TSTP Solution File: MGT027-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT027-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 05:21:57 EDT 2022
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT027-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 02:44:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.34 Usage: tptp [options] [-file:]file
% 0.18/0.34 -h, -? prints this message.
% 0.18/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.34 -m, -model generate model.
% 0.18/0.34 -p, -proof generate proof.
% 0.18/0.34 -c, -core generate unsat core of named formulas.
% 0.18/0.34 -st, -statistics display statistics.
% 0.18/0.34 -t:timeout set timeout (in second).
% 0.18/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.34 -<param>:<value> configuration parameter and value.
% 0.18/0.34 -o:<output-file> file to place output in.
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(greater_type, type, (
% 0.18/0.39 greater: ( $i * $i ) > $o)).
% 0.18/0.39 tff(appear_type, type, (
% 0.18/0.39 appear: ( $i * $i ) > $i)).
% 0.18/0.39 tff(sk3_type, type, (
% 0.18/0.39 sk3: $i)).
% 0.18/0.39 tff(efficient_producers_type, type, (
% 0.18/0.39 efficient_producers: $i)).
% 0.18/0.39 tff(sk1_type, type, (
% 0.18/0.39 sk1: ( $i * $i ) > $i)).
% 0.18/0.39 tff(sk2_type, type, (
% 0.18/0.39 sk2: $i > $i)).
% 0.18/0.39 tff(greater_or_equal_type, type, (
% 0.18/0.39 greater_or_equal: ( $i * $i ) > $o)).
% 0.18/0.39 tff(zero_type, type, (
% 0.18/0.39 zero: $i)).
% 0.18/0.39 tff(cardinality_at_time_type, type, (
% 0.18/0.39 cardinality_at_time: ( $i * $i ) > $i)).
% 0.18/0.39 tff(in_environment_type, type, (
% 0.18/0.39 in_environment: ( $i * $i ) > $o)).
% 0.18/0.39 tff(stable_type, type, (
% 0.18/0.39 stable: $i > $o)).
% 0.18/0.39 tff(environment_type, type, (
% 0.18/0.39 environment: $i > $o)).
% 0.18/0.39 tff(contracts_from_type, type, (
% 0.18/0.39 contracts_from: ( $i * $i ) > $o)).
% 0.18/0.39 tff(first_movers_type, type, (
% 0.18/0.39 first_movers: $i)).
% 0.18/0.39 tff(subpopulations_type, type, (
% 0.18/0.39 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.18/0.39 tff(growth_rate_type, type, (
% 0.18/0.39 growth_rate: ( $i * $i ) > $i)).
% 0.18/0.39 tff(1,assumption,(~in_environment(sk3, sk1(sk2(sk3), sk3))), introduced(assumption)).
% 0.18/0.39 tff(2,assumption,(greater(sk1(sk2(sk3), sk3), sk2(sk3))), introduced(assumption)).
% 0.18/0.39 tff(3,assumption,(~in_environment(sk3, sk2(sk3))), introduced(assumption)).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (stable(sk3) <=> stable(sk3)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(5,axiom,(stable(sk3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l9_38')).
