%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT023+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 : Thu Sep 24 01:25:18 PM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 95 ( 6 unt; 14 def)
% Number of atoms : 349 ( 15 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 424 ( 170 ~; 190 |; 41 &)
% ( 14 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 14 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 85 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E] :
( ( ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To) )
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,hypothesis,
! [E,To] :
( ( ! [T] :
( ( greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& environment(E) )
=> To = critical_point(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,hypothesis,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) )
| ! [To] :
( ? [T] :
( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To) )
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f7,definition,
! [E,To,T] :
( sP0_prd(T,To,E)
<=> ( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f8,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) )
| ! [To] :
( ? [T] : sP0_prd(T,To,E)
| ~ in_environment(E,To) )
| ~ environment(E) ),
inference(formula_renaming,[status(thm)],[f6,f7]) ).
fof(f9,plain,
! [E] :
( ( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,sK1_skl(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,sK1_skl(E)),growth_rate(first_movers,sK1_skl(E)))
& in_environment(E,sK1_skl(E)) )
| ! [To] :
( sP0_prd(sK0_skl(To,E),To,E)
| ~ in_environment(E,To) )
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(T,sK0_skl(To,E)),skolemize(To,sK1_skl(E))],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( in_environment(X0,sK1_skl(X0))
| sP0_prd(sK0_skl(X1,X0),X1,X0)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sK1_skl(X0)),growth_rate(first_movers,sK1_skl(X0)))
| sP0_prd(sK0_skl(X1,X0),X1,X0)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f12,plain,
! [X0,X1,X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sK1_skl(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| sP0_prd(sK0_skl(X1,X0),X1,X0)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f13,plain,
! [E,To] :
( To = critical_point(E)
| ? [T] :
( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
! [E,To] :
( To = critical_point(E)
| ( ~ greater(growth_rate(efficient_producers,sK2_skl(To,E)),growth_rate(first_movers,sK2_skl(To,E)))
& greater(sK2_skl(To,E),To)
& subpopulations(first_movers,efficient_producers,E,sK2_skl(To,E)) )
| ~ in_environment(E,To)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(T,sK2_skl(To,E))],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| subpopulations(first_movers,efficient_producers,X0,sK2_skl(X1,X0))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| greater(sK2_skl(X1,X0),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| ~ greater(growth_rate(efficient_producers,sK2_skl(X1,X0)),growth_rate(first_movers,sK2_skl(X1,X0)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,To) )
| ~ stable(E)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [E] :
( ( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,sK3_skl(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,sK3_skl(E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(To,sK3_skl(E))],[f18]) ).
fof(f20,plain,
! [X0] :
( in_environment(X0,sK3_skl(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sK3_skl(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
? [E] :
( ~ in_environment(E,critical_point(E))
& stable(E)
& environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
( ~ in_environment(sK4_skl,critical_point(sK4_skl))
& stable(sK4_skl)
& environment(sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(E,sK4_skl)],[f22]) ).
fof(f24,plain,
environment(sK4_skl),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
stable(sK4_skl),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,plain,
~ in_environment(sK4_skl,critical_point(sK4_skl)),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f27,plain,
! [E,To,T] :
( ( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| sP0_prd(T,To,E) )
& ( ( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ sP0_prd(T,To,E) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
( ! [E,To,T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| sP0_prd(T,To,E) )
& ! [E,To,T] :
( ( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ sP0_prd(T,To,E) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( subpopulations(first_movers,efficient_producers,X2,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( greater_or_equal(X0,X1)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f33,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sK1_skl(sK4_skl)),growth_rate(first_movers,sK1_skl(sK4_skl)))
| sP0_prd(sK0_skl(X0,sK4_skl),X0,sK4_skl)
| ~ in_environment(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f11,f24]) ).
fof(f34,definition,
! [X0] :
( sQ0_spl
<=> ( sP0_prd(sK0_skl(X0,sK4_skl),X0,sK4_skl)
| ~ in_environment(sK4_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f35,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(sK0_skl(X0,sK4_skl),X0,sK4_skl)
| ~ in_environment(sK4_skl,X0) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,definition,
( sQ1_spl
<=> greater(growth_rate(efficient_producers,sK1_skl(sK4_skl)),growth_rate(first_movers,sK1_skl(sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( sQ1_spl
| ~ greater(growth_rate(efficient_producers,sK1_skl(sK4_skl)),growth_rate(first_movers,sK1_skl(sK4_skl))) ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f40,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f34,f37]) ).
fof(f41,plain,
! [X0] :
( ~ sQ0_spl
| ~ greater(growth_rate(efficient_producers,sK0_skl(X0,sK4_skl)),growth_rate(first_movers,sK0_skl(X0,sK4_skl)))
| ~ in_environment(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f35,f31]) ).
