%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT039-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:02:40 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 59
% Syntax : Number of formulae : 292 ( 40 unt; 33 def)
% Number of atoms : 918 ( 30 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 1121 ( 495 ~; 593 |; 0 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 45 ( 43 usr; 34 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 150 ( 0 sgn 150 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates_33) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulation(X1,X0,X2)
| ~ subpopulation(X3,X0,X2)
| ~ greater(cardinality_at_time(X1,X2),zero)
| cardinality_at_time(X3,X2) != zero
| selection_favors(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members_34) ).
fof(f3,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulation(X1,X0,X2)
| ~ subpopulation(X3,X0,X2)
| ~ greater(cardinality_at_time(X1,X2),zero)
| zero != cardinality_at_time(X3,X2)
| selection_favors(X1,X3,X2) ),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0] :
( ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| environment(sk1(X0))
| selection_favors(efficient_producers,first_movers,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp3_favoured_trategy_35) ).
fof(f5,axiom,
! [X0] :
( ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| in_environment(X0,sk1(X0))
| selection_favors(efficient_producers,first_movers,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp3_favoured_trategy_36) ).
fof(f6,axiom,
! [X0] :
( ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| ~ selection_favors(efficient_producers,first_movers,end_time(sk1(X0)))
| selection_favors(efficient_producers,first_movers,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp3_favoured_trategy_37) ).
fof(f7,axiom,
! [X0,X1] :
( ~ observational_period(X0)
| ~ slow_change(X0)
| ~ environment(X1)
| ~ in_environment(X0,X1)
| in_environment(X1,sk2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp4_critical_point_38) ).
fof(f8,axiom,
! [X0,X1] :
( ~ observational_period(X0)
| ~ slow_change(X0)
| ~ environment(X1)
| ~ in_environment(X0,X1)
| greater(sk2(X1,X0),critical_point(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp4_critical_point_39) ).
fof(f9,axiom,
propagation_strategy(first_movers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets1_40) ).
fof(f10,axiom,
propagation_strategy(efficient_producers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets2_41) ).
fof(f11,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ greater_or_equal(X1,start_time(X0))
| ~ greater_or_equal(end_time(X0),X1)
| in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_in_environment_42) ).
fof(f12,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| greater_or_equal(end_time(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_end_point_43) ).
fof(f13,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| subpopulations(first_movers,efficient_producers,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contains_FM_and_EP_44) ).
fof(f14,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| greater_or_equal(cardinality_at_time(first_movers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist_45) ).
fof(f15,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| subpopulation(first_movers,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_46) ).
fof(f16,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| subpopulation(efficient_producers,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_47) ).
fof(f17,axiom,
! [X0] :
( ~ environment(X0)
| greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_after_EP_48) ).
fof(f18,axiom,
! [X0] :
( ~ environment(X0)
| greater_or_equal(critical_point(X0),start_time(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_of_critical_point_49) ).
fof(f19,axiom,
! [X2,X0,X1] :
( ~ greater(X0,X1)
| ~ greater(X1,X2)
| greater(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity_50) ).
fof(f21,axiom,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_52) ).
fof(f22,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_53) ).
fof(f23,axiom,
! [X0,X1] :
( X0 != X1
| greater_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_54) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ environment(X0)
| X1 != critical_point(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_56) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ environment(X0)
| critical_point(X0) != X1
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_57) ).
fof(f29,negated_conjecture,
observational_period(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t8_58) ).
fof(f30,negated_conjecture,
slow_change(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t8_59) ).
fof(f31,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t8_60) ).
fof(f32,plain,
! [X1] : greater_or_equal(X1,X1),
inference(equality_resolution,[],[f23]) ).
fof(f34,plain,
! [X2,X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,critical_point(X0))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(equality_resolution,[],[f27]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| selection_favors(X2,X1,X3) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( greater(cardinality_at_time(X1,X2),zero)
| subpopulation(X1,X0,X2)
| subpopulation(X3,X0,X2)
| ~ environment(X0)
| zero != cardinality_at_time(X3,X2)
| selection_favors(X1,X3,X2) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f37,plain,
! [X0] :
( observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| environment(sk1(X0))
| selection_favors(efficient_producers,first_movers,X0) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f38,plain,
! [X0] :
( observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| in_environment(X0,sk1(X0))
| selection_favors(efficient_producers,first_movers,X0) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f39,plain,
! [X0] :
( observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| ~ selection_favors(efficient_producers,first_movers,end_time(sk1(X0)))
| selection_favors(efficient_producers,first_movers,X0) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f40,plain,
! [X0,X1] :
( slow_change(X0)
| observational_period(X0)
| ~ environment(X1)
| ~ in_environment(X0,X1)
| in_environment(X1,sk2(X1,X0)) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f41,plain,
! [X0,X1] :
( slow_change(X0)
| observational_period(X0)
| ~ environment(X1)
| ~ in_environment(X0,X1)
| ~ greater(sk2(X1,X0),critical_point(X1)) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f42,plain,
! [X0,X1] :
( greater_or_equal(end_time(X0),X1)
| greater_or_equal(X1,start_time(X0))
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f43,plain,
! [X0,X1] :
( ~ greater_or_equal(end_time(X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f44,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1)
| greater(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f45,plain,
! [X0,X1] :
( ~ greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f46,plain,
! [X0,X1] :
( ~ subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f47,plain,
! [X0,X1] :
( ~ subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f48,plain,
! [X0] :
( ~ greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f49,plain,
! [X0] :
( ~ greater_or_equal(critical_point(X0),start_time(X0))
| ~ environment(X0) ),
inference(consistent_polarity_flipping,[],[f18]) ).
