TSTP Solution File: MGT020-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT020-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 05:21:53 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT020-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 02:32:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(greater_or_equal_type, type, (
% 0.19/0.39 greater_or_equal: ( $i * $i ) > $o)).
% 0.19/0.39 tff(initial_FM_EP_type, type, (
% 0.19/0.39 initial_FM_EP: $i > $i)).
% 0.19/0.39 tff(sk1_type, type, (
% 0.19/0.39 sk1: $i)).
% 0.19/0.39 tff(subpopulations_type, type, (
% 0.19/0.39 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.19/0.39 tff(efficient_producers_type, type, (
% 0.19/0.39 efficient_producers: $i)).
% 0.19/0.39 tff(first_movers_type, type, (
% 0.19/0.39 first_movers: $i)).
% 0.19/0.39 tff(in_environment_type, type, (
% 0.19/0.39 in_environment: ( $i * $i ) > $o)).
% 0.19/0.39 tff(greater_type, type, (
% 0.19/0.39 greater: ( $i * $i ) > $o)).
% 0.19/0.39 tff(sk2_type, type, (
% 0.19/0.39 sk2: $i)).
% 0.19/0.39 tff(disbanding_rate_type, type, (
% 0.19/0.39 disbanding_rate: ( $i * $i ) > $i)).
% 0.19/0.39 tff(environment_type, type, (
% 0.19/0.39 environment: $i > $o)).
% 0.19/0.39 tff(start_time_type, type, (
% 0.19/0.39 start_time: $i > $i)).
% 0.19/0.39 tff(decreases_type, type, (
% 0.19/0.39 decreases: $i > $o)).
% 0.19/0.39 tff(difference_type, type, (
% 0.19/0.39 difference: ( $i * $i ) > $i)).
% 0.19/0.39 tff(1,assumption,(sk2 = initial_FM_EP(sk1)), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (disbanding_rate(efficient_producers, sk2) = disbanding_rate(efficient_producers, initial_FM_EP(sk1))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (disbanding_rate(first_movers, sk2) = disbanding_rate(first_movers, initial_FM_EP(sk1))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[1])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)) <=> greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[3, 2])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))) <=> greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))),
% 0.19/0.39 inference(symmetry,[status(thm)],[4])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (environment(sk1) <=> environment(sk1)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(7,axiom,(environment(sk1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l2_33')).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (environment(sk1)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (^[A: $i] : refl(((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A)))) <=> ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A)))) <=> ![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A)))) <=> ![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(12,axiom,(![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a8_31')).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.39 tff(14,plain,(
% 0.19/0.39 ![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (((~![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A))))) | ((~environment(sk1)) | greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))) <=> ((~![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A))))) | (~environment(sk1)) | greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 ((~![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A))))) | ((~environment(sk1)) | greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~![A: $i] : ((~environment(A)) | greater(disbanding_rate(first_movers, initial_FM_EP(A)), disbanding_rate(efficient_producers, initial_FM_EP(A))))) | (~environment(sk1)) | greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[18, 15, 8])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 5])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) <=> (~greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(22,axiom,(~greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l2_35')).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (~greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.19/0.39 tff(25,plain,(~(sk2 = initial_FM_EP(sk1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (subpopulations(first_movers, efficient_producers, sk1, sk2) <=> subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(27,axiom,(subpopulations(first_movers, efficient_producers, sk1, sk2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l2_34')).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater_or_equal(B, initial_FM_EP(A))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater_or_equal(B, initial_FM_EP(A))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.39 tff(34,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater_or_equal(B, initial_FM_EP(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_point_24')).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.39 tff(37,plain,(
% 0.19/0.39 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[36])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater_or_equal(sk2, initial_FM_EP(sk1)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater_or_equal(sk2, initial_FM_EP(sk1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater_or_equal(sk2, initial_FM_EP(sk1)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | greater_or_equal(sk2, initial_FM_EP(sk1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (greater_or_equal(sk2, initial_FM_EP(sk1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[41, 38, 8, 28])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (^[B: $i, A: $i] : refl((greater(A, B) | (A = B) | (~greater_or_equal(A, B))) <=> (greater(A, B) | (A = B) | (~greater_or_equal(A, B))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (^[B: $i, A: $i] : rewrite((((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> (greater(A, B) | (A = B) | (~greater_or_equal(A, B))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.39 tff(48,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_30')).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.19/0.39 tff(51,plain,(
% 0.19/0.39 ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[50])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | (greater(sk2, initial_FM_EP(sk1)) | (sk2 = initial_FM_EP(sk1)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))))) <=> ((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | greater(sk2, initial_FM_EP(sk1)) | (sk2 = initial_FM_EP(sk1)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | (greater(sk2, initial_FM_EP(sk1)) | (sk2 = initial_FM_EP(sk1)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | greater(sk2, initial_FM_EP(sk1)) | (sk2 = initial_FM_EP(sk1)) | (~greater_or_equal(sk2, initial_FM_EP(sk1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (greater(sk2, initial_FM_EP(sk1)) | (sk2 = initial_FM_EP(sk1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[55, 52, 42])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (greater(sk2, initial_FM_EP(sk1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 25])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (^[A: $i] : refl(((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A))) <=> ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A))) <=> ![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A))) <=> ![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(61,axiom,(![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_initial_time_27')).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.39 tff(63,plain,(
% 0.19/0.39 ![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[62])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (((~![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A)))) | ((~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), start_time(sk1)))) <=> ((~![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A)))) | (~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), start_time(sk1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 ((~![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A)))) | ((~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), start_time(sk1)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 ((~![A: $i] : ((~environment(A)) | greater_or_equal(initial_FM_EP(A), start_time(A)))) | (~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), start_time(sk1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (greater_or_equal(initial_FM_EP(sk1), start_time(sk1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 64, 8])).
