%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT023-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 01:25:18 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 31
% Syntax : Number of formulae : 114 ( 9 unt; 14 def)
% Number of atoms : 438 ( 20 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 602 ( 278 ~; 310 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 15 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 109 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in_environment(A,sk2(A))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( in_environment(A,sk2(A))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( in_environment(A,sk2(A))
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
! [A,B] :
( B = critical_point(A)
| subpopulations(first_movers,efficient_producers,A,sk3(B,A))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
! [A,B] :
( B = critical_point(A)
| greater(sk3(B,A),B)
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
! [A,B] :
( B = critical_point(A)
| ~ greater(growth_rate(efficient_producers,sk3(B,A)),growth_rate(first_movers,sk3(B,A)))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
! [A] :
( in_environment(A,sk4(A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
! [A,B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk4(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
environment(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
stable(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ in_environment(sk5,critical_point(sk5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [A] :
( in_environment(A,sk2(A))
| ! [B] :
( subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1] :
( in_environment(X0,sk2(X0))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [A] :
( in_environment(A,sk2(A))
| ! [B] :
( greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( in_environment(X0,sk2(X0))
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [A] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ! [B] :
( subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ! [A] :
( ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ! [B] :
( subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [A] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ! [B] :
( greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f27,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ! [A] :
( ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ! [B] :
( greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f29,plain,
! [X0,X1,X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [A] :
( in_environment(A,sk2(A))
| ! [B] :
( ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f31,plain,
! [X0,X1] :
( in_environment(X0,sk2(X0))
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [A] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ! [B] :
( ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f33,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ! [A] :
( ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ! [B] :
( ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f35,plain,
! [X0,X1,X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| subpopulations(first_movers,efficient_producers,X0,sk3(X1,X0))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f37,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| greater(sk3(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)],[f11]) ).
fof(f38,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| ~ greater(growth_rate(efficient_producers,sk3(X1,X0)),growth_rate(first_movers,sk3(X1,X0)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f39,plain,
! [X0] :
( in_environment(X0,sk4(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
! [B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ! [A] :
( ~ greater_or_equal(B,sk4(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f41,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk4(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
environment(sk5),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f43,plain,
stable(sk5),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f44,plain,
~ in_environment(sk5,critical_point(sk5)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f45,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk2(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X1)
| greater_or_equal(sk1(X0,sk5),X0)
| ~ in_environment(sk5,X0) ),
inference(resolution,[status(thm)],[f29,f42]) ).
fof(f46,definition,
! [X0] :
( sQ0_spl
<=> ( greater_or_equal(sk1(X0,sk5),X0)
| ~ in_environment(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f47,plain,
! [X0] :
( ~ sQ0_spl
| greater_or_equal(sk1(X0,sk5),X0)
| ~ in_environment(sk5,X0) ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,definition,
! [X1] :
( sQ1_spl
<=> ( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk2(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f50,plain,
! [X0] :
( ~ sQ1_spl
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f46,f49]) ).
fof(f53,plain,
! [X0] :
( ~ sQ0_spl
| greater(growth_rate(efficient_producers,sk1(sk4(X0),sk5)),growth_rate(first_movers,sk1(sk4(X0),sk5)))
| ~ subpopulations(first_movers,efficient_producers,X0,sk1(sk4(X0),sk5))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(sk5,sk4(X0)) ),
inference(resolution,[status(thm)],[f47,f41]) ).
fof(f54,plain,
( ~ sQ0_spl
| ~ stable(sk5)
| ~ environment(sk5)
| greater(growth_rate(efficient_producers,sk1(sk4(sk5),sk5)),growth_rate(first_movers,sk1(sk4(sk5),sk5)))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5))
| ~ stable(sk5)
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f53,f39]) ).
fof(f55,definition,
( sQ2_spl
<=> environment(sk5) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( sQ2_spl
| ~ environment(sk5) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,definition,
( sQ3_spl
<=> stable(sk5) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( sQ3_spl
| ~ stable(sk5) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,definition,
( sQ4_spl
<=> subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( sQ4_spl
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5)) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,definition,
( sQ5_spl
<=> greater(growth_rate(efficient_producers,sk1(sk4(sk5),sk5)),growth_rate(first_movers,sk1(sk4(sk5),sk5))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ5_spl
| greater(growth_rate(efficient_producers,sk1(sk4(sk5),sk5)),growth_rate(first_movers,sk1(sk4(sk5),sk5))) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f54,f55,f58,f61,f64,f46]) ).
