%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT024-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 12:02:04 PM UTC 2026
% Result : Unsatisfiable 2.07s 1.15s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of formulae : 115 ( 16 unt; 11 def)
% Number of atoms : 420 ( 21 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 500 ( 195 ~; 294 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 11 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur_24) ).
fof(f2,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_number_of_organizations_25) ).
fof(f3,axiom,
! [X0,X1] :
( ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_equilibrium_26) ).
fof(f5,axiom,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(number_of_organizations(X0,X1),zero)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_28) ).
fof(f7,axiom,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6_30) ).
fof(f8,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| growth_rate(first_movers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_31) ).
fof(f9,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| zero = growth_rate(first_movers,X1)
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| growth_rate(first_movers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_32) ).
fof(f11,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| zero = growth_rate(first_movers,X1)
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1)) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| growth_rate(first_movers,X1) = zero
| greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_33) ).
fof(f13,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| zero = growth_rate(first_movers,X1)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| growth_rate(first_movers,X1) = zero
| greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_34) ).
fof(f15,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| zero = growth_rate(first_movers,X1)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1)) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| growth_rate(efficient_producers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_35) ).
fof(f17,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| zero = growth_rate(efficient_producers,X1)
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| growth_rate(efficient_producers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_36) ).
fof(f19,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| zero = growth_rate(efficient_producers,X1)
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1)) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| growth_rate(efficient_producers,X1) = zero
| greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_37) ).
fof(f21,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| zero = growth_rate(efficient_producers,X1)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| growth_rate(efficient_producers,X1) = zero
| greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_38) ).
fof(f23,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| zero = growth_rate(efficient_producers,X1)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1)) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_39) ).
fof(f25,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_40) ).
fof(f26,negated_conjecture,
greater_or_equal(sk2,equilibrium(sk1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_41) ).
fof(f27,negated_conjecture,
( growth_rate(first_movers,sk2) != zero
| growth_rate(efficient_producers,sk2) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_42) ).
fof(f28,plain,
( zero != growth_rate(first_movers,sk2)
| zero != growth_rate(efficient_producers,sk2) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( ~ greater(growth_rate(first_movers,sk2),zero)
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_43) ).
fof(f30,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sk2),zero)
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_44) ).
fof(f31,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f32,plain,
! [X0,X1] :
( sQ0_eqProxy(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(equality_proxy_replacement,[],[f9,f31]) ).
fof(f33,plain,
! [X0,X1] :
( sQ0_eqProxy(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1)) ),
inference(equality_proxy_replacement,[],[f11,f31]) ).
fof(f34,plain,
! [X0,X1] :
( sQ0_eqProxy(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(equality_proxy_replacement,[],[f13,f31]) ).
fof(f35,plain,
! [X0,X1] :
( sQ0_eqProxy(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1)) ),
inference(equality_proxy_replacement,[],[f15,f31]) ).
fof(f36,plain,
! [X0,X1] :
( sQ0_eqProxy(zero,growth_rate(efficient_producers,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(equality_proxy_replacement,[],[f17,f31]) ).
fof(f37,plain,
! [X0,X1] :
( sQ0_eqProxy(zero,growth_rate(efficient_producers,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1)) ),
inference(equality_proxy_replacement,[],[f19,f31]) ).
fof(f38,plain,
! [X0,X1] :
( sQ0_eqProxy(zero,growth_rate(efficient_producers,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(equality_proxy_replacement,[],[f21,f31]) ).
fof(f39,plain,
! [X0,X1] :
( sQ0_eqProxy(zero,growth_rate(efficient_producers,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1)) ),
inference(equality_proxy_replacement,[],[f23,f31]) ).
fof(f40,plain,
( ~ sQ0_eqProxy(zero,growth_rate(first_movers,sk2))
| ~ sQ0_eqProxy(zero,growth_rate(efficient_producers,sk2)) ),
inference(equality_proxy_replacement,[],[f28,f31,f31]) ).