% 0.19/0.40 tff(69,assumption,(~in_environment(sk1, initial_FM_EP(sk1))), introduced(assumption)).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (^[B: $i, A: $i] : refl((in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B)) <=> (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B)) <=> ![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.40 tff(75,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_time_point_occurs_26')).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.19/0.40 tff(78,plain,(
% 0.19/0.40 ![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[77])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~![B: $i, A: $i] : (in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (in_environment(sk1, sk2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[82, 79, 8, 28])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (^[B: $i, A: $i, C: $i] : refl(((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A)))) <=> ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A)))) <=> ![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A)))) <=> ![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~greater_or_equal(B, start_time(A)))) | (~greater(C, B))) <=> ((~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))), (((((~environment(A)) | (~greater_or_equal(B, start_time(A)))) | (~greater(C, B))) | (~in_environment(A, C))) <=> (((~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A)))) | (~in_environment(A, C))))), rewrite((((~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A)))) | (~in_environment(A, C))) <=> ((~in_environment(A, C)) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))), (((((~environment(A)) | (~greater_or_equal(B, start_time(A)))) | (~greater(C, B))) | (~in_environment(A, C))) <=> ((~in_environment(A, C)) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A)))))), ((((((~environment(A)) | (~greater_or_equal(B, start_time(A)))) | (~greater(C, B))) | (~in_environment(A, C))) | in_environment(A, B)) <=> (((~in_environment(A, C)) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A)))) | in_environment(A, B)))), rewrite((((~in_environment(A, C)) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A)))) | in_environment(A, B)) <=> ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))), ((((((~environment(A)) | (~greater_or_equal(B, start_time(A)))) | (~greater(C, B))) | (~in_environment(A, C))) | in_environment(A, B)) <=> ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : (((((~environment(A)) | (~greater_or_equal(B, start_time(A)))) | (~greater(C, B))) | (~in_environment(A, C))) | in_environment(A, B)) <=> ![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.40 tff(89,axiom,(![B: $i, A: $i, C: $i] : (((((~environment(A)) | (~greater_or_equal(B, start_time(A)))) | (~greater(C, B))) | (~in_environment(A, C))) | in_environment(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_times_in_order_28')).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.19/0.40 tff(92,plain,(
% 0.19/0.40 ![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[91])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (((~![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))) | ((~environment(sk1)) | in_environment(sk1, initial_FM_EP(sk1)) | (~greater_or_equal(initial_FM_EP(sk1), start_time(sk1))) | (~greater(sk2, initial_FM_EP(sk1))) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))) | (~environment(sk1)) | in_environment(sk1, initial_FM_EP(sk1)) | (~greater_or_equal(initial_FM_EP(sk1), start_time(sk1))) | (~greater(sk2, initial_FM_EP(sk1))) | (~in_environment(sk1, sk2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (((~in_environment(sk1, sk2)) | in_environment(sk1, initial_FM_EP(sk1)) | (~greater(sk2, initial_FM_EP(sk1))) | (~environment(sk1)) | (~greater_or_equal(initial_FM_EP(sk1), start_time(sk1)))) <=> ((~environment(sk1)) | in_environment(sk1, initial_FM_EP(sk1)) | (~greater_or_equal(initial_FM_EP(sk1), start_time(sk1))) | (~greater(sk2, initial_FM_EP(sk1))) | (~in_environment(sk1, sk2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (((~![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))) | ((~in_environment(sk1, sk2)) | in_environment(sk1, initial_FM_EP(sk1)) | (~greater(sk2, initial_FM_EP(sk1))) | (~environment(sk1)) | (~greater_or_equal(initial_FM_EP(sk1), start_time(sk1))))) <=> ((~![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))) | ((~environment(sk1)) | in_environment(sk1, initial_FM_EP(sk1)) | (~greater_or_equal(initial_FM_EP(sk1), start_time(sk1))) | (~greater(sk2, initial_FM_EP(sk1))) | (~in_environment(sk1, sk2))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (((~![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))) | ((~in_environment(sk1, sk2)) | in_environment(sk1, initial_FM_EP(sk1)) | (~greater(sk2, initial_FM_EP(sk1))) | (~environment(sk1)) | (~greater_or_equal(initial_FM_EP(sk1), start_time(sk1))))) <=> ((~![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))) | (~environment(sk1)) | in_environment(sk1, initial_FM_EP(sk1)) | (~greater_or_equal(initial_FM_EP(sk1), start_time(sk1))) | (~greater(sk2, initial_FM_EP(sk1))) | (~in_environment(sk1, sk2)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))) | ((~in_environment(sk1, sk2)) | in_environment(sk1, initial_FM_EP(sk1)) | (~greater(sk2, initial_FM_EP(sk1))) | (~environment(sk1)) | (~greater_or_equal(initial_FM_EP(sk1), start_time(sk1))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ((~![B: $i, A: $i, C: $i] : ((~in_environment(A, C)) | in_environment(A, B) | (~greater(C, B)) | (~environment(A)) | (~greater_or_equal(B, start_time(A))))) | (~environment(sk1)) | in_environment(sk1, initial_FM_EP(sk1)) | (~greater_or_equal(initial_FM_EP(sk1), start_time(sk1))) | (~greater(sk2, initial_FM_EP(sk1))) | (~in_environment(sk1, sk2))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[99, 93, 8, 83, 69, 68, 57])).