% 0.18/0.39 tff(6,plain,
% 0.18/0.39 (stable(sk3)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.39 tff(7,plain,
% 0.18/0.39 (environment(sk3) <=> environment(sk3)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(8,axiom,(environment(sk3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l9_37')).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 (environment(sk3)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 (^[A: $i] : refl(((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A))) <=> ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(11,plain,
% 0.18/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.18/0.39 tff(12,plain,
% 0.18/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | greater(sk2(A), appear(efficient_producers, A))) <=> ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (![A: $i] : (((~environment(A)) | (~stable(A))) | greater(sk2(A), appear(efficient_producers, A))) <=> ![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.39 tff(15,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | greater(sk2(A), appear(efficient_producers, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l10_35')).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.18/0.39 tff(18,plain,(
% 0.18/0.39 ![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[17])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 (((~![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A)))) | ((~stable(sk3)) | (~environment(sk3)) | greater(sk2(sk3), appear(efficient_producers, sk3)))) <=> ((~![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A)))) | (~stable(sk3)) | (~environment(sk3)) | greater(sk2(sk3), appear(efficient_producers, sk3)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A)))) | ((~stable(sk3)) | (~environment(sk3)) | greater(sk2(sk3), appear(efficient_producers, sk3)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 ((~![A: $i] : ((~stable(A)) | (~environment(A)) | greater(sk2(A), appear(efficient_producers, A)))) | (~stable(sk3)) | (~environment(sk3)) | greater(sk2(sk3), appear(efficient_producers, sk3))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (greater(sk2(sk3), appear(efficient_producers, sk3))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[22, 19, 9, 6])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (^[A: $i] : refl((in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A))) <=> (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A))) <=> ![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A))) <=> ![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | in_environment(A, appear(efficient_producers, A))) <=> (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, appear(efficient_producers, A))) <=> ![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.39 tff(29,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, appear(efficient_producers, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_EP_in_stable_environments_29')).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.18/0.39 tff(32,plain,(
% 0.18/0.39 ![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[31])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 (((~![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, appear(efficient_producers, sk3)) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A)))) | in_environment(sk3, appear(efficient_producers, sk3)) | (~stable(sk3)) | (~environment(sk3)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 ((~![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, appear(efficient_producers, sk3)) | (~stable(sk3)) | (~environment(sk3)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 ((~![A: $i] : (in_environment(A, appear(efficient_producers, A)) | (~stable(A)) | (~environment(A)))) | in_environment(sk3, appear(efficient_producers, sk3)) | (~stable(sk3)) | (~environment(sk3))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (in_environment(sk3, appear(efficient_producers, sk3))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[36, 33, 9, 6])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (^[B: $i, A: $i, C: $i] : refl((in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> ![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> ![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(C, B))) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | (~greater(C, B))))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | (~greater(C, B))) <=> ((~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(C, B))) <=> ((~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(C, B))) | in_environment(A, C)) <=> (((~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | in_environment(A, C)))), rewrite((((~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | in_environment(A, C)) <=> (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(C, B))) | in_environment(A, C)) <=> (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (![B: $i, A: $i, C: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(C, B))) | in_environment(A, C)) <=> ![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.18/0.39 tff(43,axiom,(![B: $i, A: $i, C: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(C, B))) | in_environment(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_long_stable_environments_28')).
% 0.18/0.39 tff(44,plain,
% 0.18/0.39 (![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.18/0.39 tff(46,plain,(
% 0.18/0.39 ![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[45])).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 (![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, appear(efficient_producers, sk3))) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | in_environment(sk3, sk2(sk3)))) <=> ((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, appear(efficient_producers, sk3))) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | in_environment(sk3, sk2(sk3)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 ((in_environment(sk3, sk2(sk3)) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~in_environment(sk3, appear(efficient_producers, sk3))) | (~stable(sk3)) | (~environment(sk3))) <=> ((~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, appear(efficient_producers, sk3))) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | in_environment(sk3, sk2(sk3)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk2(sk3)) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~in_environment(sk3, appear(efficient_producers, sk3))) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, appear(efficient_producers, sk3))) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | in_environment(sk3, sk2(sk3))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 (((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk2(sk3)) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~in_environment(sk3, appear(efficient_producers, sk3))) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, appear(efficient_producers, sk3))) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | in_environment(sk3, sk2(sk3)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[50, 48])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 ((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk2(sk3)) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~in_environment(sk3, appear(efficient_producers, sk3))) | (~stable(sk3)) | (~environment(sk3)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 ((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, appear(efficient_producers, sk3))) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | in_environment(sk3, sk2(sk3))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[53, 47, 9, 6, 37, 23, 3])).
% 0.18/0.39 tff(55,plain,(in_environment(sk3, sk2(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, sk2(sk3))) | in_environment(sk3, sk1(sk2(sk3), sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, sk2(sk3))) | in_environment(sk3, sk1(sk2(sk3), sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 ((in_environment(sk3, sk1(sk2(sk3), sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3))) <=> ((~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, sk2(sk3))) | in_environment(sk3, sk1(sk2(sk3), sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk1(sk2(sk3), sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, sk2(sk3))) | in_environment(sk3, sk1(sk2(sk3), sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3)))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[57])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 (((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk1(sk2(sk3), sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, sk2(sk3))) | in_environment(sk3, sk1(sk2(sk3), sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[58, 56])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 ((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (in_environment(sk3, sk1(sk2(sk3), sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 ((~![B: $i, A: $i, C: $i] : (in_environment(A, C) | (~greater(C, B)) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | (~in_environment(sk3, sk2(sk3))) | in_environment(sk3, sk1(sk2(sk3), sk3)) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[61, 47, 9, 6, 55, 2, 1])).