fof(f44,definition,
( spl1_1
<=> greater(zero,growth_rate(first_movers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f47,definition,
( spl1_2
<=> greater(growth_rate(efficient_producers,sk2),zero) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f49,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f30,f47,f44]) ).
fof(f51,definition,
( spl1_3
<=> greater(zero,growth_rate(efficient_producers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f54,definition,
( spl1_4
<=> greater(growth_rate(first_movers,sk2),zero) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f56,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f29,f54,f51]) ).
fof(f58,definition,
( spl1_5
<=> sQ0_eqProxy(zero,growth_rate(efficient_producers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f59,plain,
( ~ sQ0_eqProxy(zero,growth_rate(efficient_producers,sk2))
| spl1_5 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl1_6
<=> sQ0_eqProxy(zero,growth_rate(first_movers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f62,plain,
( ~ sQ0_eqProxy(zero,growth_rate(first_movers,sk2))
| spl1_6 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( ~ spl1_5
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f40,f61,f58]) ).
fof(f66,plain,
( ~ environment(sk1)
| ~ greater(equilibrium(sk1),sk2) ),
inference(resolution,[],[f3,f26]) ).
fof(f68,definition,
( spl1_7
<=> greater(equilibrium(sk1),sk2) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f71,definition,
( spl1_8
<=> environment(sk1) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f72,plain,
( ~ environment(sk1)
| spl1_8 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( ~ spl1_7
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f66,f71,f68]) ).
fof(f74,plain,
( ~ environment(sk1)
| greater(number_of_organizations(sk1,sk2),zero) ),
inference(resolution,[],[f2,f25]) ).
fof(f76,definition,
( spl1_9
<=> greater(number_of_organizations(sk1,sk2),zero) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f78,plain,
( spl1_9
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f74,f71,f76]) ).
fof(f79,plain,
( $false
| spl1_8 ),
inference(resolution,[],[f72,f24]) ).
fof(f80,plain,
spl1_8,
inference(avatar_contradiction_clause,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(resolution,[],[f7,f1]) ).
fof(f82,plain,
! [X0,X1] :
( ~ constant(resources(X0,X1))
| ~ environment(X0)
| constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(duplicate_literal_removal,[],[f81]) ).
fof(f85,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ greater(number_of_organizations(X0,X1),zero)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(resolution,[],[f5,f1]) ).
fof(f86,plain,
! [X0,X1] :
( constant(resources(X0,X1))
| ~ greater(number_of_organizations(X0,X1),zero)
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(duplicate_literal_removal,[],[f85]) ).
fof(f87,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ constant(number_of_organizations(X0,sk2))
| ~ environment(X0)
| greater(growth_rate(first_movers,sk2),zero)
| greater(growth_rate(efficient_producers,sk2),zero) )
| spl1_6 ),
inference(resolution,[],[f32,f62]) ).
fof(f91,definition,
( spl1_10
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ constant(number_of_organizations(X0,sk2)) ) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f92,plain,
( ! [X0] :
( ~ constant(number_of_organizations(X0,sk2))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2) )
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f93,plain,
( spl1_2
| spl1_4
| spl1_10
| spl1_6 ),
inference(avatar_split_clause,[],[f87,f61,f91,f54,f47]) ).
fof(f95,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(resolution,[],[f86,f82]) ).
fof(f96,plain,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero) ),
inference(duplicate_literal_removal,[],[f95]) ).
fof(f97,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ constant(number_of_organizations(X0,sk2))
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero) )
| spl1_6 ),
inference(resolution,[],[f34,f62]) ).
fof(f99,plain,
( spl1_2
| spl1_3
| spl1_10
| spl1_6 ),
inference(avatar_split_clause,[],[f97,f61,f91,f51,f47]) ).
fof(f102,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ constant(number_of_organizations(X0,sk2))
| ~ environment(X0)
| greater(growth_rate(first_movers,sk2),zero)
| greater(growth_rate(efficient_producers,sk2),zero) )
| spl1_5 ),
inference(resolution,[],[f36,f59]) ).