fof(f68,plain,
! [X0] :
( ~ sQ5_spl
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0)
| ~ in_environment(sk5,sk4(sk5))
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f65,f35]) ).
fof(f69,plain,
( ~ sQ5_spl
| in_environment(sk5,sk2(sk5))
| ~ in_environment(sk5,sk4(sk5))
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f65,f31]) ).
fof(f70,definition,
( sQ6_spl
<=> in_environment(sk5,sk4(sk5)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( sQ6_spl
| ~ in_environment(sk5,sk4(sk5)) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( ~ sQ5_spl
| sQ1_spl
| ~ sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f68,f55,f70,f49,f64]) ).
fof(f74,definition,
( sQ7_spl
<=> in_environment(sk5,sk2(sk5)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( sQ7_spl
| ~ in_environment(sk5,sk2(sk5)) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( ~ sQ5_spl
| sQ7_spl
| ~ sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f69,f55,f70,f74,f64]) ).
fof(f78,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f42]) ).
fof(f79,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f78]) ).
fof(f80,plain,
( sQ6_spl
| ~ stable(sk5)
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f72,f39]) ).
fof(f81,plain,
( sQ6_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f80,f55,f58,f70]) ).
fof(f82,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f60,f43]) ).
fof(f83,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f82]) ).
fof(f84,plain,
! [X0] :
( ~ sQ1_spl
| sk2(sk5) = critical_point(X0)
| ~ in_environment(X0,sk2(sk5))
| greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ environment(X0)
| greater(growth_rate(efficient_producers,sk3(sk2(sk5),X0)),growth_rate(first_movers,sk3(sk2(sk5),X0)))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk3(sk2(sk5),X0)) ),
inference(resolution,[status(thm)],[f50,f37]) ).
fof(f85,definition,
! [X0] :
( sQ8_spl
<=> ( sk2(sk5) = critical_point(X0)
| ~ in_environment(X0,sk2(sk5))
| ~ environment(X0)
| greater(growth_rate(efficient_producers,sk3(sk2(sk5),X0)),growth_rate(first_movers,sk3(sk2(sk5),X0)))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk3(sk2(sk5),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f86,plain,
! [X0] :
( ~ sQ8_spl
| sk2(sk5) = critical_point(X0)
| ~ in_environment(X0,sk2(sk5))
| ~ environment(X0)
| greater(growth_rate(efficient_producers,sk3(sk2(sk5),X0)),growth_rate(first_movers,sk3(sk2(sk5),X0)))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk3(sk2(sk5),X0)) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ9_spl
<=> greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ9_spl
| greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5))) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( ~ sQ1_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f84,f85,f88,f49]) ).
fof(f92,plain,
! [X0] :
( ~ sQ8_spl
| sk2(sk5) = critical_point(X0)
| ~ in_environment(X0,sk2(sk5))
| greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ environment(X0)
| sk2(sk5) = critical_point(X0)
| ~ in_environment(X0,sk2(sk5))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,sk5,sk3(sk2(sk5),X0)) ),
inference(resolution,[status(thm)],[f86,f38]) ).
fof(f93,definition,
! [X0] :
( sQ10_spl
<=> ( sk2(sk5) = critical_point(X0)
| ~ in_environment(X0,sk2(sk5))
| ~ environment(X0)
| sk2(sk5) = critical_point(X0)
| ~ in_environment(X0,sk2(sk5))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,sk5,sk3(sk2(sk5),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f94,plain,
! [X0] :
( ~ sQ10_spl
| sk2(sk5) = critical_point(X0)
| ~ in_environment(X0,sk2(sk5))
| ~ environment(X0)
| sk2(sk5) = critical_point(X0)
| ~ in_environment(X0,sk2(sk5))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,sk5,sk3(sk2(sk5),X0)) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( ~ sQ8_spl
| sQ9_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f92,f93,f88,f85]) ).
fof(f97,plain,
! [X0] :
( ~ sQ10_spl
| sk2(sk5) = critical_point(X0)
| ~ in_environment(X0,sk2(sk5))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,sk5,sk3(sk2(sk5),X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f94]) ).