fof(f50,plain,
! [X2,X0,X1] :
( greater(X1,X2)
| greater(X0,X1)
| ~ greater(X0,X2) ),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f52,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1)
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f21]) ).
fof(f53,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| greater(X0,X1) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f54,plain,
! [X1] : ~ greater_or_equal(X1,X1),
inference(consistent_polarity_flipping,[],[f32]) ).
fof(f56,plain,
! [X2,X0] :
( greater(X2,critical_point(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(consistent_polarity_flipping,[],[f34]) ).
fof(f57,plain,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f58,plain,
~ observational_period(sk3),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f59,plain,
~ slow_change(sk3),
inference(consistent_polarity_flipping,[],[f30]) ).
fof(f61,definition,
( spl0_1
<=> propagation_strategy(efficient_producers) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f63,plain,
( ~ propagation_strategy(efficient_producers)
| spl0_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f65,definition,
( spl0_2
<=> propagation_strategy(first_movers) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f67,plain,
( ~ propagation_strategy(first_movers)
| spl0_2 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f69,definition,
( spl0_3
<=> ! [X0] :
( observational_period(X0)
| selection_favors(efficient_producers,first_movers,X0)
| ~ selection_favors(efficient_producers,first_movers,end_time(sk1(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f70,plain,
( ! [X0] :
( ~ selection_favors(efficient_producers,first_movers,end_time(sk1(X0)))
| selection_favors(efficient_producers,first_movers,X0)
| observational_period(X0) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f71,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f39,f69,f65,f61]) ).
fof(f73,definition,
( spl0_4
<=> ! [X0] :
( observational_period(X0)
| selection_favors(efficient_producers,first_movers,X0)
| in_environment(X0,sk1(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f74,plain,
( ! [X0] :
( in_environment(X0,sk1(X0))
| selection_favors(efficient_producers,first_movers,X0)
| observational_period(X0) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f75,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f38,f73,f65,f61]) ).
fof(f77,definition,
( spl0_5
<=> ! [X0] :
( observational_period(X0)
| selection_favors(efficient_producers,first_movers,X0)
| environment(sk1(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f78,plain,
( ! [X0] :
( environment(sk1(X0))
| selection_favors(efficient_producers,first_movers,X0)
| observational_period(X0) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f37,f77,f65,f61]) ).
fof(f80,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f63,f10]) ).
fof(f81,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f82,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f67,f9]) ).
fof(f83,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f82]) ).
fof(f86,plain,
! [X0] :
( ~ greater(critical_point(X0),start_time(X0))
| start_time(X0) = critical_point(X0)
| ~ environment(X0) ),
inference(resolution,[],[f52,f49]) ).
fof(f87,plain,
! [X0] :
( ~ greater(critical_point(X0),appear(efficient_producers,X0))
| critical_point(X0) = appear(efficient_producers,X0)
| ~ environment(X0) ),
inference(resolution,[],[f52,f48]) ).
fof(f88,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| end_time(X0) = X1
| ~ greater(end_time(X0),X1)
| ~ environment(X0) ),
inference(resolution,[],[f52,f43]) ).
fof(f89,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| zero = cardinality_at_time(first_movers,X1) ),
inference(resolution,[],[f45,f52]) ).
fof(f92,plain,
! [X0] :
( greater_or_equal(end_time(X0),start_time(X0))
| ~ environment(X0)
| in_environment(X0,end_time(X0)) ),
inference(resolution,[],[f42,f54]) ).
fof(f93,plain,
! [X0,X1] :
( greater_or_equal(X0,start_time(X1))
| ~ environment(X1)
| in_environment(X1,X0)
| greater(end_time(X1),X0) ),
inference(resolution,[],[f42,f53]) ).
fof(f95,plain,
! [X0] :
( ~ environment(X0)
| in_environment(X0,end_time(X0))
| ~ in_environment(X0,start_time(X0))
| ~ environment(X0) ),
inference(resolution,[],[f92,f43]) ).
fof(f96,plain,
! [X0] :
( greater(end_time(X0),start_time(X0))
| in_environment(X0,end_time(X0))
| ~ environment(X0) ),
inference(resolution,[],[f92,f53]) ).
fof(f97,plain,
! [X0] :
( in_environment(X0,end_time(X0))
| ~ environment(X0)
| ~ in_environment(X0,start_time(X0)) ),
inference(duplicate_literal_removal,[],[f95]) ).
fof(f101,plain,
! [X0] :
( greater(end_time(X0),start_time(X0))
| in_environment(X0,start_time(X0))
| ~ environment(X0) ),
inference(resolution,[],[f93,f54]) ).
fof(f104,plain,
! [X0] :
( ~ environment(X0)
| in_environment(X0,critical_point(X0))
| greater(end_time(X0),critical_point(X0))
| ~ environment(X0) ),
inference(resolution,[],[f93,f49]) ).
fof(f105,plain,
! [X0] :
( greater(end_time(X0),critical_point(X0))
| in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(duplicate_literal_removal,[],[f104]) ).
fof(f106,plain,
! [X0] :
( observational_period(sk3)
| ~ environment(X0)
| ~ in_environment(sk3,X0)
| in_environment(X0,sk2(X0,sk3)) ),
inference(resolution,[],[f40,f59]) ).
fof(f108,definition,
( spl0_6
<=> ! [X0] :
( ~ environment(X0)
| in_environment(X0,sk2(X0,sk3))
| ~ in_environment(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f109,plain,
( ! [X0] :
( in_environment(X0,sk2(X0,sk3))
| ~ environment(X0)
| ~ in_environment(sk3,X0) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl0_7
<=> observational_period(sk3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f113,plain,
( observational_period(sk3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f106,f111,f108]) ).
fof(f115,plain,
( $false
| ~ spl0_7 ),
inference(resolution,[],[f113,f58]) ).
