%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT034-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:02:36 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 34
% Syntax : Number of formulae : 134 ( 23 unt; 11 def)
% Number of atoms : 350 ( 7 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 420 ( 204 ~; 205 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 12 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 78 !; 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/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates_33) ).
fof(f2,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_34) ).
fof(f3,axiom,
! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,critical_point(X0))
| subpopulations(first_movers,efficient_producers,X0,critical_point(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP_35) ).
fof(f4,axiom,
! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,appear(efficient_producers,X0))
| subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears_36) ).
fof(f5,axiom,
! [X0] :
( ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_difference_between_founding_rates_37) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ greater_or_equal(X2,appear(efficient_producers,X0))
| ~ greater(X1,X2)
| ~ decreases(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)))
| greater(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_decreasing_function_38) ).
fof(f7,axiom,
! [X0] :
( ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_negative_growth_rate_difference_39) ).
fof(f9,axiom,
! [X0] :
( ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_growth_rate_difference_41) ).
fof(f14,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,critical_point(X0))
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(critical_point(X0),X1)
| in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_time_points_46) ).
fof(f16,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(efficient_producers,first_movers,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_48) ).
fof(f17,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater_or_equal(X1,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared_49) ).
fof(f18,axiom,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_50) ).
fof(f19,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_51) ).
fof(f20,axiom,
! [X0,X1] :
( X0 != X1
| greater_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_52) ).
fof(f21,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_relationship_of_growth_rates_53) ).
fof(f22,axiom,
! [X0,X1] :
( ~ environment(X0)
| X1 != critical_point(X0)
| ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_54) ).
fof(f23,plain,
! [X0,X1] :
( ~ environment(X0)
| critical_point(X0) != X1
| ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(reorient_equations,[],[f22]) ).
fof(f26,axiom,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X2,X3)
| subpopulations(first_movers,efficient_producers,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a10_56) ).
fof(f27,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12_57) ).
fof(f28,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_58) ).
fof(f29,negated_conjecture,
in_environment(sk1,critical_point(sk1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_59) ).
fof(f30,negated_conjecture,
greater_or_equal(sk2,appear(efficient_producers,sk1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_60) ).
fof(f31,negated_conjecture,
greater(critical_point(sk1),sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_61) ).
fof(f32,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_62) ).
fof(f33,plain,
! [X1] : greater_or_equal(X1,X1),
inference(equality_resolution,[],[f20]) ).
fof(f34,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ~ environment(X0) ),
inference(equality_resolution,[],[f23]) ).
fof(f36,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(f37,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f38,plain,
! [X0] :
( ~ environment(X0)
| in_environment(X0,critical_point(X0))
| subpopulations(first_movers,efficient_producers,X0,critical_point(X0)) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f39,plain,
! [X0] :
( ~ environment(X0)
| in_environment(X0,appear(efficient_producers,X0))
| subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f40,plain,
! [X0] :
( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| ~ decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| in_environment(X0,X1)
| ~ environment(X0)
| ~ greater_or_equal(X2,appear(efficient_producers,X0))
| ~ greater(X1,X2)
| decreases(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)))
| greater(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| in_environment(X0,critical_point(X0))
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(critical_point(X0),X1)
| ~ environment(X0) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f46,plain,
! [X0,X1] :
( ~ decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(consistent_polarity_flipping,[],[f27]) ).
fof(f47,plain,
~ in_environment(sk1,critical_point(sk1)),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f48,plain,
selection_favors(first_movers,efficient_producers,sk2),
inference(consistent_polarity_flipping,[],[f32]) ).
fof(f49,plain,
greater_or_equal(critical_point(sk1),sk2),
inference(resolution,[],[f19,f31]) ).
fof(f63,plain,
( in_environment(sk1,critical_point(sk1))
| subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1)) ),
inference(resolution,[],[f38,f28]) ).
fof(f64,plain,
subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1)),
inference(forward_subsumption_resolution,[],[f63,f47]) ).
fof(f65,plain,
( in_environment(sk1,appear(efficient_producers,sk1))
| subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)) ),
inference(resolution,[],[f39,f28]) ).
fof(f67,definition,
( spl0_3
<=> subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f68,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1))
| spl0_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f69,plain,
( subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f71,definition,
( spl0_4
<=> in_environment(sk1,appear(efficient_producers,sk1)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f73,plain,
( in_environment(sk1,appear(efficient_producers,sk1))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f65,f71,f67]) ).
fof(f77,plain,
( ~ environment(sk1)
| greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)) ),
inference(resolution,[],[f64,f17]) ).
fof(f80,plain,
greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)),
inference(forward_subsumption_resolution,[],[f77,f28]) ).
fof(f82,plain,
( greater(critical_point(sk1),appear(efficient_producers,sk1))
| critical_point(sk1) = appear(efficient_producers,sk1) ),
inference(resolution,[],[f80,f18]) ).
