%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:02:03 PM UTC 2026
% Result : Theorem 1.73s 1.12s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 116 ( 13 unt; 7 def)
% Number of atoms : 462 ( 40 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 555 ( 209 ~; 279 |; 48 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 8 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 87 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(f2,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> greater(number_of_organizations(X0,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_number_of_organizations) ).
fof(f3,axiom,
! [X0,X1] :
( ( environment(X0)
& greater_or_equal(X1,equilibrium(X0)) )
=> ~ greater(equilibrium(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_equilibrium) ).
fof(f4,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1)
& greater(number_of_organizations(X0,X1),zero) )
=> ( ( greater(equilibrium(X0),X1)
=> decreases(resources(X0,X1)) )
& ( ~ greater(equilibrium(X0),X1)
=> constant(resources(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
fof(f5,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1) )
=> ( ( decreases(resources(X0,X1))
=> ~ decreases(number_of_organizations(X0,X1)) )
& ( constant(resources(X0,X1))
=> constant(number_of_organizations(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6) ).
fof(f6,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1)
& constant(number_of_organizations(X0,X1)) )
=> ( ( growth_rate(first_movers,X1) = zero
& growth_rate(efficient_producers,X1) = zero )
| ( greater(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) )
| ( greater(growth_rate(efficient_producers,X1),zero)
& greater(zero,growth_rate(first_movers,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7) ).
fof(f7,conjecture,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1)
& greater_or_equal(X1,equilibrium(X0)) )
=> ( ( growth_rate(first_movers,X1) = zero
& growth_rate(efficient_producers,X1) = zero )
| ( greater(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) )
| ( greater(growth_rate(efficient_producers,X1),zero)
& greater(zero,growth_rate(first_movers,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1)
& greater_or_equal(X1,equilibrium(X0)) )
=> ( ( growth_rate(first_movers,X1) = zero
& growth_rate(efficient_producers,X1) = zero )
| ( greater(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) )
| ( greater(growth_rate(efficient_producers,X1),zero)
& greater(zero,growth_rate(first_movers,X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f10,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0)) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( ( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1) )
& ( constant(resources(X0,X1))
| greater(equilibrium(X0),X1) ) )
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero) ),
inference(ennf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1] :
( ( ( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1) )
& ( constant(resources(X0,X1))
| greater(equilibrium(X0),X1) ) )
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( ( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1)) )
& ( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1)) ) )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f18,plain,
! [X0,X1] :
( ( ( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1)) )
& ( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1)) ) )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( growth_rate(first_movers,X1) = zero
& growth_rate(efficient_producers,X1) = zero )
| ( greater(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) )
| ( greater(growth_rate(efficient_producers,X1),zero)
& greater(zero,growth_rate(first_movers,X1)) )
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1] :
( ( growth_rate(first_movers,X1) = zero
& growth_rate(efficient_producers,X1) = zero )
| ( greater(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) )
| ( greater(growth_rate(efficient_producers,X1),zero)
& greater(zero,growth_rate(first_movers,X1)) )
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
? [X0,X1] :
( ( zero != growth_rate(first_movers,X1)
| zero != growth_rate(efficient_producers,X1) )
& ( ~ greater(growth_rate(first_movers,X1),zero)
| ~ greater(zero,growth_rate(efficient_producers,X1)) )
& ( ~ greater(growth_rate(efficient_producers,X1),zero)
| ~ greater(zero,growth_rate(first_movers,X1)) )
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1)
& greater_or_equal(X1,equilibrium(X0)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f22,plain,
? [X0,X1] :
( ( zero != growth_rate(first_movers,X1)
| zero != growth_rate(efficient_producers,X1) )
& ( ~ greater(growth_rate(first_movers,X1),zero)
| ~ greater(zero,growth_rate(efficient_producers,X1)) )
& ( ~ greater(growth_rate(efficient_producers,X1),zero)
| ~ greater(zero,growth_rate(first_movers,X1)) )
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1)
& greater_or_equal(X1,equilibrium(X0)) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
( ( zero != growth_rate(first_movers,sK1)
| zero != growth_rate(efficient_producers,sK1) )
& ( ~ greater(growth_rate(first_movers,sK1),zero)
| ~ greater(zero,growth_rate(efficient_producers,sK1)) )
