subpopulations_type, type, (
% 0.20/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.40 tff(environment_type, type, (
% 0.20/0.40 environment: $i > $o)).
% 0.20/0.40 tff(1,assumption,(~decreases(cardinality_at_time(first_movers, sk2))), introduced(assumption)).
% 0.20/0.40 tff(2,assumption,(~constant(cardinality_at_time(first_movers, sk2))), introduced(assumption)).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (subpopulations(first_movers, efficient_producers, sk1, sk2) <=> subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,axiom,(subpopulations(first_movers, efficient_producers, sk1, sk2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_48')).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (environment(sk1) <=> environment(sk1)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(7,axiom,(environment(sk1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_47')).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (environment(sk1)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (^[B: $i, A: $i] : refl(((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B)) <=> ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B)) <=> ![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.40 tff(14,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_time_point_occur_45')).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.40 tff(17,plain,(
% 0.20/0.40 ![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[16])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (((~![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 ((~![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 ((~![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (in_environment(sk1, sk2)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[21, 18, 8, 5])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (^[B: $i, A: $i] : refl(((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B)) <=> ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~in_environment(A, B))) | subpopulation(first_movers, A, B)) <=> ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![B: $i, A: $i] : (((~environment(A)) | (~in_environment(A, B))) | subpopulation(first_movers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.40 tff(28,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~in_environment(A, B))) | subpopulation(first_movers, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_subpopulations_30')).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.40 tff(31,plain,(
% 0.20/0.40 ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.20/0.40 inference(skolemize,[status(sab)],[30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | ((~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(first_movers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(first_movers, sk1, sk2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(first_movers, sk1, sk2)) <=> ((~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(first_movers, sk1, sk2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(first_movers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | ((~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(first_movers, sk1, sk2)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(first_movers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(first_movers, sk1, sk2))),
% 0.20/0.41 inference(transitivity,[status(thm)],[35, 33])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(first_movers, sk1, sk2))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(first_movers, sk1, sk2)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (subpopulation(first_movers, sk1, sk2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[38, 32, 8, 22])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (^[B: $i, A: $i, C: $i] : refl(((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers))) <=> ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers))) <=> ![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers))) <=> ![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~subpopulation(B, A, C))) | (~(B = first_movers))) <=> ((~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))), (((((~environment(A)) | (~subpopulation(B, A, C))) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C)))) <=> (((~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C)))))), rewrite((((~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C)))) <=> ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))), (((((~environment(A)) | (~subpopulation(B, A, C))) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C)))) <=> ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : ((((~environment(A)) | (~subpopulation(B, A, C))) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C)))) <=> ![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.41 tff(45,axiom,(![B: $i, A: $i, C: $i] : ((((~environment(A)) | (~subpopulation(B, A, C))) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_only_members_29')).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.41 tff(48,plain,(
% 0.20/0.41 ![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[47])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (((~![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))) | ((~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (((number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~subpopulation(first_movers, sk1, sk2)) | (~environment(sk1)) | $false) <=> ((~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~$true) <=> $false),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((first_movers = first_movers) <=> $true),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 ((~(first_movers = first_movers)) <=> (~$true)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 ((~(first_movers = first_movers)) <=> $false),
% 0.20/0.41 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (((number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~subpopulation(first_movers, sk1, sk2)) | (~environment(sk1)) | (~(first_movers = first_movers))) <=> ((number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~subpopulation(first_movers, sk1, sk2)) | (~environment(sk1)) | $false)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (((number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~subpopulation(first_movers, sk1, sk2)) | (~environment(sk1)) | (~(first_movers = first_movers))) <=> ((~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[56, 51])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (((~![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))) | ((number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~subpopulation(first_movers, sk1, sk2)) | (~environment(sk1)) | (~(first_movers = first_movers)))) <=> ((~![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))) | ((~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (((~![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))) | ((number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~subpopulation(first_movers, sk1, sk2)) | (~environment(sk1)) | (~(first_movers = first_movers)))) <=> ((~![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[58, 50])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ((~![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))) | ((number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~subpopulation(first_movers, sk1, sk2)) | (~environment(sk1)) | (~(first_movers = first_movers)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 ((~![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[61, 49, 8, 39])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = number_of_organizations(sk1, sk2)),
% 0.20/0.41 inference(symmetry,[status(thm)],[62])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) <=> constant(number_of_organizations(sk1, sk2))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (constant(number_of_organizations(sk1, sk2)) <=> constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[64])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (constant(number_of_organizations(sk1, sk2)) <=> constant(number_of_organizations(sk1, sk2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(67,axiom,(constant(number_of_organizations(sk1, sk2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_49')).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (constant(number_of_organizations(sk1, sk2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (^[B: $i, A: $i, C: $i] : refl((decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) <=> (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(C)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | decreases(B)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) | decreases(B)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) | decreases(B)) <=> (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | decreases(B)) <=> (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | decreases(B)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.42 tff(75,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | decreases(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_34')).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.20/0.42 tff(78,plain,(