fof(f43,plain,
( ~ sQ0_spl
| ~ stable(sK4_skl)
| ~ environment(sK4_skl)
| ~ greater(growth_rate(efficient_producers,sK0_skl(sK3_skl(sK4_skl),sK4_skl)),growth_rate(first_movers,sK0_skl(sK3_skl(sK4_skl),sK4_skl))) ),
inference(resolution,[status(thm)],[f41,f20]) ).
fof(f47,definition,
( sQ3_spl
<=> environment(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ3_spl
| ~ environment(sK4_skl) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f51,definition,
( sQ4_spl
<=> greater(growth_rate(efficient_producers,sK0_skl(sK3_skl(sK4_skl),sK4_skl)),growth_rate(first_movers,sK0_skl(sK3_skl(sK4_skl),sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( sQ4_spl
| ~ greater(growth_rate(efficient_producers,sK0_skl(sK3_skl(sK4_skl),sK4_skl)),growth_rate(first_movers,sK0_skl(sK3_skl(sK4_skl),sK4_skl))) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ5_spl
<=> stable(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( sQ5_spl
| ~ stable(sK4_skl) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f43,f51,f47,f54,f34]) ).
fof(f58,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f25]) ).
fof(f59,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f58]) ).
fof(f60,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f24]) ).
fof(f61,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0] :
( sQ1_spl
| sK1_skl(sK4_skl) = critical_point(X0)
| ~ greater(growth_rate(efficient_producers,sK2_skl(sK1_skl(sK4_skl),X0)),growth_rate(first_movers,sK2_skl(sK1_skl(sK4_skl),X0)))
| ~ in_environment(X0,sK1_skl(sK4_skl))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f39,f17]) ).
fof(f63,plain,
! [X0] :
( sQ1_spl
| sK1_skl(sK4_skl) = critical_point(X0)
| greater(sK2_skl(sK1_skl(sK4_skl),X0),sK1_skl(sK4_skl))
| ~ in_environment(X0,sK1_skl(sK4_skl))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f39,f16]) ).
fof(f64,plain,
! [X0] :
( sQ1_spl
| sK1_skl(sK4_skl) = critical_point(X0)
| subpopulations(first_movers,efficient_producers,X0,sK2_skl(sK1_skl(sK4_skl),X0))
| ~ in_environment(X0,sK1_skl(sK4_skl))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f39,f15]) ).
fof(f70,plain,
! [X0] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sK3_skl(sK4_skl))
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,X0)
| ~ environment(sK4_skl) ),
inference(resolution,[status(thm)],[f21,f25]) ).
fof(f71,definition,
! [X0] :
( sQ6_spl
<=> ( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sK3_skl(sK4_skl))
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f72,plain,
! [X0] :
( ~ sQ6_spl
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sK3_skl(sK4_skl))
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,X0) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ6_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f70,f47,f71]) ).
fof(f75,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sK1_skl(sK4_skl))
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,X1)
| sP0_prd(sK0_skl(X0,sK4_skl),X0,sK4_skl)
| ~ in_environment(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f12,f24]) ).
fof(f76,definition,
! [X1] :
( sQ7_spl
<=> ( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sK1_skl(sK4_skl))
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f77,plain,
! [X0] :
( ~ sQ7_spl
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sK1_skl(sK4_skl))
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,X0) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f75,f34,f76]) ).
fof(f80,plain,
( sQ4_spl
| ~ sQ6_spl
| ~ greater_or_equal(sK0_skl(sK3_skl(sK4_skl),sK4_skl),sK3_skl(sK4_skl))
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,sK0_skl(sK3_skl(sK4_skl),sK4_skl)) ),
inference(resolution,[status(thm)],[f72,f53]) ).
fof(f81,definition,
( sQ8_spl
<=> subpopulations(first_movers,efficient_producers,sK4_skl,sK0_skl(sK3_skl(sK4_skl),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( sQ8_spl
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,sK0_skl(sK3_skl(sK4_skl),sK4_skl)) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,definition,
( sQ9_spl
<=> greater_or_equal(sK0_skl(sK3_skl(sK4_skl),sK4_skl),sK3_skl(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( sQ9_spl
| ~ greater_or_equal(sK0_skl(sK3_skl(sK4_skl),sK4_skl),sK3_skl(sK4_skl)) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,plain,
( sQ4_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f80,f81,f84,f71,f51]) ).
fof(f101,plain,
! [X0] :
( sQ9_spl
| ~ sP0_prd(sK0_skl(sK3_skl(sK4_skl),sK4_skl),sK3_skl(sK4_skl),X0) ),
inference(resolution,[status(thm)],[f86,f30]) ).
fof(f102,plain,
! [X0] :
( ~ sQ7_spl
| sQ1_spl
| greater(growth_rate(efficient_producers,sK2_skl(sK1_skl(sK4_skl),X0)),growth_rate(first_movers,sK2_skl(sK1_skl(sK4_skl),X0)))
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,sK2_skl(sK1_skl(sK4_skl),X0))
| sK1_skl(sK4_skl) = critical_point(X0)
| ~ in_environment(X0,sK1_skl(sK4_skl))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f63,f77]) ).