& ( ~ greater(growth_rate(efficient_producers,sK1),zero)
| ~ greater(zero,growth_rate(first_movers,sK1)) )
& environment(sK0)
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& greater_or_equal(sK1,equilibrium(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0,X1] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X0,X1] :
( greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(efficient_producers,X1)
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(efficient_producers,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1] :
( greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(efficient_producers,X1)
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1] :
( greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(efficient_producers,X1)
| greater(growth_rate(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(first_movers,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1] :
( greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(first_movers,X1)
| greater(growth_rate(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(first_movers,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(first_movers,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
greater_or_equal(sK1,equilibrium(sK0)),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
environment(sK0),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
( ~ greater(growth_rate(efficient_producers,sK1),zero)
| ~ greater(zero,growth_rate(first_movers,sK1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
( ~ greater(growth_rate(first_movers,sK1),zero)
| ~ greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
( zero != growth_rate(first_movers,sK1)
| zero != growth_rate(efficient_producers,sK1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,definition,
( spl2_1
<=> greater(zero,growth_rate(first_movers,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f48,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| spl2_1 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f50,definition,
( spl2_2
<=> greater(growth_rate(efficient_producers,sK1),zero) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f52,plain,
( ~ greater(growth_rate(efficient_producers,sK1),zero)
| spl2_2 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f42,f50,f46]) ).
fof(f55,definition,
( spl2_3
<=> greater(zero,growth_rate(efficient_producers,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f57,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| spl2_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f59,definition,
( spl2_4
<=> greater(growth_rate(first_movers,sK1),zero) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f61,plain,
( ~ greater(growth_rate(first_movers,sK1),zero)
| spl2_4 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f43,f59,f55]) ).
fof(f64,definition,
( spl2_5
<=> zero = growth_rate(efficient_producers,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f68,definition,
( spl2_6
<=> zero = growth_rate(first_movers,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f70,plain,
( zero != growth_rate(first_movers,sK1)
| spl2_6 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( ~ spl2_5
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f44,f68,f64]) ).
fof(f75,definition,
( spl2_7
<=> ! [X0] :
( ~ environment(X0)
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f76,plain,
( ! [X0] :
( ~ constant(number_of_organizations(X0,sK1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1) )
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,plain,
( ! [X0] :
( zero = growth_rate(efficient_producers,sK1)
| greater(zero,growth_rate(first_movers,sK1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_3 ),
inference(resolution,[],[f57,f31]) ).
fof(f82,plain,
( ! [X0] :
( greater(zero,growth_rate(efficient_producers,sK1))
| zero = growth_rate(first_movers,sK1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_1 ),
inference(resolution,[],[f35,f48]) ).
fof(f83,plain,
( ! [X0] :
( zero = growth_rate(first_movers,sK1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_1
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f82,f57]) ).
fof(f84,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_1
| spl2_3
| spl2_6 ),
inference(forward_subsumption_resolution,[],[f83,f70]) ).
fof(f85,plain,
( spl2_7
| spl2_1
| spl2_3
| spl2_6 ),
inference(avatar_split_clause,[],[f84,f68,f55,f46,f75]) ).
fof(f86,plain,
( spl2_7
| spl2_1
| spl2_5
| spl2_3 ),
inference(avatar_split_clause,[],[f78,f55,f64,f46,f75]) ).
fof(f91,plain,
( ! [X0] :
( zero = growth_rate(efficient_producers,sK1)
| greater(growth_rate(efficient_producers,sK1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_4 ),
inference(resolution,[],[f61,f34]) ).
fof(f92,plain,
( ! [X0] :
( zero = growth_rate(efficient_producers,sK1)
| greater(zero,growth_rate(first_movers,sK1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_4 ),
inference(resolution,[],[f61,f33]) ).
fof(f95,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(resources(X0,sK1))
| ~ environment(X0)
| ~ in_environment(X0,sK1) )
| ~ spl2_7 ),
inference(resolution,[],[f76,f29]) ).
fof(f96,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(resources(X0,sK1))
| ~ in_environment(X0,sK1) )
| ~ spl2_7 ),
inference(duplicate_literal_removal,[],[f95]) ).