fof(f116,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f115]) ).
fof(f117,plain,
( ! [X0] :
( ~ environment(X0)
| ~ in_environment(sk3,X0)
| end_time(X0) = sk2(X0,sk3)
| ~ greater(end_time(X0),sk2(X0,sk3))
| ~ environment(X0) )
| ~ spl0_6 ),
inference(resolution,[],[f109,f88]) ).
fof(f118,plain,
( ! [X0] :
( ~ in_environment(sk3,X0)
| ~ environment(X0)
| end_time(X0) = sk2(X0,sk3)
| ~ greater(end_time(X0),sk2(X0,sk3)) )
| ~ spl0_6 ),
inference(duplicate_literal_removal,[],[f117]) ).
fof(f119,plain,
( ~ environment(sk1(sk3))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| ~ greater(end_time(sk1(sk3)),sk2(sk1(sk3),sk3))
| selection_favors(efficient_producers,first_movers,sk3)
| observational_period(sk3)
| ~ spl0_4
| ~ spl0_6 ),
inference(resolution,[],[f118,f74]) ).
fof(f161,definition,
( spl0_17
<=> selection_favors(efficient_producers,first_movers,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f163,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl0_18
<=> greater(end_time(sk1(sk3)),sk2(sk1(sk3),sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f167,plain,
( ~ greater(end_time(sk1(sk3)),sk2(sk1(sk3),sk3))
| spl0_18 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f169,definition,
( spl0_19
<=> end_time(sk1(sk3)) = sk2(sk1(sk3),sk3) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f171,plain,
( end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f173,definition,
( spl0_20
<=> environment(sk1(sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f175,plain,
( ~ environment(sk1(sk3))
| spl0_20 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f176,plain,
( spl0_7
| spl0_17
| ~ spl0_18
| spl0_19
| ~ spl0_20
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f119,f108,f73,f173,f169,f165,f161,f111]) ).
fof(f183,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| observational_period(sk3)
| ~ spl0_5
| spl0_20 ),
inference(resolution,[],[f175,f78]) ).
fof(f184,plain,
( spl0_7
| spl0_17
| ~ spl0_5
| spl0_20 ),
inference(avatar_split_clause,[],[f183,f173,f77,f161,f111]) ).
fof(f185,plain,
( $false
| ~ spl0_17 ),
inference(resolution,[],[f163,f31]) ).
fof(f186,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f185]) ).
fof(f192,definition,
( spl0_21
<=> greater(sk2(sk1(sk3),sk3),start_time(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f193,plain,
( ~ greater(sk2(sk1(sk3),sk3),start_time(sk1(sk3)))
| spl0_21 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f194,plain,
( greater(sk2(sk1(sk3),sk3),start_time(sk1(sk3)))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f196,definition,
( spl0_22
<=> in_environment(sk1(sk3),sk2(sk1(sk3),sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f197,plain,
( ~ in_environment(sk1(sk3),sk2(sk1(sk3),sk3))
| spl0_22 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f198,plain,
( in_environment(sk1(sk3),sk2(sk1(sk3),sk3))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f200,plain,
( ~ environment(sk1(sk3))
| ~ in_environment(sk3,sk1(sk3))
| ~ spl0_6
| spl0_22 ),
inference(resolution,[],[f197,f109]) ).
fof(f202,definition,
( spl0_23
<=> in_environment(sk3,sk1(sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f204,plain,
( ~ in_environment(sk3,sk1(sk3))
| spl0_23 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f205,plain,
( ~ spl0_23
| ~ spl0_20
| ~ spl0_6
| spl0_22 ),
inference(avatar_split_clause,[],[f200,f196,f108,f173,f202]) ).
fof(f206,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| observational_period(sk3)
| ~ spl0_4
| spl0_23 ),
inference(resolution,[],[f204,f74]) ).
fof(f207,plain,
( spl0_7
| spl0_17
| ~ spl0_4
| spl0_23 ),
inference(avatar_split_clause,[],[f206,f202,f73,f161,f111]) ).
fof(f212,plain,
! [X0,X1] :
( greater(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1) ),
inference(resolution,[],[f57,f53]) ).
fof(f214,plain,
! [X0,X1] :
( ~ in_environment(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,end_time(X1))
| ~ greater(cardinality_at_time(efficient_producers,end_time(X1)),zero)
| ~ environment(X0)
| ~ environment(X1) ),
inference(resolution,[],[f57,f43]) ).
fof(f218,plain,
( in_environment(sk1(sk3),end_time(sk1(sk3)))
| ~ spl0_19
| ~ spl0_22 ),
inference(superposition,[],[f198,f171]) ).
fof(f221,definition,
( spl0_24
<=> in_environment(sk1(sk3),end_time(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f223,plain,
( in_environment(sk1(sk3),end_time(sk1(sk3)))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f225,plain,
( spl0_24
| ~ spl0_19
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f218,f196,f169,f221]) ).
fof(f228,definition,
( spl0_25
<=> in_environment(sk1(sk3),start_time(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f234,plain,
( ! [X0] :
( greater(X0,sk2(sk1(sk3),sk3))
| ~ greater(X0,start_time(sk1(sk3))) )
| spl0_21 ),
inference(resolution,[],[f193,f50]) ).
fof(f237,plain,
( ~ greater(end_time(sk1(sk3)),start_time(sk1(sk3)))
| spl0_18
| spl0_21 ),
inference(resolution,[],[f234,f167]) ).
fof(f238,plain,
( in_environment(sk1(sk3),start_time(sk1(sk3)))
| ~ environment(sk1(sk3))
| spl0_18
| spl0_21 ),
inference(resolution,[],[f237,f101]) ).
