%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT028+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 01:25:19 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 5 unt; 11 def)
% Number of atoms : 262 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 311 ( 124 ~; 126 |; 41 &)
% ( 11 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 11 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 66 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E] :
( ( ? [T1] :
( ! [T] :
( ( greater_or_equal(T,T1)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& in_environment(E,T1) )
& stable(E)
& environment(E) )
=> ? [T2] :
( ! [T] :
( ( greater_or_equal(T,T2)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& greater(T2,appear(efficient_producers,E)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,hypothesis,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) ) )
& in_environment(E,To) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& greater(To,appear(efficient_producers,E)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& greater(To,appear(efficient_producers,E)) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [E] :
( ? [T2] :
( ! [T] :
( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,T2)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& greater(T2,appear(efficient_producers,E)) )
| ! [T1] :
( ? [T] :
( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,T1)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,T1) )
| ~ stable(E)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f6,definition,
! [E,T1,T] :
( sP0_prd(T,T1,E)
<=> ( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,T1)
& subpopulations(first_movers,efficient_producers,E,T) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f7,plain,
! [E] :
( ? [T2] :
( ! [T] :
( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,T2)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& greater(T2,appear(efficient_producers,E)) )
| ! [T1] :
( ? [T] : sP0_prd(T,T1,E)
| ~ in_environment(E,T1) )
| ~ stable(E)
| ~ environment(E) ),
inference(formula_renaming,[status(thm)],[f5,f6]) ).
fof(f8,plain,
! [E] :
( ( ! [T] :
( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,sK1_skl(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& greater(sK1_skl(E),appear(efficient_producers,E)) )
| ! [T1] :
( sP0_prd(sK0_skl(T1,E),T1,E)
| ~ in_environment(E,T1) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(T,sK0_skl(T1,E)),skolemize(T2,sK1_skl(E))],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( greater(sK1_skl(X0),appear(efficient_producers,X0))
| sP0_prd(sK0_skl(X1,X0),X1,X0)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK1_skl(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| sP0_prd(sK0_skl(X1,X0),X1,X0)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
! [E] :
( ? [To] :
( ! [T] :
( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ~ 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)],[f2]) ).
fof(f12,plain,
! [E] :
( ( ! [T] :
( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ~ greater_or_equal(T,sK2_skl(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,sK2_skl(E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(To,sK2_skl(E))],[f11]) ).
fof(f13,plain,
! [X0] :
( in_environment(X0,sK2_skl(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f15,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sK2_skl(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,plain,
? [E] :
( ! [To] :
( ? [T] :
( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ greater(To,appear(efficient_producers,E)) )
& stable(E)
& environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
( ! [To] :
( ( ~ greater(zero,growth_rate(first_movers,sK4_skl(To)))
& greater_or_equal(sK4_skl(To),To)
& subpopulations(first_movers,efficient_producers,sK3_skl,sK4_skl(To)) )
| ~ greater(To,appear(efficient_producers,sK3_skl)) )
& stable(sK3_skl)
& environment(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(E,sK3_skl),skolemize(T,sK4_skl(To))],[f16]) ).
fof(f18,plain,
environment(sK3_skl),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
stable(sK3_skl),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,sK3_skl,sK4_skl(X0))
| ~ greater(X0,appear(efficient_producers,sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [X0] :
( greater_or_equal(sK4_skl(X0),X0)
| ~ greater(X0,appear(efficient_producers,sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f22,plain,
! [X0] :
( ~ greater(zero,growth_rate(first_movers,sK4_skl(X0)))
| ~ greater(X0,appear(efficient_producers,sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f23,plain,
! [E,T1,T] :
( ( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,T1)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| sP0_prd(T,T1,E) )
& ( ( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,T1)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ sP0_prd(T,T1,E) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
( ! [E,T1,T] :
( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,T1)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| sP0_prd(T,T1,E) )
& ! [E,T1,T] :
( ( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,T1)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ sP0_prd(T,T1,E) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( subpopulations(first_movers,efficient_producers,X2,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( greater_or_equal(X0,X1)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ greater(zero,growth_rate(first_movers,X0))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f29,plain,
! [X0] :
( greater(sK1_skl(sK3_skl),appear(efficient_producers,sK3_skl))
| sP0_prd(sK0_skl(X0,sK3_skl),X0,sK3_skl)
| ~ in_environment(sK3_skl,X0)
| ~ environment(sK3_skl) ),
inference(resolution,[status(thm)],[f9,f19]) ).
fof(f30,definition,
( sQ0_spl
<=> environment(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f32,plain,
( sQ0_spl
| ~ environment(sK3_skl) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,definition,
! [X0] :
( sQ1_spl
<=> ( sP0_prd(sK0_skl(X0,sK3_skl),X0,sK3_skl)
| ~ in_environment(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f34,plain,
! [X0] :
( ~ sQ1_spl
| sP0_prd(sK0_skl(X0,sK3_skl),X0,sK3_skl)
| ~ in_environment(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,definition,
( sQ2_spl
<=> greater(sK1_skl(sK3_skl),appear(efficient_producers,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ2_spl
| greater(sK1_skl(sK3_skl),appear(efficient_producers,sK3_skl)) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f30,f33,f36]) ).
fof(f40,plain,
( ~ sQ2_spl
| greater_or_equal(sK4_skl(sK1_skl(sK3_skl)),sK1_skl(sK3_skl)) ),
inference(resolution,[status(thm)],[f37,f21]) ).
fof(f45,definition,
( sQ4_spl
<=> greater(zero,growth_rate(first_movers,sK4_skl(sK1_skl(sK3_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( ~ sQ4_spl
| greater(zero,growth_rate(first_movers,sK4_skl(sK1_skl(sK3_skl)))) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f49,plain,
( ~ sQ4_spl
| ~ greater(sK1_skl(sK3_skl),appear(efficient_producers,sK3_skl)) ),
inference(resolution,[status(thm)],[f46,f22]) ).