% 0.19/0.40 tff(101,plain,(in_environment(sk1, initial_FM_EP(sk1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (^[A: $i] : refl((subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A))) <=> (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (^[A: $i] : rewrite((((~environment(A)) | (~in_environment(A, initial_FM_EP(A)))) | subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A))) <=> (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (![A: $i] : (((~environment(A)) | (~in_environment(A, initial_FM_EP(A)))) | subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.40 tff(107,axiom,(![A: $i] : (((~environment(A)) | (~in_environment(A, initial_FM_EP(A)))) | subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_point_23')).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.19/0.40 tff(110,plain,(
% 0.19/0.40 ![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[109])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))) | ((~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)) | (~in_environment(sk1, initial_FM_EP(sk1))))) <=> ((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))) | (~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)) | (~in_environment(sk1, initial_FM_EP(sk1))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 ((subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)) | (~in_environment(sk1, initial_FM_EP(sk1))) | (~environment(sk1))) <=> ((~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)) | (~in_environment(sk1, initial_FM_EP(sk1))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))) | (subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)) | (~in_environment(sk1, initial_FM_EP(sk1))) | (~environment(sk1)))) <=> ((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))) | ((~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)) | (~in_environment(sk1, initial_FM_EP(sk1)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[113])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))) | (subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)) | (~in_environment(sk1, initial_FM_EP(sk1))) | (~environment(sk1)))) <=> ((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))) | (~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)) | (~in_environment(sk1, initial_FM_EP(sk1))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[114, 112])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 ((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))) | (subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)) | (~in_environment(sk1, initial_FM_EP(sk1))) | (~environment(sk1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 ((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, initial_FM_EP(A)) | (~in_environment(A, initial_FM_EP(A))) | (~environment(A)))) | (~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)) | (~in_environment(sk1, initial_FM_EP(sk1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)) | (~in_environment(sk1, initial_FM_EP(sk1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[117, 111, 8])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[118, 101])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | ((~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | (~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (((~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))) | (~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1))) <=> ((~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))) | (~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | ((~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))) | (~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | (~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[122, 120])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))) | (~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, initial_FM_EP(A)))) | (~environment(sk1)) | greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[125, 38, 8, 119])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (^[B: $i, A: $i] : refl(((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))))) <=> ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))))) <=> ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.41 tff(132,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l3_22')).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.19/0.41 tff(135,plain,(
% 0.19/0.41 ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[134])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~environment(sk1)) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))))) <=> ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk1)) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 (((~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))) | (~environment(sk1))) <=> ((~environment(sk1)) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))) | (~environment(sk1)))) <=> ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~environment(sk1)) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[138])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))) | (~environment(sk1)))) <=> ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk1)) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[139, 137])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1))) | (~environment(sk1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk1)) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))) | (~subpopulations(first_movers, efficient_producers, sk1, initial_FM_EP(sk1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[142, 136, 8, 119])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 (^[B: $i, D: $i, A: $i, C: $i] : refl((greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))) <=> (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 (![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))) <=> ![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[144])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 (![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))) <=> ![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~greater_or_equal(B, C))) | (~greater_or_equal(D, B))) <=> ((~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))), (((((~environment(A)) | (~greater_or_equal(B, C))) | (~greater_or_equal(D, B))) | (~subpopulations(first_movers, efficient_producers, A, D))) <=> (((~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))) | (~subpopulations(first_movers, efficient_producers, A, D))))), rewrite((((~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))) | (~subpopulations(first_movers, efficient_producers, A, D))) <=> ((~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))), (((((~environment(A)) | (~greater_or_equal(B, C))) | (~greater_or_equal(D, B))) | (~subpopulations(first_movers, efficient_producers, A, D))) <=> ((~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))))), ((((((~environment(A)) | (~greater_or_equal(B, C))) | (~greater_or_equal(D, B))) | (~subpopulations(first_movers, efficient_producers, A, D))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C)))) <=> (((~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C)))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C)))) <=> ((~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))), ((((((~environment(A)) | (~greater_or_equal(B, C))) | (~greater_or_equal(D, B))) | (~subpopulations(first_movers, efficient_producers, A, D))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C)))) <=> ((~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))))), (((((((~environment(A)) | (~greater_or_equal(B, C))) | (~greater_or_equal(D, B))) | (~subpopulations(first_movers, efficient_producers, A, D))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C)))) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) <=> (((~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))))), rewrite((((~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) <=> (decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))), (((((((~environment(A)) | (~greater_or_equal(B, C))) | (~greater_or_equal(D, B))) | (~subpopulations(first_movers, efficient_producers, A, D))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C)))) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) <=> (decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))))), ((((((((~environment(A)) | (~greater_or_equal(B, C))) | (~greater_or_equal(D, B))) | (~subpopulations(first_movers, efficient_producers, A, D))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C)))) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D))) <=> ((decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))) | greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D))))), rewrite(((decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A))) | greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D))) <=> (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))), ((((((((~environment(A)) | (~greater_or_equal(B, C))) | (~greater_or_equal(D, B))) | (~subpopulations(first_movers, efficient_producers, A, D))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C)))) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D))) <=> (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 (![B: $i, D: $i, A: $i, C: $i] : (((((((~environment(A)) | (~greater_or_equal(B, C))) | (~greater_or_equal(D, B))) | (~subpopulations(first_movers, efficient_producers, A, D))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C)))) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D))) <=> ![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[147])).
% 0.19/0.42 tff(149,axiom,(![B: $i, D: $i, A: $i, C: $i] : (((((((~environment(A)) | (~greater_or_equal(B, C))) | (~greater_or_equal(D, B))) | (~subpopulations(first_movers, efficient_producers, A, D))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C)))) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_positive_function_difference_25')).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.19/0.42 tff(152,plain,(
% 0.19/0.42 ![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[151])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (((~![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))) | (greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))) | greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 ((greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))) | (~greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1))) | (~environment(sk1))) <=> (greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 (((~![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))) | (greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))) | (~greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1))) | (~environment(sk1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))) | (greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[155])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 (((~![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))) | (greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))) | (~greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1))) | (~environment(sk1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))) | greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[156, 154])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 ((~![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))) | (greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))) | (~greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1))) | (~environment(sk1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 ((~![B: $i, D: $i, A: $i, C: $i] : (greater(disbanding_rate(first_movers, D), disbanding_rate(efficient_producers, D)) | decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))) | (~greater(disbanding_rate(first_movers, C), disbanding_rate(efficient_producers, C))) | (~subpopulations(first_movers, efficient_producers, A, D)) | (~greater_or_equal(D, B)) | (~greater_or_equal(B, C)) | (~environment(A)))) | greater(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | (~greater_or_equal(sk2, initial_FM_EP(sk1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(sk1)), disbanding_rate(efficient_producers, initial_FM_EP(sk1)))) | (~greater_or_equal(initial_FM_EP(sk1), initial_FM_EP(sk1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[159, 153, 8, 28, 23, 42, 19, 143, 126])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------