% 0.20/0.42 ![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))),
% 0.20/0.42 inference(skolemize,[status(sab)],[77])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (((~![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))) | decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 ((decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | decreases(cardinality_at_time(efficient_producers, sk2))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 ((sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) <=> $true),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 ((~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) <=> (~$true)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[82])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 ((~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) <=> $false),
% 0.20/0.42 inference(transitivity,[status(thm)],[83, 52])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | decreases(cardinality_at_time(efficient_producers, sk2))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | decreases(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 ((decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | decreases(cardinality_at_time(efficient_producers, sk2))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[85, 81])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (((~![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | decreases(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (((~![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | decreases(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))) | decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[87, 80])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ((~![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | decreases(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 ((~![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))) | decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[90, 79])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (decreases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[91, 69])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (decreases(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[92, 2, 1])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (^[B: $i, A: $i] : refl(((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B)) <=> ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~in_environment(A, B))) | subpopulation(efficient_producers, A, B)) <=> ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (![B: $i, A: $i] : (((~environment(A)) | (~in_environment(A, B))) | subpopulation(efficient_producers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.42 tff(99,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~in_environment(A, B))) | subpopulation(efficient_producers, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_subpopulations_31')).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.42 tff(102,plain,(
% 0.20/0.42 ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.20/0.42 inference(skolemize,[status(sab)],[101])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | ((~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(efficient_producers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(efficient_producers, sk1, sk2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2)) <=> ((~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(efficient_producers, sk1, sk2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | ((~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(efficient_producers, sk1, sk2)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(efficient_producers, sk1, sk2))),
% 0.20/0.42 inference(transitivity,[status(thm)],[106, 104])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | subpopulation(efficient_producers, sk1, sk2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (subpopulation(efficient_producers, sk1, sk2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[109, 103, 8, 22])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (^[B: $i, A: $i] : refl(((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.42 tff(116,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(efficient_producers, B), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_non_zero_producers_44')).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.20/0.43 tff(119,plain,(
% 0.20/0.43 ![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.20/0.43 inference(skolemize,[status(sab)],[118])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (((~![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(efficient_producers, sk2), zero))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(efficient_producers, sk2), zero))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 ((~![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(efficient_producers, sk2), zero))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 ((~![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(efficient_producers, sk2), zero)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (greater(cardinality_at_time(efficient_producers, sk2), zero)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[123, 120, 8, 5])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (^[B: $i, A: $i, C: $i] : refl(((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B)))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B)))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) <=> ((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> (((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))))), rewrite((((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) <=> (((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~decreases(cardinality_at_time(C, B)))))), rewrite((((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~decreases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~decreases(cardinality_at_time(C, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~decreases(cardinality_at_time(C, B)))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B))) <=> (((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B))))), rewrite((((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.43 tff(130,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_growth_rate_42')).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.20/0.43 tff(133,plain,(
% 0.20/0.43 ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[132])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | (greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(efficient_producers, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2)))) <=> (greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(efficient_producers, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | (greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(efficient_producers, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(efficient_producers, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 (greater(zero, growth_rate(efficient_producers, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[140, 134, 8, 22, 124, 110])).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 (greater(zero, growth_rate(efficient_producers, sk2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[141, 93])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (^[B: $i, A: $i, C: $i] : refl((decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) <=> (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[143])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(B)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(B)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | decreases(B)) <=> ((increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(B)))), rewrite(((increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(B)) <=> (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | decreases(B)) <=> (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | decreases(B)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[146])).