fof(f84,definition,
( spl0_5
<=> critical_point(sk1) = appear(efficient_producers,sk1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f86,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_6
<=> greater(critical_point(sk1),appear(efficient_producers,sk1)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f90,plain,
( greater(critical_point(sk1),appear(efficient_producers,sk1))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f82,f88,f84]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ greater_or_equal(X2,X0)
| ~ greater_or_equal(X1,X2)
| subpopulations(first_movers,efficient_producers,sk1,X2) ),
inference(resolution,[],[f26,f28]) ).
fof(f93,plain,
! [X0] :
( greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[],[f21,f28]) ).
fof(f111,definition,
( spl0_8
<=> subpopulations(first_movers,efficient_producers,sk1,sk2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f112,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f116,plain,
( ! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater_or_equal(X0,X1)
| subpopulations(first_movers,efficient_producers,sk1,X1) )
| ~ spl0_3 ),
inference(resolution,[],[f92,f69]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| in_environment(X1,X0)
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ greater(X0,X2)
| decreases(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)))
| greater(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero) ),
inference(resolution,[],[f93,f41]) ).
fof(f139,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,sk1))
| in_environment(sk1,X0)
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater(X0,X1)
| decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(resolution,[],[f118,f28]) ).
fof(f146,definition,
( spl0_11
<=> greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f148,plain,
( greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f150,definition,
( spl0_12
<=> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f154,definition,
( spl0_13
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater(X0,sk2)
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| in_environment(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f155,plain,
( ! [X0] :
( ~ greater(X0,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| in_environment(sk1,X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f172,definition,
( spl0_16
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater_or_equal(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f173,plain,
( ! [X0] :
( ~ greater_or_equal(X0,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f176,plain,
( ~ environment(sk1)
| decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_8 ),
inference(resolution,[],[f112,f37]) ).
fof(f178,plain,
( ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ spl0_8 ),
inference(resolution,[],[f112,f16]) ).
fof(f179,plain,
( subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f178,f28]) ).
fof(f180,plain,
( decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f176,f28]) ).
fof(f207,definition,
( spl0_20
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f208,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f212,plain,
! [X0] :
( in_environment(sk1,X0)
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater(X0,sk2)
| decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero) ),
inference(resolution,[],[f139,f30]) ).
fof(f213,plain,
( spl0_11
| spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f212,f154,f150,f146]) ).
fof(f227,plain,
( decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))
| ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| ~ spl0_8 ),
inference(resolution,[],[f180,f40]) ).
fof(f229,definition,
( spl0_23
<=> decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f231,plain,
( decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f237,plain,
( in_environment(sk1,critical_point(sk1))
| ~ greater_or_equal(appear(efficient_producers,sk1),appear(efficient_producers,sk1))
| ~ greater(critical_point(sk1),appear(efficient_producers,sk1))
| ~ environment(sk1)
| ~ spl0_4 ),
inference(resolution,[],[f73,f44]) ).
fof(f240,plain,
( ~ greater_or_equal(appear(efficient_producers,sk1),appear(efficient_producers,sk1))
| ~ greater(critical_point(sk1),appear(efficient_producers,sk1))
| ~ environment(sk1)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f237,f47]) ).
fof(f248,plain,
( ~ greater(critical_point(sk1),appear(efficient_producers,sk1))
| ~ environment(sk1)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f240,f33]) ).
fof(f249,plain,
( ~ environment(sk1)
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f248,f90]) ).
fof(f250,plain,
( $false
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f249,f28]) ).
fof(f251,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f250]) ).
fof(f276,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f68,f86]) ).
fof(f290,plain,
( $false
| spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f276,f64]) ).
fof(f291,plain,
( spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f290]) ).
fof(f324,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater_or_equal(X0,sk2)
| subpopulations(first_movers,efficient_producers,sk1,sk2) )
| ~ spl0_3 ),
inference(resolution,[],[f116,f30]) ).
fof(f325,plain,
( greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))
| ~ spl0_11 ),
inference(resolution,[],[f148,f9]) ).
fof(f328,plain,
( ! [X0] :
( ~ subpopulations(efficient_producers,first_movers,X0,sk2)
| ~ environment(X0)
| ~ selection_favors(first_movers,efficient_producers,sk2) )
| ~ spl0_11 ),
inference(resolution,[],[f325,f36]) ).
fof(f330,plain,
( ! [X0] :
( ~ subpopulations(efficient_producers,first_movers,X0,sk2)
| ~ environment(X0) )
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f328,f48]) ).
fof(f334,plain,
( ~ environment(sk1)
| ~ spl0_8
| ~ spl0_11 ),
inference(resolution,[],[f330,f179]) ).