fof(f51,plain,
( ~ sQ1_spl
| ~ stable(sK3_skl)
| ~ environment(sK3_skl)
| sP0_prd(sK0_skl(sK2_skl(sK3_skl),sK3_skl),sK2_skl(sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f34,f13]) ).
fof(f52,definition,
( sQ5_spl
<=> sP0_prd(sK0_skl(sK2_skl(sK3_skl),sK3_skl),sK2_skl(sK3_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ5_spl
| sP0_prd(sK0_skl(sK2_skl(sK3_skl),sK3_skl),sK2_skl(sK3_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ6_spl
<=> stable(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( sQ6_spl
| ~ stable(sK3_skl) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f51,f52,f30,f55,f33]) ).
fof(f59,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f32,f18]) ).
fof(f60,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f59]) ).
fof(f61,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f19]) ).
fof(f62,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f61]) ).
fof(f65,plain,
( ~ sQ5_spl
| greater_or_equal(sK0_skl(sK2_skl(sK3_skl),sK3_skl),sK2_skl(sK3_skl)) ),
inference(resolution,[status(thm)],[f53,f26]) ).
fof(f70,definition,
( sQ8_spl
<=> greater(zero,growth_rate(first_movers,sK0_skl(sK2_skl(sK3_skl),sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ8_spl
| greater(zero,growth_rate(first_movers,sK0_skl(sK2_skl(sK3_skl),sK3_skl))) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f74,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ sP0_prd(sK0_skl(sK2_skl(sK3_skl),sK3_skl),X0,X1) ),
inference(resolution,[status(thm)],[f71,f27]) ).
fof(f75,plain,
! [X0] :
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sK2_skl(sK3_skl))
| ~ subpopulations(first_movers,efficient_producers,sK3_skl,X0)
| ~ environment(sK3_skl) ),
inference(resolution,[status(thm)],[f15,f19]) ).
fof(f76,definition,
! [X0] :
( sQ9_spl
<=> ( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sK2_skl(sK3_skl))
| ~ subpopulations(first_movers,efficient_producers,sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f77,plain,
! [X0] :
( ~ sQ9_spl
| greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sK2_skl(sK3_skl))
| ~ subpopulations(first_movers,efficient_producers,sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f75,f30,f76]) ).
fof(f80,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f53,f74]) ).
fof(f81,plain,
( ~ sQ5_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f80]) ).
fof(f83,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| greater(zero,growth_rate(first_movers,sK0_skl(sK2_skl(sK3_skl),sK3_skl)))
| ~ subpopulations(first_movers,efficient_producers,sK3_skl,sK0_skl(sK2_skl(sK3_skl),sK3_skl)) ),
inference(resolution,[status(thm)],[f77,f65]) ).
fof(f84,definition,
( sQ10_spl
<=> subpopulations(first_movers,efficient_producers,sK3_skl,sK0_skl(sK2_skl(sK3_skl),sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( sQ10_spl
| ~ subpopulations(first_movers,efficient_producers,sK3_skl,sK0_skl(sK2_skl(sK3_skl),sK3_skl)) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f83,f84,f70,f76,f52]) ).
fof(f88,plain,
! [X0] :
( sQ10_spl
| ~ sP0_prd(sK0_skl(sK2_skl(sK3_skl),sK3_skl),X0,sK3_skl) ),
inference(resolution,[status(thm)],[f86,f25]) ).
fof(f89,plain,
( ~ sQ5_spl
| sQ10_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f53,f88]) ).
fof(f90,plain,
( ~ sQ5_spl
| sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f89]) ).
fof(f92,plain,
! [X0] :
( ~ sQ2_spl
| greater(zero,growth_rate(first_movers,sK4_skl(sK1_skl(sK3_skl))))
| ~ subpopulations(first_movers,efficient_producers,sK3_skl,sK4_skl(sK1_skl(sK3_skl)))
| sP0_prd(sK0_skl(X0,sK3_skl),X0,sK3_skl)
| ~ in_environment(sK3_skl,X0)
| ~ stable(sK3_skl)
| ~ environment(sK3_skl) ),
inference(resolution,[status(thm)],[f40,f10]) ).
fof(f94,definition,
( sQ11_spl
<=> subpopulations(first_movers,efficient_producers,sK3_skl,sK4_skl(sK1_skl(sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( sQ11_spl
| ~ subpopulations(first_movers,efficient_producers,sK3_skl,sK4_skl(sK1_skl(sK3_skl))) ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,plain,
( ~ sQ2_spl
| sQ4_spl
| ~ sQ11_spl
| sQ1_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f92,f30,f55,f33,f94,f45,f36]) ).
fof(f99,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f37]) ).
fof(f100,plain,
( ~ sQ4_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f99]) ).
fof(f101,plain,
( sQ11_spl
| ~ greater(sK1_skl(sK3_skl),appear(efficient_producers,sK3_skl)) ),
inference(resolution,[status(thm)],[f96,f20]) ).
fof(f103,plain,
( sQ11_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f101,f37]) ).
fof(f104,plain,
( sQ11_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f103]) ).
fof(f105,plain,
$false,
inference(sat_refutation,[status(thm)],[f39,f58,f60,f62,f79,f81,f87,f90,f97,f100,f104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT028+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n009.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 01:22:12 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.46 % Refutation found
% 0.16/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.51 % Elapsed time: 0.063775 seconds
% 0.16/0.51 % CPU time: 0.087519 seconds
% 0.16/0.51 % Total memory used: 4.394 MB
% 0.16/0.51 % Net memory used: 4.353 MB
%------------------------------------------------------------------------------