% 0.20/0.44 tff(148,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | decreases(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_32')).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.20/0.44 tff(151,plain,(
% 0.20/0.44 ![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[150])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))) | (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 ((decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false) <=> (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 ((decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 ((decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[155, 154])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))) | (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))) | (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[156])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 (((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))) | (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[157, 153])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 ((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))) | (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 ((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[160, 152])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[161, 69])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 (increases(cardinality_at_time(first_movers, sk2))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[162, 2, 1])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 (^[B: $i, A: $i] : refl(((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 (![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(first_movers, B), zero)) <=> ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(first_movers, B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.44 tff(169,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(first_movers, B), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_non_zero_producers_43')).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 (![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.20/0.44 tff(172,plain,(
% 0.20/0.44 ![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[171])).
% 0.20/0.44 tff(173,plain,
% 0.20/0.44 (![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 (((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 (((~environment(sk1)) | greater(cardinality_at_time(first_movers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2))) <=> ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(176,plain,
% 0.20/0.44 (((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | greater(cardinality_at_time(first_movers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[175])).
% 0.20/0.44 tff(177,plain,
% 0.20/0.44 (((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | greater(cardinality_at_time(first_movers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero))),
% 0.20/0.44 inference(transitivity,[status(thm)],[176, 174])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 ((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | greater(cardinality_at_time(first_movers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 ((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.44 tff(180,plain,
% 0.20/0.44 (greater(cardinality_at_time(first_movers, sk2), zero)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[179, 173, 8, 5])).
% 0.20/0.44 tff(181,plain,
% 0.20/0.44 (^[B: $i, A: $i, C: $i] : refl(((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(182,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B)))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[181])).
% 0.20/0.44 tff(183,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B)))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(184,plain,
% 0.20/0.44 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) <=> ((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> (((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))))), rewrite((((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) <=> (((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~increases(cardinality_at_time(C, B)))))), rewrite((((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~increases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~increases(cardinality_at_time(C, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~increases(cardinality_at_time(C, B)))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero)) <=> (((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero)))), rewrite((((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero)) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero)) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(185,plain,
% 0.20/0.44 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero)) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[184])).
% 0.20/0.45 tff(186,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_growth_rate_41')).
% 0.20/0.45 tff(187,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.45 tff(188,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.20/0.45 tff(189,plain,(
% 0.20/0.45 ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[188])).
% 0.20/0.45 tff(190,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.20/0.45 tff(191,plain,
% 0.20/0.45 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | (greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~increases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~increases(cardinality_at_time(first_movers, sk2))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(192,plain,
% 0.20/0.45 (((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~increases(cardinality_at_time(first_movers, sk2)))) <=> (greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~increases(cardinality_at_time(first_movers, sk2))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(193,plain,
% 0.20/0.45 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~increases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | (greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~increases(cardinality_at_time(first_movers, sk2)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[192])).
% 0.20/0.45 tff(194,plain,
% 0.20/0.45 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~increases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~increases(cardinality_at_time(first_movers, sk2))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[193, 191])).
% 0.20/0.45 tff(195,plain,
% 0.20/0.45 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~increases(cardinality_at_time(first_movers, sk2))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(196,plain,
% 0.20/0.45 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~increases(cardinality_at_time(first_movers, sk2)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.45 tff(197,plain,
% 0.20/0.45 (greater(growth_rate(first_movers, sk2), zero) | (~increases(cardinality_at_time(first_movers, sk2)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[196, 190, 8, 22, 180, 39])).
% 0.20/0.45 tff(198,plain,
% 0.20/0.45 (greater(growth_rate(first_movers, sk2), zero)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[197, 163])).
% 0.20/0.45 tff(199,plain,
% 0.20/0.45 (((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))) <=> ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(200,axiom,((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_51')).
% 0.20/0.45 tff(201,plain,
% 0.20/0.45 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.20/0.45 tff(202,plain,
% 0.20/0.45 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[201, 199])).
% 0.20/0.45 tff(203,plain,
% 0.20/0.45 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[202, 199])).
% 0.20/0.45 tff(204,plain,
% 0.20/0.45 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.20/0.45 tff(205,plain,
% 0.20/0.45 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[204, 199])).
% 0.20/0.45 tff(206,plain,
% 0.20/0.45 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[205, 199])).
% 0.20/0.45 tff(207,plain,
% 0.20/0.45 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[206, 199])).
% 0.20/0.45 tff(208,plain,
% 0.20/0.45 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[207, 199])).
% 0.20/0.45 tff(209,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[208, 198, 142])).
