%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT032-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 01:25:21 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 7 unt; 6 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 133 ( 64 ~; 63 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 7 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,hypothesis,
! [A] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,hypothesis,
! [A,B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
environment(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
stable(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [A] :
( subpopulations(first_movers,efficient_producers,sk2,sk3(A))
| ~ in_environment(sk2,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [A] :
( greater_or_equal(sk3(A),A)
| ~ in_environment(sk2,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
! [A] :
( ~ selection_favors(efficient_producers,first_movers,sk3(A))
| ~ in_environment(sk2,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [B,C,D] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ! [A] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0] :
( in_environment(X0,sk1(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ! [A] :
( ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
environment(sk2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
stable(sk2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,sk2,sk3(X0))
| ~ in_environment(sk2,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0] :
( greater_or_equal(sk3(X0),X0)
| ~ in_environment(sk2,X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
! [X0] :
( ~ selection_favors(efficient_producers,first_movers,sk3(X0))
| ~ in_environment(sk2,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f19,plain,
( in_environment(sk2,sk1(sk2))
| ~ stable(sk2) ),
inference(resolution,[status(thm)],[f11,f14]) ).
fof(f20,definition,
( sQ0_spl
<=> stable(sk2) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( sQ0_spl
| ~ stable(sk2) ),
inference(component_clause,[status(thm)],[f20]) ).
fof(f23,definition,
( sQ1_spl
<=> in_environment(sk2,sk1(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f24,plain,
( ~ sQ1_spl
| in_environment(sk2,sk1(sk2)) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f26,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f20,f23]) ).
fof(f27,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22,f15]) ).
fof(f28,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f27]) ).
fof(f29,plain,
( ~ sQ1_spl
| greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) ),
inference(resolution,[status(thm)],[f24,f17]) ).
fof(f30,plain,
( ~ sQ1_spl
| subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) ),
inference(resolution,[status(thm)],[f16,f24]) ).
fof(f31,plain,
( ~ sQ1_spl
| greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2))
| ~ stable(sk2)
| ~ environment(sk2) ),
inference(resolution,[status(thm)],[f30,f13]) ).
fof(f32,plain,
( ~ sQ1_spl
| selection_favors(efficient_producers,first_movers,sk3(sk1(sk2)))
| ~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ environment(sk2) ),
inference(resolution,[status(thm)],[f30,f10]) ).
fof(f33,definition,
( sQ2_spl
<=> environment(sk2) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( sQ2_spl
| ~ environment(sk2) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,definition,
( sQ3_spl
<=> greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( sQ3_spl
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ4_spl
<=> greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2)))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( ~ sQ1_spl
| sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f31,f33,f20,f36,f39,f23]) ).
fof(f43,definition,
( sQ5_spl
<=> selection_favors(efficient_producers,first_movers,sk3(sk1(sk2))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ5_spl
| selection_favors(efficient_producers,first_movers,sk3(sk1(sk2))) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,plain,
( ~ sQ1_spl
| sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f32,f33,f39,f43,f23]) ).
fof(f47,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f35,f14]) ).
fof(f48,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f47]) ).
fof(f49,plain,
( sQ3_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f29]) ).
fof(f50,plain,
( sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f49]) ).
fof(f51,plain,
( ~ sQ5_spl
| ~ in_environment(sk2,sk1(sk2)) ),
inference(resolution,[status(thm)],[f44,f18]) ).
fof(f52,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f51,f24]) ).
fof(f53,plain,
( ~ sQ5_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f52]) ).
fof(f54,plain,
$false,
inference(sat_refutation,[status(thm)],[f26,f28,f42,f46,f48,f50,f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT032-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 01:22:54 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.054778 seconds
% 0.14/0.41 % CPU time: 0.155268 seconds
% 0.14/0.41 % Total memory used: 55.543 MB
% 0.14/0.41 % Net memory used: 55.101 MB
%------------------------------------------------------------------------------