fof(f97,plain,
( ! [X0] :
( ~ constant(resources(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f96,f24]) ).
fof(f98,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| greater(equilibrium(X0),sK1)
| ~ environment(X0)
| ~ in_environment(X0,sK1)
| ~ greater(number_of_organizations(X0,sK1),zero) )
| ~ spl2_7 ),
inference(resolution,[],[f97,f27]) ).
fof(f99,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| greater(equilibrium(X0),sK1)
| ~ in_environment(X0,sK1)
| ~ greater(number_of_organizations(X0,sK1),zero) )
| ~ spl2_7 ),
inference(duplicate_literal_removal,[],[f98]) ).
fof(f100,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| greater(equilibrium(X0),sK1)
| ~ greater(number_of_organizations(X0,sK1),zero) )
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f99,f24]) ).
fof(f101,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| greater(equilibrium(X0),sK1) )
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f100,f25]) ).
fof(f103,plain,
( ~ environment(sK0)
| greater(equilibrium(sK0),sK1)
| ~ spl2_7 ),
inference(resolution,[],[f101,f40]) ).
fof(f104,plain,
( greater(equilibrium(sK0),sK1)
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f103,f41]) ).
fof(f106,plain,
( ~ environment(sK0)
| ~ greater_or_equal(sK1,equilibrium(sK0))
| ~ spl2_7 ),
inference(resolution,[],[f104,f26]) ).
fof(f107,plain,
( ~ greater_or_equal(sK1,equilibrium(sK0))
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f106,f41]) ).
fof(f109,plain,
( $false
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f107,f39]) ).
fof(f110,plain,
~ spl2_7,
inference(avatar_contradiction_clause,[],[f109]) ).
fof(f126,plain,
( spl2_7
| spl2_2
| spl2_5
| spl2_4 ),
inference(avatar_split_clause,[],[f91,f59,f64,f50,f75]) ).
fof(f127,plain,
( spl2_7
| spl2_1
| spl2_5
| spl2_4 ),
inference(avatar_split_clause,[],[f92,f59,f64,f46,f75]) ).
fof(f128,plain,
( ! [X0] :
( greater(growth_rate(first_movers,sK1),zero)
| zero = growth_rate(first_movers,sK1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_1 ),
inference(resolution,[],[f48,f37]) ).
fof(f130,plain,
( ! [X0] :
( zero = growth_rate(first_movers,sK1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_1
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f128,f61]) ).
fof(f131,plain,
( spl2_7
| spl2_6
| spl2_1
| spl2_4 ),
inference(avatar_split_clause,[],[f130,f59,f46,f68,f75]) ).
fof(f132,plain,
( ! [X0] :
( greater(growth_rate(first_movers,sK1),zero)
| zero = growth_rate(first_movers,sK1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_2 ),
inference(resolution,[],[f52,f38]) ).
fof(f133,plain,
( ! [X0] :
( greater(zero,growth_rate(efficient_producers,sK1))
| zero = growth_rate(efficient_producers,sK1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_2 ),
inference(resolution,[],[f52,f32]) ).
fof(f134,plain,
( spl2_7
| spl2_5
| spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f133,f50,f55,f64,f75]) ).
fof(f135,plain,
( spl2_7
| spl2_6
| spl2_4
| spl2_2 ),
inference(avatar_split_clause,[],[f132,f50,f59,f68,f75]) ).
fof(f136,plain,
( ! [X0] :
( zero = growth_rate(first_movers,sK1)
| greater(growth_rate(efficient_producers,sK1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_3 ),
inference(resolution,[],[f57,f36]) ).
fof(f138,plain,
( ! [X0] :
( zero = growth_rate(first_movers,sK1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(number_of_organizations(X0,sK1)) )
| spl2_2
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f136,f52]) ).
fof(f139,plain,
( spl2_7
| spl2_6
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f138,f55,f50,f68,f75]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s2,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f62]) ).
cnf(s3,plain,
( ~ spl2_5
| ~ spl2_6 ),
inference(sat_conversion,[],[f71]) ).
cnf(s6,plain,
( spl2_1
| spl2_3
| spl2_6
| spl2_7 ),
inference(sat_conversion,[],[f85]) ).