% 0.20/0.45 tff(210,plain,(constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(first_movers, sk2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(211,plain,
% 0.20/0.45 (constant(cardinality_at_time(first_movers, sk2))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[210, 1])).
% 0.20/0.45 tff(212,plain,
% 0.20/0.45 (^[B: $i, A: $i, C: $i] : refl(((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) <=> ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(213,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[212])).
% 0.20/0.45 tff(214,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(215,plain,
% 0.20/0.45 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) <=> ((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> (((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))))), rewrite((((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) <=> (((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~constant(cardinality_at_time(C, B)))))), rewrite((((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~constant(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) | (growth_rate(C, B) = zero)) <=> (((~environment(A)) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (growth_rate(C, B) = zero)))), rewrite((((~environment(A)) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (growth_rate(C, B) = zero)) <=> ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) | (growth_rate(C, B) = zero)) <=> ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(216,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) | (growth_rate(C, B) = zero)) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[215])).
% 0.20/0.45 tff(217,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) | (growth_rate(C, B) = zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_growth_rate_40')).
% 0.20/0.45 tff(218,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.20/0.45 tff(219,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.20/0.45 tff(220,plain,(
% 0.20/0.45 ![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[219])).
% 0.20/0.45 tff(221,plain,
% 0.20/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.20/0.45 tff(222,plain,
% 0.20/0.45 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~constant(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~constant(cardinality_at_time(first_movers, sk2))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(223,plain,
% 0.20/0.46 (((~environment(sk1)) | (growth_rate(first_movers, sk2) = zero) | (~constant(cardinality_at_time(first_movers, sk2))) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2))) <=> ((growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~constant(cardinality_at_time(first_movers, sk2))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(224,plain,
% 0.20/0.46 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(first_movers, sk2) = zero) | (~constant(cardinality_at_time(first_movers, sk2))) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~constant(cardinality_at_time(first_movers, sk2)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[223])).
% 0.20/0.46 tff(225,plain,
% 0.20/0.46 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(first_movers, sk2) = zero) | (~constant(cardinality_at_time(first_movers, sk2))) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~constant(cardinality_at_time(first_movers, sk2))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[224, 222])).
% 0.20/0.46 tff(226,plain,
% 0.20/0.46 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(first_movers, sk2) = zero) | (~constant(cardinality_at_time(first_movers, sk2))) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(227,plain,
% 0.20/0.46 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~constant(cardinality_at_time(first_movers, sk2)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.20/0.46 tff(228,plain,
% 0.20/0.46 ((growth_rate(first_movers, sk2) = zero) | (~constant(cardinality_at_time(first_movers, sk2)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[227, 221, 8, 22, 180, 39])).
% 0.20/0.46 tff(229,plain,
% 0.20/0.46 (growth_rate(first_movers, sk2) = zero),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[228, 211])).
% 0.20/0.46 tff(230,plain,
% 0.20/0.46 (((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))) <=> ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(231,axiom,((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_50')).
% 0.20/0.46 tff(232,plain,
% 0.20/0.46 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.20/0.46 tff(233,plain,
% 0.20/0.46 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[232, 230])).
% 0.20/0.46 tff(234,plain,
% 0.20/0.46 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[233, 230])).
% 0.20/0.46 tff(235,plain,
% 0.20/0.46 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.20/0.46 tff(236,plain,
% 0.20/0.46 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[235, 230])).
% 0.20/0.46 tff(237,plain,
% 0.20/0.46 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[236, 230])).
% 0.20/0.46 tff(238,plain,
% 0.20/0.46 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.20/0.46 tff(239,plain,
% 0.20/0.46 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[238, 230])).
% 0.20/0.46 tff(240,plain,
% 0.20/0.46 (~(growth_rate(efficient_producers, sk2) = zero)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[239, 229])).
% 0.20/0.46 tff(241,plain,
% 0.20/0.46 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~constant(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~constant(cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(242,plain,
% 0.20/0.46 (((~environment(sk1)) | (growth_rate(efficient_producers, sk2) = zero) | (~constant(cardinality_at_time(efficient_producers, sk2))) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2))) <=> ((growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~constant(cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(243,plain,
% 0.20/0.46 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(efficient_producers, sk2) = zero) | (~constant(cardinality_at_time(efficient_producers, sk2))) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~constant(cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[242])).