% 0.18/0.40 tff(63,plain,((~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | in_environment(sk3, sk1(sk2(sk3), sk3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (~greater(sk1(sk2(sk3), sk3), sk2(sk3))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[63, 1])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (^[A: $i] : refl(((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3)))) <=> ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3)))) <=> ![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3)))) <=> ![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (^[A: $i] : rewrite(((~greater(A, appear(efficient_producers, sk3))) | (~contracts_from(A, first_movers))) <=> ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (![A: $i] : ((~greater(A, appear(efficient_producers, sk3))) | (~contracts_from(A, first_movers))) <=> ![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.40 tff(70,axiom,(![A: $i] : ((~greater(A, appear(efficient_producers, sk3))) | (~contracts_from(A, first_movers)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l9_39')).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.18/0.40 tff(73,plain,(
% 0.18/0.40 ![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[72])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (((~![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3))))) | ((~contracts_from(sk2(sk3), first_movers)) | (~greater(sk2(sk3), appear(efficient_producers, sk3))))) <=> ((~![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3))))) | (~contracts_from(sk2(sk3), first_movers)) | (~greater(sk2(sk3), appear(efficient_producers, sk3))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 ((~![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3))))) | ((~contracts_from(sk2(sk3), first_movers)) | (~greater(sk2(sk3), appear(efficient_producers, sk3))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 ((~![A: $i] : ((~contracts_from(A, first_movers)) | (~greater(A, appear(efficient_producers, sk3))))) | (~contracts_from(sk2(sk3), first_movers)) | (~greater(sk2(sk3), appear(efficient_producers, sk3)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 (~contracts_from(sk2(sk3), first_movers)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[77, 74, 23])).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (^[B: $i, A: $i] : refl((greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> ![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 (![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> ![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater_or_equal(sk1(B, A), B)))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater_or_equal(sk1(B, A), B)) <=> (greater_or_equal(sk1(B, A), B) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> (greater_or_equal(sk1(B, A), B) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | contracts_from(B, first_movers)) <=> ((greater_or_equal(sk1(B, A), B) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | contracts_from(B, first_movers)))), rewrite(((greater_or_equal(sk1(B, A), B) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | contracts_from(B, first_movers)) <=> (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | contracts_from(B, first_movers)) <=> (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | contracts_from(B, first_movers)) <=> ![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[82])).
% 0.18/0.40 tff(84,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | contracts_from(B, first_movers))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_contracts_from_25')).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 (![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 (![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.18/0.40 tff(87,plain,(
% 0.18/0.40 ![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[86])).
% 0.18/0.40 tff(88,plain,
% 0.18/0.40 (![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 (((~![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3)))) <=> ((~![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 ((greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3))) <=> ((~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(91,plain,
% 0.18/0.40 (((~![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[90])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 (((~![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[91, 89])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 ((~![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 ((~![B: $i, A: $i] : (greater_or_equal(sk1(B, A), B) | contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[94, 88, 9, 6, 78, 55])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 (^[B: $i, A: $i] : refl(((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ((A = B) | greater(A, B) | (~greater_or_equal(A, B))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[96])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 (^[B: $i, A: $i] : rewrite((((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> ((A = B) | greater(A, B) | (~greater_or_equal(A, B))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 (![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.40 tff(101,axiom,(![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_or_equal_31')).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.18/0.40 tff(104,plain,(
% 0.18/0.40 ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[103])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))) | (sk1(sk2(sk3), sk3) = sk2(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3)))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))) | (sk1(sk2(sk3), sk3) = sk2(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(107,plain,
% 0.18/0.40 (((sk1(sk2(sk3), sk3) = sk2(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3)) | (~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3)))) <=> ((~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))) | (sk1(sk2(sk3), sk3) = sk2(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(108,plain,
% 0.18/0.41 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk1(sk2(sk3), sk3) = sk2(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3)) | (~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))) | (sk1(sk2(sk3), sk3) = sk2(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[107])).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk1(sk2(sk3), sk3) = sk2(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3)) | (~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))) | (sk1(sk2(sk3), sk3) = sk2(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[108, 106])).