fof(f335,plain,
( $false
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f334,f28]) ).
fof(f336,plain,
( ~ spl0_8
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f381,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) )
| ~ spl0_23 ),
inference(resolution,[],[f231,f46]) ).
fof(f382,plain,
( spl0_20
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f381,f229,f207]) ).
fof(f384,plain,
( spl0_8
| spl0_16
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f324,f67,f172,f111]) ).
fof(f387,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| ~ spl0_16 ),
inference(resolution,[],[f173,f49]) ).
fof(f388,plain,
( $false
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f387,f64]) ).
fof(f389,plain,
~ spl0_16,
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f390,plain,
( ~ spl0_12
| spl0_23
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f227,f111,f229,f150]) ).
fof(f399,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))
| in_environment(sk1,critical_point(sk1))
| ~ spl0_13 ),
inference(resolution,[],[f155,f31]) ).
fof(f400,plain,
( greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))
| in_environment(sk1,critical_point(sk1))
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f399,f64]) ).
fof(f401,plain,
( greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f400,f47]) ).
fof(f429,plain,
( greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1)))
| ~ spl0_13 ),
inference(resolution,[],[f401,f7]) ).
fof(f435,plain,
( ~ environment(sk1)
| ~ spl0_13 ),
inference(resolution,[],[f429,f34]) ).
fof(f447,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f435,f28]) ).
fof(f448,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f447]) ).
fof(f457,plain,
( ~ environment(sk1)
| ~ spl0_8
| ~ spl0_20 ),
inference(resolution,[],[f208,f112]) ).
fof(f458,plain,
( $false
| ~ spl0_8
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f457,f28]) ).
fof(f459,plain,
( ~ spl0_8
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f458]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f74]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f91]) ).
cnf(s14,plain,
( spl0_11
| spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f213]) ).
cnf(s21,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f251]) ).
cnf(s31,plain,
( spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f291]) ).
cnf(s39,plain,
( ~ spl0_8
| ~ spl0_11 ),
inference(sat_conversion,[],[f336]) ).
cnf(s43,plain,
( spl0_20
| ~ spl0_23 ),
inference(sat_conversion,[],[f382]) ).
cnf(s45,plain,
( ~ spl0_3
| spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f384]) ).
cnf(s47,plain,
~ spl0_16,
inference(sat_conversion,[],[f389]) ).
cnf(s48,plain,
( ~ spl0_8
| ~ spl0_12
| spl0_23 ),
inference(sat_conversion,[],[f390]) ).
cnf(s55,plain,
~ spl0_13,
inference(sat_conversion,[],[f448]) ).
cnf(s59,plain,
( ~ spl0_8
| ~ spl0_20 ),
inference(sat_conversion,[],[f459]) ).
cnf(s60,plain,
( ~ spl0_3
| spl0_8 ),
inference(rat,[],[s45,s47]) ).
cnf(s64,plain,
( spl0_11
| spl0_12 ),
inference(rat,[],[s14,s55]) ).
cnf(s68,plain,
spl0_3,
inference(rat,[],[s21,s3,s2,s31]) ).
cnf(s69,plain,
spl0_8,
inference(rat,[],[s60,s68]) ).
cnf(s72,plain,
~ spl0_20,
inference(rat,[],[s59,s69]) ).
cnf(s73,plain,
~ spl0_11,
inference(rat,[],[s39,s69]) ).
cnf(s74,plain,
~ spl0_23,
inference(rat,[],[s43,s72]) ).
cnf(s75,plain,
spl0_12,
inference(rat,[],[s64,s73]) ).
cnf(s76,plain,
$false,
inference(rat,[],[s48,s69,s74,s75]) ).
fof(f460,plain,
$false,
inference(avatar_sat_refutation,[],[s76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT034-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 17:21:37 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.48 % (435591)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (435598)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1900647294:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (435597)% WARNING: option uhcvi not known.
% 0.16/0.48 % (435596)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2744681923_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (435597)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1985151073:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (435599)dis+10_1_sil=32000:sp=arity:random_seed=1231969273:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (435600)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3274360893:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (435602)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4259979996:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (435601)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3641980288:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % (435597) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-435591-435597"...
% 0.16/0.48 % (435601) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-435591-435601"...
% 0.16/0.48 % (435597)...printing done.
% 0.16/0.48 % (435601)...printing done.
% 0.16/0.48 % (435597)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (435597)------------------------------
% 0.16/0.48 % (435597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (435597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (435597)CaDiCaL version: 2.1.3
% 0.16/0.48 % (435597)Termination reason: Refutation
% 0.16/0.48 % (435597)Time elapsed: 0.017 s
% 0.16/0.48 % (435597)Peak memory usage: 12 MB
% 0.16/0.48 % (435597)Instructions burned: 22 (million)
% 0.16/0.48 % (435591)Success in time 0.055 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------