% 0.20/0.46 tff(244,plain,
% 0.20/0.46 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(efficient_producers, sk2) = zero) | (~constant(cardinality_at_time(efficient_producers, sk2))) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~constant(cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[243, 241])).
% 0.20/0.46 tff(245,plain,
% 0.20/0.46 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(efficient_producers, sk2) = zero) | (~constant(cardinality_at_time(efficient_producers, sk2))) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(246,plain,
% 0.20/0.46 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.46 tff(247,plain,
% 0.20/0.46 ((growth_rate(efficient_producers, sk2) = zero) | (~constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[246, 221, 8, 22, 124, 110])).
% 0.20/0.46 tff(248,plain,
% 0.20/0.46 (~constant(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[247, 240])).
% 0.20/0.46 tff(249,plain,
% 0.20/0.46 (^[B: $i, A: $i, C: $i] : refl((decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) <=> (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(250,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[249])).
% 0.20/0.46 tff(251,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(252,plain,
% 0.20/0.46 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C)))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) <=> (((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | decreases(B)) <=> (((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) | decreases(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) | decreases(B)) <=> (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | decreases(B)) <=> (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(253,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | decreases(B)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[252])).
% 0.20/0.46 tff(254,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | decreases(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_38')).
% 0.20/0.46 tff(255,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.20/0.46 tff(256,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[255, 251])).
% 0.20/0.46 tff(257,plain,(
% 0.20/0.46 ![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))),
% 0.20/0.46 inference(skolemize,[status(sab)],[256])).
% 0.20/0.46 tff(258,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[257, 250])).
% 0.20/0.46 tff(259,plain,
% 0.20/0.46 (((~![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))) | decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(260,plain,
% 0.20/0.46 ((decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(261,plain,
% 0.20/0.46 ((decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.46 tff(262,plain,
% 0.20/0.46 ((decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[261, 260])).
% 0.20/0.46 tff(263,plain,
% 0.20/0.46 (((~![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[262])).
% 0.20/0.46 tff(264,plain,
% 0.20/0.46 (((~![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))) | decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[263, 259])).
% 0.20/0.46 tff(265,plain,
% 0.20/0.46 ((~![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(266,plain,
% 0.20/0.46 ((~![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))) | decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.20/0.46 tff(267,plain,
% 0.20/0.46 (decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[266, 258])).
% 0.20/0.46 tff(268,plain,
% 0.20/0.46 (decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[267, 69])).
% 0.20/0.46 tff(269,plain,
% 0.20/0.46 (decreases(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[268, 248, 1])).
% 0.20/0.46 tff(270,plain,
% 0.20/0.46 (greater(zero, growth_rate(efficient_producers, sk2))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[141, 269])).
% 0.20/0.46 tff(271,plain,
% 0.20/0.46 (^[B: $i, A: $i, C: $i] : refl((decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) <=> (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(272,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[271])).
% 0.20/0.46 tff(273,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(274,plain,
% 0.20/0.46 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C)))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) <=> (((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(B)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | decreases(B)) <=> ((increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(B)))), rewrite(((increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(B)) <=> (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | decreases(B)) <=> (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(275,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | decreases(B)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[274])).
% 0.20/0.46 tff(276,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | decreases(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_36')).
% 0.20/0.46 tff(277,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.20/0.46 tff(278,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.20/0.46 tff(279,plain,(
% 0.20/0.46 ![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))),
% 0.20/0.46 inference(skolemize,[status(sab)],[278])).
% 0.20/0.46 tff(280,plain,
% 0.20/0.46 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[279, 272])).
% 0.20/0.46 tff(281,plain,
% 0.20/0.46 (((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(282,plain,
% 0.20/0.47 ((decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | constant(cardinality_at_time(efficient_producers, sk2))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(283,plain,
% 0.20/0.47 ((decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | constant(cardinality_at_time(efficient_producers, sk2))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.47 tff(284,plain,
% 0.20/0.47 ((decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | constant(cardinality_at_time(efficient_producers, sk2))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[283, 282])).
% 0.20/0.47 tff(285,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | constant(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[284])).
% 0.20/0.47 tff(286,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | constant(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[285, 281])).
% 0.20/0.47 tff(287,plain,
% 0.20/0.47 ((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))) | (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(288,plain,
% 0.20/0.47 ((~![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.20/0.47 tff(289,plain,
% 0.20/0.47 (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[288, 280])).