fof(f239,plain,
( in_environment(sk1(sk3),end_time(sk1(sk3)))
| ~ environment(sk1(sk3))
| spl0_18
| spl0_21 ),
inference(resolution,[],[f237,f96]) ).
fof(f247,plain,
( ~ spl0_20
| spl0_24
| spl0_18
| spl0_21 ),
inference(avatar_split_clause,[],[f239,f192,f165,f221,f173]) ).
fof(f248,plain,
( ~ spl0_20
| spl0_25
| spl0_18
| spl0_21 ),
inference(avatar_split_clause,[],[f238,f192,f165,f228,f173]) ).
fof(f250,plain,
! [X0] :
( observational_period(sk3)
| ~ environment(X0)
| ~ in_environment(sk3,X0)
| ~ greater(sk2(X0,sk3),critical_point(X0)) ),
inference(resolution,[],[f41,f59]) ).
fof(f252,definition,
( spl0_27
<=> ! [X0] :
( ~ environment(X0)
| ~ greater(sk2(X0,sk3),critical_point(X0))
| ~ in_environment(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f253,plain,
( ! [X0] :
( ~ in_environment(sk3,X0)
| ~ greater(sk2(X0,sk3),critical_point(X0))
| ~ environment(X0) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( spl0_27
| spl0_7 ),
inference(avatar_split_clause,[],[f250,f111,f252]) ).
fof(f256,plain,
( ~ greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3)))
| ~ environment(sk1(sk3))
| selection_favors(efficient_producers,first_movers,sk3)
| observational_period(sk3)
| ~ spl0_4
| ~ spl0_27 ),
inference(resolution,[],[f253,f74]) ).
fof(f260,definition,
( spl0_28
<=> greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f262,plain,
( ~ greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3)))
| spl0_28 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f263,plain,
( spl0_7
| spl0_17
| ~ spl0_20
| ~ spl0_28
| ~ spl0_4
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f256,f252,f73,f260,f173,f161,f111]) ).
fof(f265,plain,
( ! [X0] :
( greater(X0,sk2(sk1(sk3),sk3))
| ~ greater(X0,critical_point(sk1(sk3))) )
| spl0_28 ),
inference(resolution,[],[f262,f50]) ).
fof(f266,plain,
( ~ greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| spl0_18
| spl0_28 ),
inference(resolution,[],[f265,f167]) ).
fof(f267,plain,
( in_environment(sk1(sk3),critical_point(sk1(sk3)))
| ~ environment(sk1(sk3))
| spl0_18
| spl0_28 ),
inference(resolution,[],[f266,f105]) ).
fof(f271,definition,
( spl0_29
<=> greater(critical_point(sk1(sk3)),start_time(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f272,plain,
( ~ greater(critical_point(sk1(sk3)),start_time(sk1(sk3)))
| spl0_29 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f273,plain,
( greater(critical_point(sk1(sk3)),start_time(sk1(sk3)))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f275,definition,
( spl0_30
<=> in_environment(sk1(sk3),critical_point(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f279,plain,
( ~ spl0_20
| spl0_30
| spl0_18
| spl0_28 ),
inference(avatar_split_clause,[],[f267,f260,f165,f275,f173]) ).
fof(f281,plain,
( ! [X0] :
( greater(X0,critical_point(sk1(sk3)))
| ~ greater(X0,start_time(sk1(sk3))) )
| spl0_29 ),
inference(resolution,[],[f272,f50]) ).
fof(f284,plain,
( ~ greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| ~ spl0_19
| spl0_28 ),
inference(superposition,[],[f262,f171]) ).
fof(f288,plain,
( in_environment(sk1(sk3),critical_point(sk1(sk3)))
| ~ environment(sk1(sk3))
| ~ spl0_19
| spl0_28 ),
inference(resolution,[],[f284,f105]) ).
fof(f292,plain,
( ~ spl0_20
| spl0_30
| ~ spl0_19
| spl0_28 ),
inference(avatar_split_clause,[],[f288,f260,f169,f275,f173]) ).
fof(f307,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1(sk3),end_time(sk1(sk3)))
| ~ environment(sk1(sk3))
| ~ greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3))))
| spl0_18
| spl0_28 ),
inference(resolution,[],[f56,f266]) ).
fof(f319,definition,
( spl0_34
<=> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f321,plain,
( ~ greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3))))
| spl0_34 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f323,definition,
( spl0_35
<=> subpopulations(first_movers,efficient_producers,sk1(sk3),end_time(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f325,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1(sk3),end_time(sk1(sk3)))
| spl0_35 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f326,plain,
( ~ spl0_34
| ~ spl0_20
| ~ spl0_35
| spl0_18
| spl0_28 ),
inference(avatar_split_clause,[],[f307,f260,f165,f323,f173,f319]) ).
fof(f328,plain,
( ~ greater(sk2(sk1(sk3),sk3),start_time(sk1(sk3)))
| spl0_28
| spl0_29 ),
inference(resolution,[],[f281,f262]) ).
fof(f329,plain,
( ~ spl0_21
| spl0_28
| spl0_29 ),
inference(avatar_split_clause,[],[f328,f271,f260,f192]) ).
fof(f330,plain,
( start_time(sk1(sk3)) = critical_point(sk1(sk3))
| ~ environment(sk1(sk3))
| ~ spl0_29 ),
inference(resolution,[],[f273,f86]) ).
fof(f332,definition,
( spl0_36
<=> start_time(sk1(sk3)) = critical_point(sk1(sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f334,plain,
( start_time(sk1(sk3)) = critical_point(sk1(sk3))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f335,plain,
( ~ spl0_20
| spl0_36
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f330,f271,f332,f173]) ).
fof(f337,plain,
( greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3)))
| ~ spl0_21
| ~ spl0_36 ),
inference(superposition,[],[f194,f334]) ).