cnf(s7,plain,
( spl2_1
| spl2_3
| spl2_5
| spl2_7 ),
inference(sat_conversion,[],[f86]) ).
cnf(s11,plain,
~ spl2_7,
inference(sat_conversion,[],[f110]) ).
cnf(s14,plain,
( spl2_2
| spl2_4
| spl2_5
| spl2_7 ),
inference(sat_conversion,[],[f126]) ).
cnf(s15,plain,
( spl2_1
| spl2_4
| spl2_5
| spl2_7 ),
inference(sat_conversion,[],[f127]) ).
cnf(s16,plain,
( spl2_1
| spl2_4
| spl2_6
| spl2_7 ),
inference(sat_conversion,[],[f131]) ).
cnf(s17,plain,
( spl2_2
| spl2_3
| spl2_5
| spl2_7 ),
inference(sat_conversion,[],[f134]) ).
cnf(s18,plain,
( spl2_2
| spl2_4
| spl2_6
| spl2_7 ),
inference(sat_conversion,[],[f135]) ).
cnf(s19,plain,
( spl2_2
| spl2_3
| spl2_6
| spl2_7 ),
inference(sat_conversion,[],[f139]) ).
cnf(s23,plain,
( spl2_1
| spl2_3
| spl2_5 ),
inference(rat,[],[s7,s11]) ).
cnf(s24,plain,
( spl2_1
| spl2_3
| spl2_6 ),
inference(rat,[],[s6,s11]) ).
cnf(s27,plain,
( spl2_3
| spl2_2 ),
inference(rat,[],[s3,s17,s19,s11]) ).
cnf(s28,plain,
( spl2_4
| spl2_1 ),
inference(rat,[],[s3,s15,s16,s11]) ).
cnf(s29,plain,
( spl2_3
| spl2_1 ),
inference(rat,[],[s3,s24,s23]) ).
cnf(s30,plain,
spl2_1,
inference(rat,[],[s29,s2,s28]) ).
cnf(s31,plain,
~ spl2_2,
inference(rat,[],[s1,s30]) ).
cnf(s32,plain,
spl2_3,
inference(rat,[],[s27,s31]) ).
cnf(s33,plain,
~ spl2_4,
inference(rat,[],[s2,s32]) ).
cnf(s34,plain,
spl2_6,
inference(rat,[],[s18,s11,s31,s33]) ).
cnf(s35,plain,
spl2_5,
inference(rat,[],[s14,s11,s31,s33]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s3,s34,s35]) ).
fof(f140,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 17:22:46 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 1.73/1.12 % (3821351)Detected formulas, will run a generic FOF schedule.
% 1.73/1.12 % (3821361)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1490277282:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.73/1.12 % (3821361)First to succeed.
% 1.73/1.12 % (3821361)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3821351"
% 1.73/1.12 % (3821360)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2009349189:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.73/1.12 % (3821358)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1811675977:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.73/1.12 % (3821359)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3862516968:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.73/1.12 % (3821357)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3902709134:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.73/1.12 % (3821356)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=2276684510:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.73/1.12 % (3821360)Also succeeded, but the first one will report.
% 1.73/1.12 % (3821359)Also succeeded, but the first one will report.
% 1.73/1.12 % (3821362)dis-21_1_sil=8000:lcm=predicate:random_seed=3966116047:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.73/1.12 % (3821362)Also succeeded, but the first one will report.
% 1.73/1.12 % (3821361)Refutation found. Thanks to Tanya!
% 1.73/1.12 % SZS status Theorem for theBenchmark
% 1.73/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.31 % (3821361)------------------------------
% 2.56/1.31 % (3821361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.31 % (3821361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.31 % (3821361)CaDiCaL version: 2.1.3
% 2.56/1.31 % (3821361)Termination reason: Refutation
% 2.56/1.31 % (3821361)Time elapsed: 0.004 s
% 2.56/1.31 % (3821361)Peak memory usage: 90 MB
% 2.56/1.31 % (3821361)Instructions burned: 8 (million)
% 2.56/1.31 % (3821361)------------------------------
% 2.56/1.31 % (3821361)------------------------------
% 2.56/1.31 % (3821351)Success in time 0.274 s
% 2.56/1.31 % Vampire exiting
%------------------------------------------------------------------------------