% 0.20/0.47 tff(290,plain,
% 0.20/0.47 (decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[289, 69])).
% 0.20/0.47 tff(291,plain,
% 0.20/0.47 (increases(cardinality_at_time(first_movers, sk2))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[290, 248, 1])).
% 0.20/0.47 tff(292,plain,
% 0.20/0.47 (greater(growth_rate(first_movers, sk2), zero)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[197, 291])).
% 0.20/0.47 tff(293,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[208, 292, 270])).
% 0.20/0.47 tff(294,plain,(decreases(cardinality_at_time(first_movers, sk2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(295,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | (greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(296,plain,
% 0.20/0.47 (((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2)))) <=> (greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(297,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | (greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[296])).
% 0.20/0.47 tff(298,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[297, 295])).
% 0.20/0.47 tff(299,plain,
% 0.20/0.47 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(300,plain,
% 0.20/0.47 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.20/0.47 tff(301,plain,
% 0.20/0.47 (greater(zero, growth_rate(first_movers, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[300, 134, 8, 22, 180, 39])).
% 0.20/0.47 tff(302,plain,
% 0.20/0.47 (greater(zero, growth_rate(first_movers, sk2))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[301, 294])).
% 0.20/0.47 tff(303,plain,
% 0.20/0.47 (((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))) <=> ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(304,axiom,((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_52')).
% 0.20/0.47 tff(305,plain,
% 0.20/0.47 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.20/0.47 tff(306,plain,
% 0.20/0.47 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[305, 303])).
% 0.20/0.47 tff(307,plain,
% 0.20/0.47 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[306, 303])).
% 0.20/0.47 tff(308,plain,
% 0.20/0.47 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[307, 303])).
% 0.20/0.47 tff(309,plain,
% 0.20/0.47 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[308, 303])).
% 0.20/0.47 tff(310,plain,
% 0.20/0.47 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[309, 303])).
% 0.20/0.47 tff(311,plain,
% 0.20/0.47 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[310, 303])).
% 0.20/0.47 tff(312,plain,
% 0.20/0.47 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[311, 303])).
% 0.20/0.47 tff(313,plain,
% 0.20/0.47 (~greater(growth_rate(efficient_producers, sk2), zero)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[312, 302])).
% 0.20/0.47 tff(314,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | (greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~increases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~increases(cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(315,plain,
% 0.20/0.47 (((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~increases(cardinality_at_time(efficient_producers, sk2)))) <=> (greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~increases(cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(316,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~increases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | (greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~increases(cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[315])).
% 0.20/0.47 tff(317,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~increases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~increases(cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[316, 314])).
% 0.20/0.47 tff(318,plain,
% 0.20/0.47 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~increases(cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(319,plain,
% 0.20/0.47 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~increases(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.20/0.47 tff(320,plain,
% 0.20/0.47 (greater(growth_rate(efficient_producers, sk2), zero) | (~increases(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[319, 190, 8, 22, 124, 110])).
% 0.20/0.47 tff(321,plain,
% 0.20/0.47 (~increases(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[320, 313])).
% 0.20/0.47 tff(322,assumption,(~increases(cardinality_at_time(efficient_producers, sk2))), introduced(assumption)).
% 0.20/0.47 tff(323,assumption,(~decreases(cardinality_at_time(efficient_producers, sk2))), introduced(assumption)).
% 0.20/0.47 tff(324,plain,
% 0.20/0.47 (^[B: $i, A: $i, C: $i] : refl(((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(325,plain,
% 0.20/0.47 (![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C)) <=> ![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[324])).
% 0.20/0.47 tff(326,plain,
% 0.20/0.47 (![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C)) <=> ![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(327,plain,
% 0.20/0.47 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C)))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) <=> (((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | increases(C)) <=> (((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) | increases(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) | increases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | increases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(328,plain,
% 0.20/0.47 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | increases(C)) <=> ![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[327])).
% 0.20/0.47 tff(329,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | increases(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_39')).
% 0.20/0.47 tff(330,plain,
% 0.20/0.47 (![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.20/0.47 tff(331,plain,
% 0.20/0.47 (![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[330, 326])).
% 0.20/0.47 tff(332,plain,(
% 0.20/0.47 ![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))),
% 0.20/0.47 inference(skolemize,[status(sab)],[331])).