% 0.18/0.41 tff(110,plain,
% 0.18/0.41 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sk1(sk2(sk3), sk3) = sk2(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3)) | (~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(111,plain,
% 0.18/0.41 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))) | (sk1(sk2(sk3), sk3) = sk2(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 ((sk1(sk2(sk3), sk3) = sk2(sk3)) | greater(sk1(sk2(sk3), sk3), sk2(sk3))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[111, 105, 95])).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 (sk1(sk2(sk3), sk3) = sk2(sk3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[112, 64])).
% 0.18/0.41 tff(114,plain,
% 0.18/0.41 (in_environment(sk3, sk1(sk2(sk3), sk3)) <=> in_environment(sk3, sk2(sk3))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[113])).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 (in_environment(sk3, sk2(sk3)) <=> in_environment(sk3, sk1(sk2(sk3), sk3))),
% 0.18/0.41 inference(symmetry,[status(thm)],[114])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 (in_environment(sk3, sk1(sk2(sk3), sk3))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[55, 115])).
% 0.18/0.41 tff(117,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[1, 116])).
% 0.18/0.41 tff(118,plain,(in_environment(sk3, sk1(sk2(sk3), sk3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 (^[B: $i, A: $i] : refl((contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(120,plain,
% 0.18/0.41 (![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[119])).
% 0.18/0.41 tff(121,plain,
% 0.18/0.41 (![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | contracts_from(B, first_movers)) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | contracts_from(B, first_movers)))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | contracts_from(B, first_movers)) <=> (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | contracts_from(B, first_movers)) <=> (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | contracts_from(B, first_movers)) <=> ![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[122])).
% 0.18/0.41 tff(124,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | (~greater(zero, growth_rate(first_movers, sk1(B, A))))) | contracts_from(B, first_movers))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_contracts_from_26')).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 (![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 (![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.18/0.41 tff(127,plain,(
% 0.18/0.41 ![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[126])).
% 0.18/0.41 tff(128,plain,
% 0.18/0.41 (![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 (((~![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | ((~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3)))))) <=> ((~![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 ((contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)) | (~greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3))))) <=> ((~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 (((~![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)) | (~greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3)))))) <=> ((~![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | ((~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[130])).
% 0.18/0.41 tff(132,plain,
% 0.18/0.41 (((~![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)) | (~greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3)))))) <=> ((~![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3)))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[131, 129])).
% 0.18/0.41 tff(133,plain,
% 0.18/0.41 ((~![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)) | (~greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 ((~![B: $i, A: $i] : (contracts_from(B, first_movers) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)) | (~greater(zero, growth_rate(first_movers, sk1(B, A)))))) | (~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | (~greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.18/0.41 tff(135,plain,
% 0.18/0.41 (~greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[134, 128, 9, 6, 78, 55])).
% 0.18/0.41 tff(136,plain,
% 0.18/0.41 (^[B: $i, A: $i] : refl(((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(137,plain,
% 0.18/0.41 (![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[136])).
% 0.18/0.41 tff(138,plain,
% 0.18/0.41 (![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(139,plain,
% 0.18/0.42 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~stable(A)) | (~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk2(A)))) <=> (((~stable(A)) | (~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk2(A)))))), rewrite((((~stable(A)) | (~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk2(A)))) <=> ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk2(A)))) <=> ((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk2(A)))) | greater(zero, growth_rate(first_movers, B))) <=> (((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, growth_rate(first_movers, B))))), rewrite((((~stable(A)) | (~environment(A)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, growth_rate(first_movers, B))) <=> ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk2(A)))) | greater(zero, growth_rate(first_movers, B))) <=> ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(140,plain,
% 0.18/0.42 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk2(A)))) | greater(zero, growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[139])).
% 0.18/0.42 tff(141,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk2(A)))) | greater(zero, growth_rate(first_movers, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l10_36')).
