%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 12:02:32 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 121 ( 17 unt; 7 def)
% Number of atoms : 438 ( 48 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 499 ( 182 ~; 250 |; 48 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 68 ( 0 sgn 64 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| constant(resources(X0,X1)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0,X1] :
( ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0)
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ~ environment(X0)
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0)
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero)
| ~ environment(X0)
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0)
| zero = growth_rate(first_movers,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ~ environment(X0)
| zero = growth_rate(first_movers,X1)
| ~ constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0)
| zero = growth_rate(first_movers,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(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(f56,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(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(f65,plain,
( zero = growth_rate(efficient_producers,sK1)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl2_6
<=> zero = growth_rate(first_movers,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f71,plain,
( ~ spl2_5
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f44,f68,f64]) ).
fof(f72,plain,
( ~ environment(sK0)
| in_environment(sK0,sK1) ),
inference(resolution,[],[f24,f40]) ).
fof(f73,plain,
in_environment(sK0,sK1),
inference(forward_subsumption_resolution,[],[f72,f41]) ).
fof(f74,plain,
( ~ environment(sK0)
| ~ greater(equilibrium(sK0),sK1) ),
inference(resolution,[],[f26,f39]) ).
fof(f75,plain,
~ greater(equilibrium(sK0),sK1),
inference(forward_subsumption_resolution,[],[f74,f41]) ).
fof(f76,plain,
( ~ environment(sK0)
| greater(number_of_organizations(sK0,sK1),zero) ),
inference(resolution,[],[f25,f40]) ).
fof(f77,plain,
greater(number_of_organizations(sK0,sK1),zero),
inference(forward_subsumption_resolution,[],[f76,f41]) ).
fof(f78,plain,
( greater(equilibrium(sK0),sK1)
| ~ environment(sK0)
| ~ in_environment(sK0,sK1)
| constant(resources(sK0,sK1)) ),
inference(resolution,[],[f27,f77]) ).
fof(f79,plain,
( ~ environment(sK0)
| ~ in_environment(sK0,sK1)
| constant(resources(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f78,f75]) ).
fof(f80,plain,
( ~ in_environment(sK0,sK1)
| constant(resources(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f79,f41]) ).
fof(f81,plain,
constant(resources(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f80,f73]) ).
fof(f83,plain,
( constant(number_of_organizations(sK0,sK1))
| ~ environment(sK0)
| ~ in_environment(sK0,sK1) ),
inference(resolution,[],[f81,f29]) ).
fof(f84,plain,
( constant(number_of_organizations(sK0,sK1))
| ~ in_environment(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f83,f41]) ).
fof(f85,plain,
constant(number_of_organizations(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f84,f73]) ).
fof(f86,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| ~ environment(sK0)
| zero = growth_rate(efficient_producers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolution,[],[f31,f40]) ).
fof(f90,definition,
( spl2_7
<=> constant(number_of_organizations(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f91,plain,
( constant(number_of_organizations(sK0,sK1))
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero)
| ~ environment(sK0)
| zero = growth_rate(efficient_producers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolution,[],[f32,f40]) ).
fof(f97,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero)
| zero = growth_rate(efficient_producers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f94,f41]) ).
fof(f98,plain,
spl2_7,
inference(avatar_split_clause,[],[f85,f90]) ).
fof(f99,plain,
( ~ spl2_7
| spl2_5
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f97,f55,f50,f64,f90]) ).
fof(f100,plain,
( greater(growth_rate(first_movers,sK1),zero)
| greater(zero,growth_rate(first_movers,sK1))
| ~ environment(sK0)
| zero = growth_rate(efficient_producers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolution,[],[f33,f40]) ).
fof(f106,plain,
( greater(zero,zero)
| ~ spl2_3
| ~ spl2_5 ),
inference(superposition,[],[f56,f65]) ).
fof(f107,plain,
( greater(growth_rate(first_movers,sK1),zero)
| greater(growth_rate(efficient_producers,sK1),zero)
| ~ environment(sK0)
| zero = growth_rate(efficient_producers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolution,[],[f34,f40]) ).
fof(f108,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| ~ environment(sK0)
| zero = growth_rate(first_movers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolution,[],[f35,f40]) ).
fof(f109,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero)
| ~ environment(sK0)
| zero = growth_rate(first_movers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolution,[],[f36,f40]) ).
fof(f110,plain,
( greater(growth_rate(first_movers,sK1),zero)
| greater(zero,growth_rate(first_movers,sK1))
| ~ environment(sK0)
| zero = growth_rate(first_movers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolution,[],[f37,f40]) ).
fof(f127,plain,
( greater(growth_rate(first_movers,sK1),zero)
| greater(zero,growth_rate(first_movers,sK1))
| zero = growth_rate(efficient_producers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f100,f41]) ).
fof(f128,plain,
( greater(growth_rate(first_movers,sK1),zero)
| greater(zero,growth_rate(first_movers,sK1))
| zero = growth_rate(first_movers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f110,f41]) ).
fof(f129,plain,
( greater(growth_rate(first_movers,sK1),zero)
| greater(growth_rate(efficient_producers,sK1),zero)
| zero = growth_rate(efficient_producers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f107,f41]) ).
fof(f130,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| zero = growth_rate(first_movers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f108,f41]) ).
fof(f131,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero)
| zero = growth_rate(first_movers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f109,f41]) ).
fof(f132,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| zero = growth_rate(efficient_producers,sK1)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f86,f41]) ).
fof(f133,plain,
( greater(growth_rate(first_movers,sK1),zero)
| greater(zero,growth_rate(first_movers,sK1))
| zero = growth_rate(efficient_producers,sK1)
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f127,f91]) ).