% 0.20/0.47 tff(333,plain,
% 0.20/0.47 (![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[332, 325])).
% 0.20/0.47 tff(334,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))) | (decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(335,plain,
% 0.20/0.47 (((~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))) <=> (decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(336,plain,
% 0.20/0.47 (((~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))) <=> ((~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.47 tff(337,plain,
% 0.20/0.47 (((~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))) <=> (decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[336, 335])).
% 0.20/0.47 tff(338,plain,
% 0.20/0.47 (((~![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))) | ((~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))) | (decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[337])).
% 0.20/0.48 tff(339,plain,
% 0.20/0.48 (((~![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))) | ((~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[338, 334])).
% 0.20/0.48 tff(340,plain,
% 0.20/0.48 ((~![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))) | ((~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(341,plain,
% 0.20/0.48 ((~![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.20/0.48 tff(342,plain,
% 0.20/0.48 (decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[341, 333])).
% 0.20/0.48 tff(343,plain,
% 0.20/0.48 (decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[342, 69])).
% 0.20/0.48 tff(344,plain,
% 0.20/0.48 (constant(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[343, 323, 322])).
% 0.20/0.48 tff(345,plain,
% 0.20/0.48 (growth_rate(efficient_producers, sk2) = zero),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[247, 344])).
% 0.20/0.48 tff(346,plain,
% 0.20/0.48 (^[B: $i, A: $i, C: $i] : refl((constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(347,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C)) <=> ![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[346])).
% 0.20/0.48 tff(348,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C)) <=> ![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(349,plain,
% 0.20/0.48 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(C)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | increases(C)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) | increases(C)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) | increases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | increases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(350,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | increases(C)) <=> ![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[349])).
% 0.20/0.48 tff(351,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | increases(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_35')).
% 0.20/0.48 tff(352,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.20/0.48 tff(353,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[352, 348])).
% 0.20/0.48 tff(354,plain,(
% 0.20/0.48 ![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))),
% 0.20/0.48 inference(skolemize,[status(sab)],[353])).
% 0.20/0.48 tff(355,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[354, 347])).
% 0.20/0.48 tff(356,plain,
% 0.20/0.48 (((~![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))) | (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(357,plain,
% 0.20/0.48 ((constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2))) <=> (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(358,plain,
% 0.20/0.48 ((constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2))) <=> (constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.48 tff(359,plain,
% 0.20/0.48 ((constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2))) <=> (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[358, 357])).
% 0.20/0.48 tff(360,plain,
% 0.20/0.48 (((~![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))) | (constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))) | (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[359])).
% 0.20/0.48 tff(361,plain,
% 0.20/0.48 (((~![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))) | (constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[360, 356])).
% 0.20/0.48 tff(362,plain,
% 0.20/0.48 ((~![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))) | (constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(363,plain,
% 0.20/0.48 ((~![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.20/0.48 tff(364,plain,
% 0.20/0.48 (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[363, 355])).
% 0.20/0.48 tff(365,plain,
% 0.20/0.48 (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[364, 69])).
% 0.20/0.48 tff(366,plain,
% 0.20/0.48 (constant(cardinality_at_time(first_movers, sk2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[365, 323, 322])).
% 0.20/0.48 tff(367,plain,
% 0.20/0.48 (growth_rate(first_movers, sk2) = zero),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[228, 366])).
% 0.20/0.48 tff(368,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[239, 367, 345])).
% 0.20/0.48 tff(369,plain,(decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(370,plain,
% 0.20/0.48 (decreases(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[369, 321])).
% 0.20/0.48 tff(371,plain,
% 0.20/0.48 (greater(zero, growth_rate(efficient_producers, sk2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[141, 370])).
% 0.20/0.48 tff(372,plain,
% 0.20/0.48 (~greater(growth_rate(first_movers, sk2), zero)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[208, 371])).
% 0.20/0.48 tff(373,plain,
% 0.20/0.48 (~increases(cardinality_at_time(first_movers, sk2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[197, 372])).
% 0.20/0.48 tff(374,plain,
% 0.20/0.48 (^[B: $i, A: $i, C: $i] : refl((increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(375,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C)) <=> ![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[374])).
% 0.20/0.48 tff(376,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C)) <=> ![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(377,plain,
% 0.20/0.48 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C)))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) <=> (((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(B)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | increases(C)) <=> ((increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(C)))), rewrite(((increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(C)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | increases(C)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(378,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | increases(C)) <=> ![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[377])).