fof(f103,plain,
( spl1_2
| spl1_4
| spl1_10
| spl1_5 ),
inference(avatar_split_clause,[],[f102,f58,f91,f54,f47]) ).
fof(f104,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| greater(equilibrium(X0),sk2)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ greater(number_of_organizations(X0,sk2),zero) )
| ~ spl1_10 ),
inference(resolution,[],[f92,f96]) ).
fof(f105,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0)
| greater(equilibrium(X0),sk2)
| ~ greater(number_of_organizations(X0,sk2),zero) )
| ~ spl1_10 ),
inference(duplicate_literal_removal,[],[f104]) ).
fof(f106,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ constant(number_of_organizations(X0,sk2))
| ~ environment(X0)
| greater(growth_rate(first_movers,sk2),zero)
| greater(zero,growth_rate(first_movers,sk2)) )
| spl1_5 ),
inference(resolution,[],[f37,f59]) ).
fof(f107,plain,
( ~ environment(sk1)
| greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero)
| ~ spl1_10 ),
inference(resolution,[],[f105,f25]) ).
fof(f110,plain,
( ~ spl1_9
| spl1_7
| ~ spl1_8
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f107,f91,f71,f68,f76]) ).
fof(f112,plain,
( spl1_1
| spl1_4
| spl1_10
| spl1_5 ),
inference(avatar_split_clause,[],[f106,f58,f91,f54,f44]) ).
fof(f113,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ constant(number_of_organizations(X0,sk2))
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero) )
| spl1_5 ),
inference(resolution,[],[f38,f59]) ).
fof(f114,plain,
( spl1_2
| spl1_3
| spl1_10
| spl1_5 ),
inference(avatar_split_clause,[],[f113,f58,f91,f51,f47]) ).
fof(f115,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ constant(number_of_organizations(X0,sk2))
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) )
| spl1_5 ),
inference(resolution,[],[f39,f59]) ).
fof(f116,plain,
( spl1_1
| spl1_3
| spl1_10
| spl1_5 ),
inference(avatar_split_clause,[],[f115,f58,f91,f51,f44]) ).
fof(f117,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ constant(number_of_organizations(X0,sk2))
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) )
| spl1_6 ),
inference(resolution,[],[f62,f35]) ).
fof(f119,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ constant(number_of_organizations(X0,sk2))
| ~ environment(X0)
| greater(growth_rate(first_movers,sk2),zero)
| greater(zero,growth_rate(first_movers,sk2)) )
| spl1_6 ),
inference(resolution,[],[f62,f33]) ).
fof(f122,plain,
( spl1_1
| spl1_4
| spl1_10
| spl1_6 ),
inference(avatar_split_clause,[],[f119,f61,f91,f54,f44]) ).
fof(f123,plain,
( spl1_1
| spl1_3
| spl1_10
| spl1_6 ),
inference(avatar_split_clause,[],[f117,f61,f91,f51,f44]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s2,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f56]) ).
cnf(s3,plain,
( ~ spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f63]) ).
cnf(s4,plain,
( ~ spl1_7
| ~ spl1_8 ),
inference(sat_conversion,[],[f73]) ).
cnf(s5,plain,
( ~ spl1_8
| spl1_9 ),
inference(sat_conversion,[],[f78]) ).
cnf(s6,plain,
spl1_8,
inference(sat_conversion,[],[f80]) ).
cnf(s7,plain,
( spl1_2
| spl1_4
| spl1_6
| spl1_10 ),
inference(sat_conversion,[],[f93]) ).
cnf(s8,plain,
( spl1_2
| spl1_3
| spl1_6
| spl1_10 ),
inference(sat_conversion,[],[f99]) ).
cnf(s9,plain,
( spl1_2
| spl1_4
| spl1_5
| spl1_10 ),
inference(sat_conversion,[],[f103]) ).