% 0.18/0.42 tff(142,plain,
% 0.18/0.42 (![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.18/0.42 tff(143,plain,
% 0.18/0.42 (![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.18/0.42 tff(144,plain,(
% 0.18/0.42 ![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[143])).
% 0.18/0.42 tff(145,plain,
% 0.18/0.42 (![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~stable(sk3)) | (~environment(sk3)) | greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))))) <=> ((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~stable(sk3)) | (~environment(sk3)) | greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~stable(sk3)) | (~environment(sk3)) | greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((~stable(A)) | (~environment(A)) | greater(zero, growth_rate(first_movers, B)) | (~greater_or_equal(B, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~stable(sk3)) | (~environment(sk3)) | greater(zero, growth_rate(first_movers, sk1(sk2(sk3), sk3))) | (~greater_or_equal(sk1(sk2(sk3), sk3), sk2(sk3))) | (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (~subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[148, 145, 9, 6, 135, 95])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (^[B: $i, A: $i] : refl((contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> ![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[150])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 (![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) <=> ![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) <=> ((~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero)) <=> (((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero)))), rewrite((((~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero)) <=> (greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero)) <=> (greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero)) | contracts_from(B, first_movers)) <=> ((greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | contracts_from(B, first_movers)))), rewrite(((greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A))) | contracts_from(B, first_movers)) <=> (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))), ((((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero)) | contracts_from(B, first_movers)) <=> (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero)) | contracts_from(B, first_movers)) <=> ![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[153])).
% 0.19/0.42 tff(155,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~in_environment(A, B))) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero)) | contracts_from(B, first_movers))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_contracts_from_24')).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 (![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.19/0.42 tff(158,plain,(
% 0.19/0.42 ![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[157])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 (![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero))) <=> ((~![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 ((contracts_from(sk2(sk3), first_movers) | greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3))) <=> ((~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (contracts_from(sk2(sk3), first_movers) | greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | ((~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[161])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (contracts_from(sk2(sk3), first_movers) | greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)))) <=> ((~![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero))),
% 0.19/0.42 inference(transitivity,[status(thm)],[162, 160])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (contracts_from(sk2(sk3), first_movers) | greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero) | (~in_environment(sk3, sk2(sk3))) | (~stable(sk3)) | (~environment(sk3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : (contracts_from(B, first_movers) | greater(cardinality_at_time(first_movers, sk1(B, A)), zero) | (~in_environment(A, B)) | (~stable(A)) | (~environment(A)))) | (~stable(sk3)) | (~environment(sk3)) | contracts_from(sk2(sk3), first_movers) | (~in_environment(sk3, sk2(sk3))) | greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 (greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[165, 159, 9, 6, 78, 55])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 (^[B: $i, A: $i] : refl(((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero))) <=> ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero))) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[167])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero))) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(170,plain,
% 0.19/0.43 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(first_movers, B), zero))) <=> ((~in_environment(A, B)) | (~environment(A)) | (~greater(cardinality_at_time(first_movers, B), zero)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(first_movers, B), zero))) | (~greater(cardinality_at_time(efficient_producers, B), zero))) <=> (((~in_environment(A, B)) | (~environment(A)) | (~greater(cardinality_at_time(first_movers, B), zero))) | (~greater(cardinality_at_time(efficient_producers, B), zero))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | (~greater(cardinality_at_time(first_movers, B), zero))) | (~greater(cardinality_at_time(efficient_producers, B), zero))) <=> ((~in_environment(A, B)) | (~environment(A)) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(first_movers, B), zero))) | (~greater(cardinality_at_time(efficient_producers, B), zero))) <=> ((~in_environment(A, B)) | (~environment(A)) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(first_movers, B), zero))) | (~greater(cardinality_at_time(efficient_producers, B), zero))) | subpopulations(first_movers, efficient_producers, A, B)) <=> (((~in_environment(A, B)) | (~environment(A)) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero))) | subpopulations(first_movers, efficient_producers, A, B)))), rewrite((((~in_environment(A, B)) | (~environment(A)) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero))) | subpopulations(first_movers, efficient_producers, A, B)) <=> ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(first_movers, B), zero))) | (~greater(cardinality_at_time(efficient_producers, B), zero))) | subpopulations(first_movers, efficient_producers, A, B)) <=> ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(171,plain,
% 0.19/0.43 (![B: $i, A: $i] : (((((~environment(A)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(first_movers, B), zero))) | (~greater(cardinality_at_time(efficient_producers, B), zero))) | subpopulations(first_movers, efficient_producers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[170])).