fof(f134,plain,
( greater(growth_rate(first_movers,sK1),zero)
| greater(zero,growth_rate(first_movers,sK1))
| zero = growth_rate(first_movers,sK1)
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f128,f91]) ).
fof(f135,plain,
( greater(growth_rate(first_movers,sK1),zero)
| greater(growth_rate(efficient_producers,sK1),zero)
| zero = growth_rate(efficient_producers,sK1)
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f129,f91]) ).
fof(f136,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| zero = growth_rate(first_movers,sK1)
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f130,f91]) ).
fof(f137,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero)
| zero = growth_rate(first_movers,sK1)
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f131,f91]) ).
fof(f138,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| zero = growth_rate(efficient_producers,sK1)
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f132,f91]) ).
fof(f139,plain,
( spl2_5
| spl2_1
| spl2_4
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f133,f90,f59,f46,f64]) ).
fof(f140,plain,
( spl2_6
| spl2_1
| spl2_4
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f134,f90,f59,f46,f68]) ).
fof(f141,plain,
( spl2_5
| spl2_2
| spl2_4
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f135,f90,f59,f50,f64]) ).
fof(f142,plain,
( spl2_6
| spl2_1
| spl2_3
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f136,f90,f55,f46,f68]) ).
fof(f143,plain,
( spl2_6
| spl2_2
| spl2_3
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f137,f90,f55,f50,f68]) ).
fof(f144,plain,
( spl2_5
| spl2_1
| spl2_3
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f138,f90,f55,f46,f64]) ).
fof(f146,plain,
( ~ greater(zero,zero)
| spl2_2
| ~ spl2_5 ),
inference(superposition,[],[f52,f65]) ).
fof(f147,plain,
( $false
| spl2_2
| ~ spl2_3
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f146,f106]) ).
fof(f148,plain,
( spl2_2
| ~ spl2_3
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f147]) ).
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_7,
inference(sat_conversion,[],[f98]) ).
cnf(s7,plain,
( spl2_2
| spl2_3
| spl2_5
| ~ spl2_7 ),
inference(sat_conversion,[],[f99]) ).
cnf(s13,plain,
( spl2_1
| spl2_4
| spl2_5
| ~ spl2_7 ),
inference(sat_conversion,[],[f139]) ).
cnf(s14,plain,
( spl2_1
| spl2_4
| spl2_6
| ~ spl2_7 ),
inference(sat_conversion,[],[f140]) ).
cnf(s15,plain,
( spl2_2
| spl2_4
| spl2_5
| ~ spl2_7 ),
inference(sat_conversion,[],[f141]) ).
cnf(s16,plain,
( spl2_1
| spl2_3
| spl2_6
| ~ spl2_7 ),
inference(sat_conversion,[],[f142]) ).
cnf(s17,plain,
( spl2_2
| spl2_3
| spl2_6
| ~ spl2_7 ),
inference(sat_conversion,[],[f143]) ).
cnf(s18,plain,
( spl2_1
| spl2_3
| spl2_5
| ~ spl2_7 ),
inference(sat_conversion,[],[f144]) ).
cnf(s19,plain,
( spl2_2
| ~ spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f148]) ).
cnf(s21,plain,
( spl2_3
| spl2_1 ),
inference(rat,[],[s3,s16,s18,s6]) ).
cnf(s22,plain,
( spl2_4
| spl2_1 ),
inference(rat,[],[s3,s14,s13,s6]) ).
cnf(s23,plain,
spl2_1,
inference(rat,[],[s22,s2,s21]) ).
cnf(s24,plain,
~ spl2_2,
inference(rat,[],[s1,s23]) ).
cnf(s25,plain,
~ spl2_5,
inference(rat,[],[s17,s19,s3,s24,s6]) ).
cnf(s26,plain,
spl2_3,
inference(rat,[],[s7,s6,s24,s25]) ).
cnf(s27,plain,
spl2_4,
inference(rat,[],[s15,s6,s24,s25]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s2,s27,s26]) ).
fof(f149,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 17:20:45 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.16/0.46 % (2638290)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (2638295)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=729743617_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % (2638296)% WARNING: option uhcvi not known.
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % TRYING [3]
% 0.16/0.46 % (2638299)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2865012659:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (2638296)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2004866008:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (2638297)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2165390914:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (2638298)dis+10_1_sil=32000:sp=arity:random_seed=1410469797:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % TRYING [4]
% 0.16/0.46 % (2638300)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3485444815:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (2638301)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2763454595:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % TRYING [5]
% 0.16/0.46 % (2638298) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2638290-2638298"...
% 0.16/0.46 % (2638299) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2638290-2638299"...
% 0.16/0.46 % (2638300) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2638290-2638300"...
% 0.16/0.46 % (2638296) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2638290-2638296"...
% 0.16/0.46 % (2638301) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2638290-2638301"...
% 0.16/0.46 % (2638298)...printing done.
% 0.16/0.46 % (2638300)...printing done.
% 0.16/0.46 % (2638296)...printing done.
% 0.16/0.46 % (2638299)...printing done.
% 0.16/0.46 % (2638301)...printing done.
% 0.16/0.46 % (2638298)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (2638298)------------------------------
% 0.16/0.47 % (2638298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (2638298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (2638298)CaDiCaL version: 2.1.3
% 0.16/0.47 % (2638298)Termination reason: Refutation
% 0.16/0.47 % (2638298)Time elapsed: 0.005 s
% 0.16/0.47 % (2638298)Peak memory usage: 12 MB
% 0.16/0.47 % (2638298)Instructions burned: 7 (million)
% 0.16/0.47 % (2638290)Success in time 0.039 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------