fof(f350,plain,
( spl0_28
| ~ spl0_21
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f337,f332,f192,f260]) ).
fof(f362,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,end_time(sk1(sk3)))
| ~ environment(X0)
| selection_favors(efficient_producers,first_movers,end_time(sk1(sk3))) )
| spl0_34 ),
inference(resolution,[],[f35,f321]) ).
fof(f364,definition,
( spl0_38
<=> selection_favors(efficient_producers,first_movers,end_time(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f366,plain,
( selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f368,definition,
( spl0_39
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,end_time(sk1(sk3)))
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f369,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,end_time(sk1(sk3)))
| ~ environment(X0) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f370,plain,
( spl0_38
| spl0_39
| spl0_34 ),
inference(avatar_split_clause,[],[f362,f319,f368,f364]) ).
fof(f371,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| observational_period(sk3)
| ~ spl0_3
| ~ spl0_38 ),
inference(resolution,[],[f366,f70]) ).
fof(f372,plain,
( spl0_7
| spl0_17
| ~ spl0_3
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f371,f364,f69,f161,f111]) ).
fof(f383,plain,
! [X0,X1] :
( greater(X1,critical_point(X0))
| ~ environment(X0)
| critical_point(X0) = appear(efficient_producers,X0)
| ~ greater(X1,appear(efficient_producers,X0)) ),
inference(resolution,[],[f87,f50]) ).
fof(f390,plain,
( ~ environment(sk1(sk3))
| ~ greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)
| zero = cardinality_at_time(first_movers,end_time(sk1(sk3)))
| ~ spl0_24 ),
inference(resolution,[],[f89,f223]) ).
fof(f424,definition,
( spl0_48
<=> zero = cardinality_at_time(first_movers,end_time(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f426,plain,
( zero = cardinality_at_time(first_movers,end_time(sk1(sk3)))
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f428,definition,
( spl0_49
<=> greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero) ),
introduced(definition,[new_symbols(definition,[spl0_49])],[avatar_definition]) ).
fof(f431,plain,
( spl0_48
| ~ spl0_49
| ~ spl0_20
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f390,f221,f173,f428,f424]) ).
fof(f478,plain,
( ~ environment(sk1(sk3))
| critical_point(sk1(sk3)) = appear(efficient_producers,sk1(sk3))
| ~ greater(end_time(sk1(sk3)),appear(efficient_producers,sk1(sk3)))
| spl0_18
| spl0_28 ),
inference(resolution,[],[f383,f266]) ).
fof(f485,definition,
( spl0_52
<=> critical_point(sk1(sk3)) = appear(efficient_producers,sk1(sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f487,plain,
( critical_point(sk1(sk3)) = appear(efficient_producers,sk1(sk3))
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f490,definition,
( spl0_53
<=> greater(end_time(sk1(sk3)),appear(efficient_producers,sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_53])],[avatar_definition]) ).
fof(f492,plain,
( ~ greater(end_time(sk1(sk3)),appear(efficient_producers,sk1(sk3)))
| spl0_53 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f493,plain,
( ~ spl0_53
| spl0_52
| ~ spl0_20
| spl0_18
| spl0_28 ),
inference(avatar_split_clause,[],[f478,f260,f165,f173,f485,f490]) ).
fof(f495,plain,
( ~ environment(sk1(sk3))
| ~ greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)
| ~ in_environment(sk1(sk3),end_time(sk1(sk3)))
| spl0_53 ),
inference(resolution,[],[f492,f212]) ).
fof(f498,definition,
( spl0_54
<=> greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero) ),
introduced(definition,[new_symbols(definition,[spl0_54])],[avatar_definition]) ).
fof(f500,plain,
( ~ greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)
| spl0_54 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f501,plain,
( ~ spl0_24
| ~ spl0_54
| ~ spl0_20
| spl0_53 ),
inference(avatar_split_clause,[],[f495,f490,f173,f498,f221]) ).
fof(f507,definition,
( spl0_56
<=> in_environment(sk1(sk3),appear(efficient_producers,sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_56])],[avatar_definition]) ).
fof(f508,plain,
( ~ in_environment(sk1(sk3),appear(efficient_producers,sk1(sk3)))
| spl0_56 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f509,plain,
( in_environment(sk1(sk3),appear(efficient_producers,sk1(sk3)))
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f511,plain,
( ! [X0] :
( ~ in_environment(X0,end_time(sk1(sk3)))
| greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,end_time(sk1(sk3))) )
| spl0_54 ),
inference(resolution,[],[f500,f44]) ).
fof(f512,plain,
( ! [X0,X1] :
( zero != cardinality_at_time(X1,end_time(sk1(sk3)))
| subpopulation(X1,X0,end_time(sk1(sk3)))
| ~ environment(X0)
| subpopulation(efficient_producers,X0,end_time(sk1(sk3)))
| selection_favors(efficient_producers,X1,end_time(sk1(sk3))) )
| spl0_54 ),
inference(resolution,[],[f500,f36]) ).
fof(f515,definition,
( spl0_57
<=> ! [X0] :
( ~ in_environment(X0,end_time(sk1(sk3)))
| subpopulations(first_movers,efficient_producers,X0,end_time(sk1(sk3)))
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_57])],[avatar_definition]) ).
fof(f516,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,X0,end_time(sk1(sk3)))
| ~ in_environment(X0,end_time(sk1(sk3)))
| ~ environment(X0) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f517,plain,
( spl0_49
| spl0_57
| spl0_54 ),
inference(avatar_split_clause,[],[f511,f498,f515,f428]) ).