cnf(s10,plain,
( spl1_7
| ~ spl1_8
| ~ spl1_9
| ~ spl1_10 ),
inference(sat_conversion,[],[f110]) ).
cnf(s11,plain,
( spl1_1
| spl1_4
| spl1_5
| spl1_10 ),
inference(sat_conversion,[],[f112]) ).
cnf(s12,plain,
( spl1_2
| spl1_3
| spl1_5
| spl1_10 ),
inference(sat_conversion,[],[f114]) ).
cnf(s13,plain,
( spl1_1
| spl1_3
| spl1_5
| spl1_10 ),
inference(sat_conversion,[],[f116]) ).
cnf(s14,plain,
( spl1_1
| spl1_4
| spl1_6
| spl1_10 ),
inference(sat_conversion,[],[f122]) ).
cnf(s15,plain,
( spl1_1
| spl1_3
| spl1_6
| spl1_10 ),
inference(sat_conversion,[],[f123]) ).
cnf(s16,plain,
spl1_9,
inference(rat,[],[s5,s6]) ).
cnf(s17,plain,
~ spl1_7,
inference(rat,[],[s4,s6]) ).
cnf(s18,plain,
~ spl1_10,
inference(rat,[],[s10,s16,s6,s17]) ).
cnf(s19,plain,
( spl1_3
| spl1_1 ),
inference(rat,[],[s3,s13,s15,s18]) ).
cnf(s20,plain,
( spl1_4
| spl1_1 ),
inference(rat,[],[s3,s11,s14,s18]) ).
cnf(s21,plain,
spl1_1,
inference(rat,[],[s20,s2,s19]) ).
cnf(s22,plain,
~ spl1_2,
inference(rat,[],[s1,s21]) ).
cnf(s23,plain,
spl1_6,
inference(rat,[],[s2,s8,s7,s22,s18]) ).
cnf(s24,plain,
~ spl1_5,
inference(rat,[],[s3,s23]) ).
cnf(s25,plain,
spl1_4,
inference(rat,[],[s9,s18,s22,s24]) ).
cnf(s26,plain,
spl1_3,
inference(rat,[],[s12,s18,s22,s24]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s2,s25,s26]) ).
fof(f124,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT024-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n013.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 17:20:07 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.07/1.15 % (434779)Input is clausal, will run a generic CNF schedule.
% 2.07/1.15 % (434790)dis-21_1_sil=8000:lcm=predicate:random_seed=596947559:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.07/1.15 % (434790)First to succeed.
% 2.07/1.15 % (434790)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-434779"
% 2.07/1.15 % (434788)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3898937508:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.07/1.15 % (434785)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4199539551:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.07/1.15 % (434787)lrs+10_1_sil=8000:sp=occurrence:random_seed=1079137846:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.07/1.15 % (434786)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=648945898:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.07/1.15 % (434789)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1851604887:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.07/1.15 % (434784)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1828588154:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.07/1.15 % (434787)Also succeeded, but the first one will report.
% 2.07/1.15 % (434788)Also succeeded, but the first one will report.
% 2.07/1.15 % (434789)Also succeeded, but the first one will report.
% 2.07/1.15 % (434790)Refutation found. Thanks to Tanya!
% 2.07/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.07/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.35 % (434790)------------------------------
% 2.56/1.35 % (434790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.35 % (434790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.35 % (434790)CaDiCaL version: 2.1.3
% 2.56/1.35 % (434790)Termination reason: Refutation
% 2.56/1.35 % (434790)Time elapsed: 0.003 s
% 2.56/1.35 % (434790)Peak memory usage: 89 MB
% 2.56/1.35 % (434790)Instructions burned: 6 (million)
% 2.56/1.35 % (434790)------------------------------
% 2.56/1.35 % (434790)------------------------------
% 2.56/1.35 % (434779)Success in time 0.285 s
% 2.56/1.35 % Vampire exiting
%------------------------------------------------------------------------------