fof(f98,plain,
! [X0] :
( ~ sQ9_spl
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk5)),growth_rate(first_movers,sk1(X0,sk5)))
| ~ in_environment(sk5,X0)
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f89,f33]) ).
fof(f99,plain,
! [X0] :
( ~ sQ9_spl
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ in_environment(sk5,X0)
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f89,f23]) ).
fof(f100,plain,
! [X0] :
( ~ sQ9_spl
| greater_or_equal(sk1(X0,sk5),X0)
| ~ in_environment(sk5,X0)
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f89,f27]) ).
fof(f101,definition,
! [X0] :
( sQ11_spl
<=> ( ~ greater(growth_rate(efficient_producers,sk1(X0,sk5)),growth_rate(first_movers,sk1(X0,sk5)))
| ~ in_environment(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f102,plain,
! [X0] :
( ~ sQ11_spl
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk5)),growth_rate(first_movers,sk1(X0,sk5)))
| ~ in_environment(sk5,X0) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( ~ sQ9_spl
| sQ11_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f98,f55,f101,f88]) ).
fof(f105,definition,
! [X0] :
( sQ12_spl
<=> ( subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ in_environment(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f106,plain,
! [X0] :
( ~ sQ12_spl
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ in_environment(sk5,X0) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( ~ sQ9_spl
| sQ12_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f99,f55,f105,f88]) ).
fof(f109,plain,
( ~ sQ9_spl
| sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f100,f55,f46,f88]) ).
fof(f110,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ subpopulations(first_movers,efficient_producers,X0,sk1(sk4(X0),sk5))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(sk5,sk4(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f102]) ).
fof(f112,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ stable(sk5)
| ~ environment(sk5)
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5))
| ~ stable(sk5)
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f110,f39]) ).
fof(f113,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f112,f55,f58,f61,f101,f46]) ).
fof(f114,plain,
! [X0] :
( sQ4_spl
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0)
| ~ in_environment(sk5,sk4(sk5))
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f63,f25]) ).
fof(f115,plain,
( sQ4_spl
| sQ1_spl
| ~ sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f114,f55,f70,f49,f61]) ).
fof(f116,plain,
( sQ4_spl
| ~ sQ12_spl
| ~ in_environment(sk5,sk4(sk5)) ),
inference(resolution,[status(thm)],[f106,f63]) ).
fof(f117,plain,
( sQ4_spl
| ~ sQ12_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f116,f70,f105,f61]) ).
fof(f118,plain,
( ~ sQ10_spl
| sk2(sk5) = critical_point(sk5)
| ~ in_environment(sk5,sk2(sk5))
| greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ environment(sk5)
| sk2(sk5) = critical_point(sk5)
| ~ in_environment(sk5,sk2(sk5))
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f97,f36]) ).
fof(f119,definition,
( sQ13_spl
<=> sk2(sk5) = critical_point(sk5) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ13_spl
| sk2(sk5) = critical_point(sk5) ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( ~ sQ10_spl
| sQ9_spl
| sQ13_spl
| ~ sQ7_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f118,f55,f74,f119,f88,f93]) ).
fof(f123,plain,
( ~ sQ13_spl
| ~ in_environment(sk5,sk2(sk5)) ),
inference(backward_demodulation,[status(thm)],[f120,f44]) ).
fof(f128,plain,
! [X0] :
( sQ7_spl
| greater_or_equal(sk1(X0,sk5),X0)
| ~ in_environment(sk5,X0)
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f76,f21]) ).
fof(f129,plain,
! [X0] :
( sQ7_spl
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ in_environment(sk5,X0)
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[f76,f19]) ).
fof(f130,plain,
( sQ7_spl
| sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f128,f55,f46,f74]) ).
fof(f131,plain,
( sQ7_spl
| sQ12_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f129,f55,f105,f74]) ).
fof(f133,plain,
( ~ sQ13_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f123,f74,f119]) ).
fof(f135,plain,
$false,
inference(sat_refutation,[status(thm)],[f52,f67,f73,f77,f79,f81,f83,f91,f96,f104,f108,f109,f113,f115,f117,f122,f130,f131,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 01:21:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.035649 seconds
% 0.13/0.39 % CPU time: 0.090379 seconds
% 0.13/0.39 % Total memory used: 15.745 MB
% 0.13/0.39 % Net memory used: 15.725 MB
%------------------------------------------------------------------------------