fof(f540,plain,
( ~ in_environment(sk1(sk3),end_time(sk1(sk3)))
| ~ environment(sk1(sk3))
| spl0_35
| ~ spl0_57 ),
inference(resolution,[],[f516,f325]) ).
fof(f541,plain,
( ! [X0] :
( ~ in_environment(X0,end_time(sk1(sk3)))
| ~ environment(X0)
| ~ environment(X0) )
| ~ spl0_39
| ~ spl0_57 ),
inference(resolution,[],[f516,f369]) ).
fof(f542,plain,
( ! [X0] :
( ~ in_environment(X0,end_time(sk1(sk3)))
| ~ environment(X0) )
| ~ spl0_39
| ~ spl0_57 ),
inference(duplicate_literal_removal,[],[f541]) ).
fof(f544,plain,
( ~ environment(sk1(sk3))
| ~ spl0_24
| ~ spl0_39
| ~ spl0_57 ),
inference(resolution,[],[f542,f223]) ).
fof(f546,plain,
( ~ spl0_20
| ~ spl0_24
| ~ spl0_39
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f544,f515,f368,f221,f173]) ).
fof(f574,plain,
( ! [X0] :
( zero != zero
| subpopulation(first_movers,X0,end_time(sk1(sk3)))
| ~ environment(X0)
| subpopulation(efficient_producers,X0,end_time(sk1(sk3)))
| selection_favors(efficient_producers,first_movers,end_time(sk1(sk3))) )
| ~ spl0_48
| spl0_54 ),
inference(superposition,[],[f512,f426]) ).
fof(f575,plain,
( ! [X0] :
( subpopulation(first_movers,X0,end_time(sk1(sk3)))
| ~ environment(X0)
| subpopulation(efficient_producers,X0,end_time(sk1(sk3)))
| selection_favors(efficient_producers,first_movers,end_time(sk1(sk3))) )
| ~ spl0_48
| spl0_54 ),
inference(trivial_inequality_removal,[],[f574]) ).
fof(f577,definition,
( spl0_64
<=> ! [X0] :
( subpopulation(first_movers,X0,end_time(sk1(sk3)))
| subpopulation(efficient_producers,X0,end_time(sk1(sk3)))
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_64])],[avatar_definition]) ).
fof(f578,plain,
( ! [X0] :
( subpopulation(efficient_producers,X0,end_time(sk1(sk3)))
| subpopulation(first_movers,X0,end_time(sk1(sk3)))
| ~ environment(X0) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f579,plain,
( spl0_38
| spl0_64
| ~ spl0_48
| spl0_54 ),
inference(avatar_split_clause,[],[f575,f498,f424,f577,f364]) ).
fof(f580,plain,
( ! [X0] :
( subpopulation(first_movers,X0,end_time(sk1(sk3)))
| ~ environment(X0)
| ~ in_environment(X0,end_time(sk1(sk3)))
| ~ environment(X0) )
| ~ spl0_64 ),
inference(resolution,[],[f578,f47]) ).
fof(f581,plain,
( ! [X0] :
( subpopulation(first_movers,X0,end_time(sk1(sk3)))
| ~ environment(X0)
| ~ in_environment(X0,end_time(sk1(sk3))) )
| ~ spl0_64 ),
inference(duplicate_literal_removal,[],[f580]) ).
fof(f582,plain,
( ! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,end_time(sk1(sk3)))
| ~ in_environment(X0,end_time(sk1(sk3)))
| ~ environment(X0) )
| ~ spl0_64 ),
inference(resolution,[],[f581,f46]) ).
fof(f583,plain,
( ! [X0] :
( ~ in_environment(X0,end_time(sk1(sk3)))
| ~ environment(X0) )
| ~ spl0_64 ),
inference(duplicate_literal_removal,[],[f582]) ).
fof(f584,plain,
( ~ environment(sk1(sk3))
| ~ environment(sk1(sk3))
| ~ in_environment(sk1(sk3),start_time(sk1(sk3)))
| ~ spl0_64 ),
inference(resolution,[],[f583,f97]) ).
fof(f585,plain,
( ~ environment(sk1(sk3))
| ~ spl0_24
| ~ spl0_64 ),
inference(resolution,[],[f583,f223]) ).
fof(f586,plain,
( ~ environment(sk1(sk3))
| ~ in_environment(sk1(sk3),start_time(sk1(sk3)))
| ~ spl0_64 ),
inference(duplicate_literal_removal,[],[f584]) ).
fof(f587,plain,
( ~ spl0_20
| ~ spl0_24
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f585,f577,f221,f173]) ).
fof(f588,plain,
( ~ spl0_25
| ~ spl0_20
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f586,f577,f173,f228]) ).
fof(f594,plain,
( ~ in_environment(sk1(sk3),critical_point(sk1(sk3)))
| ~ spl0_52
| spl0_56 ),
inference(superposition,[],[f508,f487]) ).
fof(f612,plain,
( ~ spl0_30
| ~ spl0_52
| spl0_56 ),
inference(avatar_split_clause,[],[f594,f507,f485,f275]) ).
fof(f615,plain,
( ~ in_environment(sk1(sk3),end_time(sk1(sk3)))
| ~ greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)
| ~ environment(sk1(sk3))
| ~ environment(sk1(sk3))
| ~ spl0_56 ),
inference(resolution,[],[f509,f214]) ).
fof(f619,plain,
( ~ in_environment(sk1(sk3),end_time(sk1(sk3)))
| ~ greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)
| ~ environment(sk1(sk3))
| ~ spl0_56 ),
inference(duplicate_literal_removal,[],[f615]) ).
fof(f634,plain,
( ~ spl0_20
| ~ spl0_54
| ~ spl0_24
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f619,f507,f221,f498,f173]) ).