% 0.19/0.43 tff(172,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(first_movers, B), zero))) | (~greater(cardinality_at_time(efficient_producers, B), zero))) | subpopulations(first_movers, efficient_producers, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_non_empty_fm_and_ep_27')).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.19/0.43 tff(175,plain,(
% 0.19/0.43 ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[174])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))) | ((~environment(sk3)) | (~greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero)))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))) | (~environment(sk3)) | (~greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (((~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero)) | (~greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero))) <=> ((~environment(sk3)) | (~greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))) | ((~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero)) | (~greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))) | ((~environment(sk3)) | (~greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[178])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))) | ((~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero)) | (~greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))) | (~environment(sk3)) | (~greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[179, 177])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))) | ((~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero)) | (~greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulations(first_movers, efficient_producers, A, B) | (~greater(cardinality_at_time(efficient_producers, B), zero)) | (~greater(cardinality_at_time(first_movers, B), zero)))) | (~environment(sk3)) | (~greater(cardinality_at_time(first_movers, sk1(sk2(sk3), sk3)), zero)) | subpopulations(first_movers, efficient_producers, sk3, sk1(sk2(sk3), sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 ((~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[182, 176, 9, 166, 149])).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 (~greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[183, 118])).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (^[B: $i, A: $i] : refl(((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(186,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[185])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(188,plain,
% 0.19/0.44 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ((~in_environment(A, B)) | (~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A))))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> (((~in_environment(A, B)) | (~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | greater(cardinality_at_time(efficient_producers, B), zero)))), rewrite((((~in_environment(A, B)) | (~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(189,plain,
% 0.19/0.44 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[188])).
% 0.19/0.44 tff(190,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | greater(cardinality_at_time(efficient_producers, B), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t6_34')).
% 0.19/0.44 tff(191,plain,
% 0.19/0.44 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.44 tff(192,plain,
% 0.19/0.44 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.19/0.44 tff(193,plain,(
% 0.19/0.44 ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[192])).
% 0.19/0.44 tff(194,plain,
% 0.19/0.44 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.19/0.44 tff(195,plain,
% 0.19/0.44 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero) | (~greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero) | (~greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(196,plain,
% 0.19/0.44 (((~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero) | (~greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)))) <=> ((~environment(sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero) | (~greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(197,plain,
% 0.19/0.44 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero) | (~greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~environment(sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero) | (~greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[196])).
% 0.19/0.44 tff(198,plain,
% 0.19/0.44 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero) | (~greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero) | (~greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[197, 195])).
% 0.19/0.44 tff(199,plain,
% 0.19/0.44 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk3, sk1(sk2(sk3), sk3))) | (~environment(sk3)) | greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero) | (~greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(200,plain,
% 0.19/0.44 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater(cardinality_at_time(efficient_producers, B), zero) | (~greater_or_equal(B, appear(efficient_producers, A))))) | (~environment(sk3)) | (~in_environment(sk3, sk1(sk2(sk3), sk3))) | greater(cardinality_at_time(efficient_producers, sk1(sk2(sk3), sk3)), zero) | (~greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.19/0.44 tff(201,plain,
% 0.19/0.44 (~greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[200, 194, 9, 118, 184])).
% 0.19/0.44 tff(202,plain,
% 0.19/0.44 (^[B: $i, A: $i] : refl(((~greater(A, B)) | greater_or_equal(A, B)) <=> ((~greater(A, B)) | greater_or_equal(A, B)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(203,plain,
% 0.19/0.44 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[202])).
% 0.19/0.44 tff(204,plain,
% 0.19/0.44 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(205,axiom,(![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_or_equal_32')).
% 0.19/0.44 tff(206,plain,
% 0.19/0.44 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.19/0.44 tff(207,plain,(
% 0.19/0.44 ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.19/0.44 inference(skolemize,[status(sab)],[206])).
