%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT030-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 01:25:20 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.33s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 29
% Syntax : Number of formulae : 106 ( 7 unt; 13 def)
% Number of atoms : 366 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 485 ( 225 ~; 247 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 14 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 95 !; 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] :
( in_environment(A,sk3(A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
! [A,B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk3(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
environment(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
stable(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [A] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(A))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
! [A] :
( greater(sk5(A),A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
! [A] :
( ~ greater(growth_rate(efficient_producers,sk5(A)),growth_rate(first_movers,sk5(A)))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,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(f18,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)],[f17]) ).
fof(f19,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(f20,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)],[f19]) ).
fof(f21,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(f22,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)],[f21]) ).
fof(f23,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(f24,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)],[f23]) ).
fof(f25,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(f26,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)],[f25]) ).
fof(f27,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(f28,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)],[f27]) ).
fof(f29,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(f30,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)],[f29]) ).
fof(f31,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(f32,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)],[f31]) ).
fof(f33,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(f34,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)],[f33]) ).
fof(f35,plain,
! [X0] :
( in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
! [B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ! [A] :
( ~ greater_or_equal(B,sk3(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f37,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
environment(sk4),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f39,plain,
stable(sk4),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f41,plain,
! [X0] :
( greater(sk5(X0),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f42,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sk5(X0)),growth_rate(first_movers,sk5(X0)))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f43,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[f28,f38]) ).
fof(f44,definition,
! [X0] :
( sQ0_spl
<=> ( greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f45,plain,
! [X0] :
( ~ sQ0_spl
| greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,definition,
! [X1] :
( sQ1_spl
<=> ( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f48,plain,
! [X0] :
( ~ sQ1_spl
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f44,f47]) ).
fof(f51,plain,
! [X0] :
( ~ sQ0_spl
| greater(growth_rate(efficient_producers,sk1(sk3(X0),sk4)),growth_rate(first_movers,sk1(sk3(X0),sk4)))
| ~ subpopulations(first_movers,efficient_producers,X0,sk1(sk3(X0),sk4))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(sk4,sk3(X0)) ),
inference(resolution,[status(thm)],[f45,f37]) ).
fof(f52,plain,
( ~ sQ0_spl
| ~ stable(sk4)
| ~ environment(sk4)
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ stable(sk4)
| ~ environment(sk4) ),
inference(resolution,[status(thm)],[f51,f35]) ).
fof(f53,definition,
( sQ2_spl
<=> environment(sk4) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ2_spl
| ~ environment(sk4) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ3_spl
<=> stable(sk4) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( sQ3_spl
| ~ stable(sk4) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,definition,
( sQ4_spl
<=> subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( sQ4_spl
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,definition,
( sQ5_spl
<=> greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( ~ sQ5_spl
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f52,f53,f56,f59,f62,f44]) ).
fof(f66,plain,
! [X0] :
( ~ sQ5_spl
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ in_environment(sk4,sk3(sk4))
| ~ environment(sk4) ),
inference(resolution,[status(thm)],[f63,f34]) ).
fof(f67,plain,
( ~ sQ5_spl
| in_environment(sk4,sk2(sk4))
| ~ in_environment(sk4,sk3(sk4))
| ~ environment(sk4) ),
inference(resolution,[status(thm)],[f63,f30]) ).
fof(f68,definition,
( sQ6_spl
<=> in_environment(sk4,sk3(sk4)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( sQ6_spl
| ~ in_environment(sk4,sk3(sk4)) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( ~ sQ5_spl
| sQ1_spl
| ~ sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f66,f53,f68,f47,f62]) ).
fof(f72,definition,
( sQ7_spl
<=> in_environment(sk4,sk2(sk4)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( sQ7_spl
| ~ in_environment(sk4,sk2(sk4)) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,plain,
( ~ sQ5_spl
| sQ7_spl
| ~ sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f67,f53,f68,f72,f62]) ).
fof(f76,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f38]) ).
fof(f77,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f78,plain,
( ~ sQ1_spl
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ in_environment(sk4,sk2(sk4))
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(resolution,[status(thm)],[f48,f41]) ).