fof(f704,plain,
( ~ environment(sk1(sk3))
| critical_point(sk1(sk3)) = appear(efficient_producers,sk1(sk3))
| ~ greater(end_time(sk1(sk3)),appear(efficient_producers,sk1(sk3)))
| ~ spl0_19
| spl0_28 ),
inference(resolution,[],[f284,f383]) ).
fof(f706,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1(sk3),end_time(sk1(sk3)))
| ~ environment(sk1(sk3))
| ~ greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3))))
| ~ spl0_19
| spl0_28 ),
inference(resolution,[],[f284,f56]) ).
fof(f708,plain,
( ~ spl0_34
| ~ spl0_20
| ~ spl0_35
| ~ spl0_19
| spl0_28 ),
inference(avatar_split_clause,[],[f706,f260,f169,f323,f173,f319]) ).
fof(f709,plain,
( ~ spl0_53
| spl0_52
| ~ spl0_20
| ~ spl0_19
| spl0_28 ),
inference(avatar_split_clause,[],[f704,f260,f169,f173,f485,f490]) ).
fof(f710,plain,
( ~ spl0_20
| ~ spl0_24
| spl0_35
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f540,f515,f323,f221,f173]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f71]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f75]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f79]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f81]) ).
cnf(s5,plain,
spl0_2,
inference(sat_conversion,[],[f83]) ).
cnf(s6,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f114]) ).
cnf(s7,plain,
~ spl0_7,
inference(sat_conversion,[],[f116]) ).
cnf(s10,plain,
( ~ spl0_4
| ~ spl0_6
| spl0_7
| spl0_17
| ~ spl0_18
| spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f176]) ).
cnf(s11,plain,
( ~ spl0_5
| spl0_7
| spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f184]) ).
cnf(s12,plain,
~ spl0_17,
inference(sat_conversion,[],[f186]) ).
cnf(s14,plain,
( ~ spl0_6
| ~ spl0_20
| spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f205]) ).
cnf(s15,plain,
( ~ spl0_4
| spl0_7
| spl0_17
| spl0_23 ),
inference(sat_conversion,[],[f207]) ).
cnf(s17,plain,
( ~ spl0_19
| ~ spl0_22
| spl0_24 ),
inference(sat_conversion,[],[f225]) ).
cnf(s20,plain,
( spl0_18
| ~ spl0_20
| spl0_21
| spl0_24 ),
inference(sat_conversion,[],[f247]) ).
cnf(s21,plain,
( spl0_18
| ~ spl0_20
| spl0_21
| spl0_25 ),
inference(sat_conversion,[],[f248]) ).
cnf(s22,plain,
( spl0_7
| spl0_27 ),
inference(sat_conversion,[],[f254]) ).
cnf(s23,plain,
( ~ spl0_4
| spl0_7
| spl0_17
| ~ spl0_20
| ~ spl0_27
| ~ spl0_28 ),
inference(sat_conversion,[],[f263]) ).
cnf(s26,plain,
( spl0_18
| ~ spl0_20
| spl0_28
| spl0_30 ),
inference(sat_conversion,[],[f279]) ).
cnf(s29,plain,
( ~ spl0_19
| ~ spl0_20
| spl0_28
| spl0_30 ),
inference(sat_conversion,[],[f292]) ).
cnf(s32,plain,
( spl0_18
| ~ spl0_20
| spl0_28
| ~ spl0_34
| ~ spl0_35 ),
inference(sat_conversion,[],[f326]) ).
cnf(s33,plain,
( ~ spl0_21
| spl0_28
| spl0_29 ),
inference(sat_conversion,[],[f329]) ).
cnf(s34,plain,
( ~ spl0_20
| ~ spl0_29
| spl0_36 ),
inference(sat_conversion,[],[f335]) ).
cnf(s37,plain,
( ~ spl0_21
| spl0_28
| ~ spl0_36 ),
inference(sat_conversion,[],[f350]) ).
cnf(s38,plain,
( spl0_34
| spl0_38
| spl0_39 ),
inference(sat_conversion,[],[f370]) ).
cnf(s39,plain,
( ~ spl0_3
| spl0_7
| spl0_17
| ~ spl0_38 ),
inference(sat_conversion,[],[f372]) ).
cnf(s44,plain,
( ~ spl0_20
| ~ spl0_24
| spl0_48
| ~ spl0_49 ),
inference(sat_conversion,[],[f431]) ).
cnf(s47,plain,
( spl0_18
| ~ spl0_20
| spl0_28
| spl0_52
| ~ spl0_53 ),
inference(sat_conversion,[],[f493]) ).
cnf(s48,plain,
( ~ spl0_20
| ~ spl0_24
| spl0_53
| ~ spl0_54 ),
inference(sat_conversion,[],[f501]) ).
cnf(s50,plain,
( spl0_49
| spl0_54
| spl0_57 ),
inference(sat_conversion,[],[f517]) ).
cnf(s53,plain,
( ~ spl0_20
| ~ spl0_24
| ~ spl0_39
| ~ spl0_57 ),
inference(sat_conversion,[],[f546]) ).
cnf(s59,plain,
( spl0_38
| ~ spl0_48
| spl0_54
| spl0_64 ),
inference(sat_conversion,[],[f579]) ).
cnf(s60,plain,
( ~ spl0_20
| ~ spl0_24
| ~ spl0_64 ),
inference(sat_conversion,[],[f587]) ).
cnf(s61,plain,
( ~ spl0_20
| ~ spl0_25
| ~ spl0_64 ),
inference(sat_conversion,[],[f588]) ).
cnf(s67,plain,
( ~ spl0_30
| ~ spl0_52
| spl0_56 ),
inference(sat_conversion,[],[f612]) ).
cnf(s71,plain,
( ~ spl0_20
| ~ spl0_24
| ~ spl0_54
| ~ spl0_56 ),
inference(sat_conversion,[],[f634]) ).