% 0.19/0.44 tff(208,plain,
% 0.19/0.44 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.19/0.44 tff(209,plain,
% 0.19/0.44 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))) | greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))) | greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(210,plain,
% 0.19/0.44 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))) | greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(211,plain,
% 0.19/0.44 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))) | greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.19/0.44 tff(212,plain,
% 0.19/0.44 (~greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[211, 208, 201])).
% 0.19/0.44 tff(213,assumption,(sk1(sk2(sk3), sk3) = sk2(sk3)), introduced(assumption)).
% 0.19/0.44 tff(214,plain,
% 0.19/0.44 (greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)) <=> greater_or_equal(sk2(sk3), appear(efficient_producers, sk3))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[213])).
% 0.19/0.44 tff(215,plain,
% 0.19/0.44 (greater_or_equal(sk2(sk3), appear(efficient_producers, sk3)) <=> greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))),
% 0.19/0.44 inference(symmetry,[status(thm)],[214])).
% 0.19/0.44 tff(216,plain,
% 0.19/0.44 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk2(sk3), appear(efficient_producers, sk3))) | greater_or_equal(sk2(sk3), appear(efficient_producers, sk3)))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | greater_or_equal(sk2(sk3), appear(efficient_producers, sk3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(217,plain,
% 0.19/0.44 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(sk2(sk3), appear(efficient_producers, sk3))) | greater_or_equal(sk2(sk3), appear(efficient_producers, sk3)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(218,plain,
% 0.19/0.44 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | greater_or_equal(sk2(sk3), appear(efficient_producers, sk3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.19/0.44 tff(219,plain,
% 0.19/0.44 (greater_or_equal(sk2(sk3), appear(efficient_producers, sk3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[218, 208, 23])).
% 0.19/0.44 tff(220,plain,
% 0.19/0.44 (greater_or_equal(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.19/0.44 tff(221,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[201, 220])).
% 0.19/0.44 tff(222,plain,(~(sk1(sk2(sk3), sk3) = sk2(sk3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(223,plain,
% 0.19/0.44 (greater(sk1(sk2(sk3), sk3), sk2(sk3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[112, 222])).
% 0.19/0.44 tff(224,plain,
% 0.19/0.44 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B))) <=> ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(225,plain,
% 0.19/0.44 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B))) <=> ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(226,plain,
% 0.19/0.44 (^[B: $i, A: $i, C: $i] : rewrite((((~greater(A, B)) | (~greater(B, C))) | greater(A, C)) <=> (greater(A, C) | (~greater(B, C)) | (~greater(A, B))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(227,plain,
% 0.19/0.44 (![B: $i, A: $i, C: $i] : (((~greater(A, B)) | (~greater(B, C))) | greater(A, C)) <=> ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[226])).
% 0.19/0.44 tff(228,axiom,(![B: $i, A: $i, C: $i] : (((~greater(A, B)) | (~greater(B, C))) | greater(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_transitivity_30')).
% 0.19/0.44 tff(229,plain,
% 0.19/0.44 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.19/0.44 tff(230,plain,
% 0.19/0.44 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[229, 225])).
% 0.19/0.44 tff(231,plain,(
% 0.19/0.44 ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[230])).
% 0.19/0.44 tff(232,plain,
% 0.19/0.44 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[231, 224])).
% 0.19/0.44 tff(233,plain,
% 0.19/0.44 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | ((~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(234,plain,
% 0.19/0.44 ((greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3)))) <=> ((~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(235,plain,
% 0.19/0.44 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | ((~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[234])).
% 0.19/0.44 tff(236,plain,
% 0.19/0.44 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[235, 233])).
% 0.19/0.44 tff(237,plain,
% 0.19/0.44 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3)) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(238,plain,
% 0.19/0.44 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (~greater(sk2(sk3), appear(efficient_producers, sk3))) | (~greater(sk1(sk2(sk3), sk3), sk2(sk3))) | greater(sk1(sk2(sk3), sk3), appear(efficient_producers, sk3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.19/0.45 tff(239,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[238, 232, 23, 223, 212])).
% 0.19/0.45 % SZS output end Proof
%------------------------------------------------------------------------------