fof(f107,definition,
( sQ13_spl
<=> sK1_skl(sK4_skl) = critical_point(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ13_spl
| sK1_skl(sK4_skl) = critical_point(sK4_skl) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f111,plain,
( ~ sQ13_spl
| ~ in_environment(sK4_skl,sK1_skl(sK4_skl)) ),
inference(backward_demodulation,[status(thm)],[f108,f26]) ).
fof(f112,plain,
! [X0] :
( ~ sQ13_spl
| sP0_prd(sK0_skl(X0,sK4_skl),X0,sK4_skl)
| ~ in_environment(sK4_skl,X0)
| ~ environment(sK4_skl) ),
inference(resolution,[status(thm)],[f111,f10]) ).
fof(f113,plain,
( ~ sQ13_spl
| sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f112,f47,f34,f107]) ).
fof(f118,definition,
( sQ14_spl
<=> subpopulations(first_movers,efficient_producers,sK4_skl,sK2_skl(sK1_skl(sK4_skl),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( sQ14_spl
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,sK2_skl(sK1_skl(sK4_skl),sK4_skl)) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f126,plain,
( sQ1_spl
| sQ14_spl
| sK1_skl(sK4_skl) = critical_point(sK4_skl)
| ~ in_environment(sK4_skl,sK1_skl(sK4_skl))
| ~ environment(sK4_skl) ),
inference(resolution,[status(thm)],[f120,f64]) ).
fof(f128,definition,
( sQ16_spl
<=> in_environment(sK4_skl,sK1_skl(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( sQ16_spl
| ~ in_environment(sK4_skl,sK1_skl(sK4_skl)) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,plain,
( sQ1_spl
| sQ14_spl
| sQ13_spl
| ~ sQ16_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f126,f47,f128,f107,f118,f37]) ).
fof(f132,plain,
! [X0] :
( sQ16_spl
| sP0_prd(sK0_skl(X0,sK4_skl),X0,sK4_skl)
| ~ in_environment(sK4_skl,X0)
| ~ environment(sK4_skl) ),
inference(resolution,[status(thm)],[f130,f10]) ).
fof(f133,plain,
( sQ16_spl
| sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f132,f47,f34,f128]) ).
fof(f134,plain,
! [X0] :
( ~ sQ7_spl
| sQ1_spl
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,sK2_skl(sK1_skl(sK4_skl),X0))
| sK1_skl(sK4_skl) = critical_point(X0)
| ~ in_environment(X0,sK1_skl(sK4_skl))
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f62]) ).
fof(f135,plain,
! [X0] :
( ~ sQ7_spl
| sQ1_spl
| sP0_prd(sK0_skl(X0,sK4_skl),X0,sK4_skl)
| ~ in_environment(sK4_skl,X0)
| ~ environment(sK4_skl)
| ~ subpopulations(first_movers,efficient_producers,sK4_skl,sK2_skl(sK1_skl(sK4_skl),sK4_skl))
| sK1_skl(sK4_skl) = critical_point(sK4_skl)
| ~ environment(sK4_skl) ),
inference(resolution,[status(thm)],[f134,f10]) ).
fof(f136,plain,
( ~ sQ7_spl
| sQ1_spl
| sQ0_spl
| ~ sQ14_spl
| sQ13_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f135,f47,f107,f118,f34,f37,f76]) ).
fof(f138,plain,
( ~ sQ0_spl
| ~ stable(sK4_skl)
| ~ environment(sK4_skl)
| sP0_prd(sK0_skl(sK3_skl(sK4_skl),sK4_skl),sK3_skl(sK4_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f35,f20]) ).
fof(f143,definition,
( sQ18_spl
<=> sP0_prd(sK0_skl(sK3_skl(sK4_skl),sK4_skl),sK3_skl(sK4_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ18_spl
| sP0_prd(sK0_skl(sK3_skl(sK4_skl),sK4_skl),sK3_skl(sK4_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f138,f143,f47,f54,f34]) ).
fof(f147,plain,
( ~ sQ18_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f101]) ).
fof(f148,plain,
( ~ sQ18_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f154,plain,
! [X0] :
( sQ8_spl
| ~ sP0_prd(sK0_skl(sK3_skl(sK4_skl),sK4_skl),X0,sK4_skl) ),
inference(resolution,[status(thm)],[f83,f29]) ).
fof(f155,plain,
( ~ sQ18_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f154]) ).
fof(f156,plain,
( ~ sQ18_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f157,plain,
$false,
inference(sat_refutation,[status(thm)],[f40,f57,f59,f61,f74,f79,f87,f113,f131,f133,f136,f146,f148,f156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 01:21:49 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.45 % Elapsed time: 0.070323 seconds
% 0.10/0.45 % CPU time: 0.169509 seconds
% 0.10/0.45 % Total memory used: 81.324 MB
% 0.10/0.45 % Net memory used: 80.876 MB
%------------------------------------------------------------------------------