% 0.20/0.48 tff(379,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | increases(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_37')).
% 0.20/0.48 tff(380,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.20/0.48 tff(381,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[380, 376])).
% 0.20/0.48 tff(382,plain,(
% 0.20/0.48 ![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))),
% 0.20/0.48 inference(skolemize,[status(sab)],[381])).
% 0.20/0.48 tff(383,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[382, 375])).
% 0.20/0.48 tff(384,plain,
% 0.20/0.48 (((~![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))) | (increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))) | increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(385,plain,
% 0.20/0.48 ((increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))) <=> (increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(386,plain,
% 0.20/0.48 ((increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))) <=> (increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.48 tff(387,plain,
% 0.20/0.48 ((increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))) <=> (increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[386, 385])).
% 0.20/0.48 tff(388,plain,
% 0.20/0.48 (((~![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))) | (increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))) | (increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[387])).
% 0.20/0.48 tff(389,plain,
% 0.20/0.48 (((~![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))) | (increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))) | increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[388, 384])).
% 0.20/0.48 tff(390,plain,
% 0.20/0.48 ((~![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))) | (increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(391,plain,
% 0.20/0.48 ((~![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))) | increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.20/0.48 tff(392,plain,
% 0.20/0.48 (increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[391, 383])).
% 0.20/0.48 tff(393,plain,
% 0.20/0.48 (increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[392, 69])).
% 0.20/0.48 tff(394,plain,
% 0.20/0.48 (constant(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[393, 373, 321])).
% 0.20/0.48 tff(395,plain,
% 0.20/0.48 (growth_rate(efficient_producers, sk2) = zero),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[247, 394])).
% 0.20/0.48 tff(396,plain,
% 0.20/0.48 (^[B: $i, A: $i, C: $i] : refl((increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(397,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C)) <=> ![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[396])).
% 0.20/0.48 tff(398,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C)) <=> ![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(399,plain,
% 0.20/0.48 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(B)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(B)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | increases(C)) <=> ((increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(C)))), rewrite(((increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(C)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | increases(C)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(400,plain,
% 0.20/0.49 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | increases(C)) <=> ![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[399])).
% 0.20/0.49 tff(401,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | increases(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_33')).
% 0.20/0.49 tff(402,plain,
% 0.20/0.49 (![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.20/0.49 tff(403,plain,
% 0.20/0.49 (![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[402, 398])).
% 0.20/0.49 tff(404,plain,(
% 0.20/0.49 ![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))),
% 0.20/0.49 inference(skolemize,[status(sab)],[403])).
% 0.20/0.49 tff(405,plain,
% 0.20/0.49 (![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[404, 397])).
% 0.20/0.49 tff(406,plain,
% 0.20/0.49 (((~![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))) | (increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(407,plain,
% 0.20/0.49 ((increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | increases(cardinality_at_time(efficient_producers, sk2))) <=> (increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(408,plain,
% 0.20/0.49 ((increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2))) <=> (increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | $false | increases(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.49 tff(409,plain,
% 0.20/0.49 ((increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2))) <=> (increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[408, 407])).
% 0.20/0.49 tff(410,plain,
% 0.20/0.49 (((~![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))) | (increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))) | (increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[409])).
% 0.20/0.49 tff(411,plain,
% 0.20/0.49 (((~![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))) | (increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[410, 406])).
% 0.20/0.49 tff(412,plain,
% 0.20/0.49 ((~![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))) | (increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | (~(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))) | increases(cardinality_at_time(efficient_producers, sk2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(413,plain,
% 0.20/0.49 ((~![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))) | increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.20/0.49 tff(414,plain,
% 0.20/0.49 (increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[413, 405])).
% 0.20/0.49 tff(415,plain,
% 0.20/0.49 (increases(cardinality_at_time(first_movers, sk2)) | constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[414, 69])).
% 0.20/0.49 tff(416,plain,
% 0.20/0.49 (constant(cardinality_at_time(first_movers, sk2))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[415, 373, 321])).
% 0.20/0.49 tff(417,plain,
% 0.20/0.49 (growth_rate(first_movers, sk2) = zero),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[228, 416])).
% 0.20/0.49 tff(418,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[239, 417, 395])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------