fof(f79,definition,
( sQ8_spl
<=> subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( sQ8_spl
| ~ subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,definition,
( sQ9_spl
<=> greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4)))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ9_spl
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4)))) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ10_spl
<=> greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ10_spl
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( ~ sQ1_spl
| sQ10_spl
| ~ sQ7_spl
| sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f78,f79,f82,f72,f85,f47]) ).
fof(f89,plain,
! [X0] :
( ~ sQ10_spl
| greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0)
| ~ environment(sk4) ),
inference(resolution,[status(thm)],[f86,f26]) ).
fof(f90,plain,
! [X0] :
( ~ sQ10_spl
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0)
| ~ environment(sk4) ),
inference(resolution,[status(thm)],[f86,f32]) ).
fof(f91,plain,
! [X0] :
( ~ sQ10_spl
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0)
| ~ environment(sk4) ),
inference(resolution,[status(thm)],[f86,f22]) ).
fof(f92,plain,
( ~ sQ10_spl
| sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f89,f53,f44,f85]) ).
fof(f93,definition,
! [X0] :
( sQ11_spl
<=> ( ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f94,plain,
! [X0] :
( ~ sQ11_spl
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( ~ sQ10_spl
| sQ11_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f90,f53,f93,f85]) ).
fof(f97,definition,
! [X0] :
( sQ12_spl
<=> ( subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f98,plain,
! [X0] :
( ~ sQ12_spl
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( ~ sQ10_spl
| sQ12_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f91,f53,f97,f85]) ).
fof(f101,plain,
( sQ6_spl
| ~ stable(sk4)
| ~ environment(sk4) ),
inference(resolution,[status(thm)],[f70,f35]) ).
fof(f102,plain,
( sQ6_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f101,f53,f56,f68]) ).
fof(f103,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f39]) ).
fof(f104,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f103]) ).
fof(f105,plain,
! [X0] :
( sQ4_spl
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ in_environment(sk4,sk3(sk4))
| ~ environment(sk4) ),
inference(resolution,[status(thm)],[f61,f24]) ).
fof(f106,plain,
( sQ4_spl
| sQ1_spl
| ~ sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f105,f53,f68,f47,f59]) ).
fof(f107,plain,
( ~ sQ9_spl
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ in_environment(sk4,sk2(sk4)) ),
inference(resolution,[status(thm)],[f83,f42]) ).
fof(f108,plain,
( ~ sQ9_spl
| sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f107,f72,f85,f82]) ).
fof(f116,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ in_environment(sk4,sk3(sk4)) ),
inference(resolution,[status(thm)],[f63,f94]) ).
fof(f119,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f116,f68,f62,f93]) ).
fof(f122,plain,
! [X0] :
( sQ7_spl
| greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0)
| ~ environment(sk4) ),
inference(resolution,[status(thm)],[f74,f20]) ).
fof(f123,plain,
! [X0] :
( sQ7_spl
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0)
| ~ environment(sk4) ),
inference(resolution,[status(thm)],[f74,f18]) ).
fof(f124,plain,
( sQ7_spl
| sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f122,f53,f44,f72]) ).
fof(f125,plain,
( sQ7_spl
| sQ12_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f123,f53,f97,f72]) ).
fof(f126,plain,
( sQ8_spl
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ in_environment(sk4,sk2(sk4)) ),
inference(resolution,[status(thm)],[f81,f40]) ).
fof(f127,plain,
( sQ8_spl
| sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f126,f72,f85,f79]) ).
fof(f131,plain,
( sQ4_spl
| ~ sQ12_spl
| ~ in_environment(sk4,sk3(sk4)) ),
inference(resolution,[status(thm)],[f98,f61]) ).
fof(f132,plain,
( sQ4_spl
| ~ sQ12_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f131,f68,f97,f59]) ).
fof(f133,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f65,f71,f75,f77,f88,f92,f96,f100,f102,f104,f106,f108,f119,f124,f125,f127,f132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT030-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 01:21:54 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.33 % Refutation found
% 0.03/0.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.34 % Elapsed time: 0.040279 seconds
% 0.08/0.34 % CPU time: 0.095337 seconds
% 0.08/0.34 % Total memory used: 17.610 MB
% 0.08/0.34 % Net memory used: 17.213 MB
%------------------------------------------------------------------------------