cnf(s83,plain,
( ~ spl0_19
| ~ spl0_20
| spl0_28
| ~ spl0_34
| ~ spl0_35 ),
inference(sat_conversion,[],[f708]) ).
cnf(s84,plain,
( ~ spl0_19
| ~ spl0_20
| spl0_28
| spl0_52
| ~ spl0_53 ),
inference(sat_conversion,[],[f709]) ).
cnf(s85,plain,
( ~ spl0_20
| ~ spl0_24
| spl0_35
| ~ spl0_57 ),
inference(sat_conversion,[],[f710]) ).
cnf(s86,plain,
( ~ spl0_5
| spl0_7
| spl0_20 ),
inference(rat,[],[s11,s12]) ).
cnf(s87,plain,
( ~ spl0_4
| ~ spl0_6
| spl0_7
| ~ spl0_18
| spl0_19
| ~ spl0_20 ),
inference(rat,[],[s10,s12]) ).
cnf(s88,plain,
spl0_27,
inference(rat,[],[s22,s7]) ).
cnf(s89,plain,
spl0_6,
inference(rat,[],[s6,s7]) ).
cnf(s90,plain,
spl0_5,
inference(rat,[],[s3,s5,s4]) ).
cnf(s91,plain,
spl0_20,
inference(rat,[],[s86,s7,s90]) ).
cnf(s92,plain,
spl0_4,
inference(rat,[],[s2,s5,s4]) ).
cnf(s93,plain,
~ spl0_28,
inference(rat,[],[s23,s91,s88,s7,s12,s92]) ).
cnf(s94,plain,
spl0_23,
inference(rat,[],[s15,s7,s12,s92]) ).
cnf(s95,plain,
spl0_22,
inference(rat,[],[s14,s91,s89,s94]) ).
cnf(s96,plain,
spl0_3,
inference(rat,[],[s1,s5,s4]) ).
cnf(s97,plain,
~ spl0_38,
inference(rat,[],[s39,s7,s12,s96]) ).
cnf(s98,plain,
( spl0_54
| spl0_57
| spl0_64
| ~ spl0_24 ),
inference(rat,[],[s44,s59,s50,s91,s97]) ).
cnf(s99,plain,
( ~ spl0_54
| ~ spl0_24
| spl0_18 ),
inference(rat,[],[s47,s67,s48,s71,s26,s91,s93]) ).
cnf(s100,plain,
( spl0_21
| spl0_18 ),
inference(rat,[],[s38,s32,s53,s85,s98,s99,s61,s20,s21,s93,s91,s97]) ).
cnf(s101,plain,
~ spl0_21,
inference(rat,[],[s34,s33,s37,s91,s93]) ).
cnf(s102,plain,
spl0_18,
inference(rat,[],[s100,s101]) ).
cnf(s103,plain,
spl0_19,
inference(rat,[],[s87,s91,s92,s89,s7,s102]) ).
cnf(s105,plain,
spl0_30,
inference(rat,[],[s29,s93,s91,s103]) ).
cnf(s106,plain,
spl0_24,
inference(rat,[],[s17,s95,s103]) ).
cnf(s109,plain,
~ spl0_64,
inference(rat,[],[s60,s91,s106]) ).
cnf(s111,plain,
~ spl0_54,
inference(rat,[],[s84,s67,s48,s71,s91,s93,s103,s105,s106]) ).
cnf(s113,plain,
spl0_57,
inference(rat,[],[s98,s106,s109,s111]) ).
cnf(s115,plain,
spl0_35,
inference(rat,[],[s85,s106,s91,s113]) ).
cnf(s116,plain,
~ spl0_39,
inference(rat,[],[s53,s106,s91,s113]) ).
cnf(s118,plain,
~ spl0_34,
inference(rat,[],[s83,s103,s93,s91,s115]) ).
cnf(s119,plain,
$false,
inference(rat,[],[s38,s97,s116,s118]) ).
fof(f711,plain,
$false,
inference(avatar_sat_refutation,[],[s119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT039-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n007.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 17:21:41 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.44 Running first-order model finding
% 0.13/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.50 % (1677350)Will run a generic schedule for satisfiability detection.
% 0.18/0.50 % (1677359)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=383138850:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.50 % (1677356)% WARNING: option uhcvi not known.
% 0.18/0.50 % (1677355)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1749739431_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.50 % (1677360)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1914207268:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.50 % (1677356)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3076548071:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.50 % (1677357)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3875922827:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.50 % (1677358)dis+10_1_sil=32000:sp=arity:random_seed=3231041706:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.50 % (1677361)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4047809909:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.50 % TRYING [1]
% 0.18/0.50 % TRYING [2]
% 0.18/0.50 % TRYING [3]
% 0.18/0.50 % (1677361) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1677350-1677361"...
% 0.18/0.50 % (1677356) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1677350-1677356"...
% 0.18/0.50 % (1677360) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1677350-1677360"...
% 0.18/0.50 % (1677361)...printing done.
% 0.18/0.50 % (1677361)Refutation found. Thanks to Tanya!
% 0.18/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50 % (1677361)------------------------------
% 0.18/0.50 % (1677361)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.50 % (1677361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.50 % (1677361)CaDiCaL version: 2.1.3
% 0.18/0.50 % (1677361)Termination reason: Refutation
% 0.18/0.50 % (1677361)Time elapsed: 0.019 s
% 0.18/0.50 % (1677361)Peak memory usage: 13 MB
% 0.18/0.50 % (1677361)Instructions burned: 25 (million)
% 0.18/0.50 % (1677350)Success in time 0.054 s
% 0.18/0.50 % Vampire exiting
%------------------------------------------------------------------------------