%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU386+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 02:20:22 PM UTC 2026
% Result : Theorem 0.26s 0.55s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 92 ( 20 unt; 13 def)
% Number of atoms : 428 ( 7 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 539 ( 203 ~; 233 |; 62 &)
% ( 19 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 14 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 91 ( 84 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& directed_relstr(B)
& transitive_relstr(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ( C = lim_points_of_net(A,B)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,C)
<=> ! [E] :
( point_neighbourhood(E,A,D)
=> is_eventually_in(A,B,E) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(A))
=> ( is_a_cluster_point_of_netstr(A,B,C)
<=> ! [D] :
( point_neighbourhood(D,A,C)
=> is_often_in(A,B,D) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( ( net_str(B,A)
& directed_relstr(B)
& transitive_relstr(B)
& ~ empty_carrier(B)
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> element(lim_points_of_net(A,B),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( top_str(A)
=> one_sorted_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& directed_relstr(B)
& transitive_relstr(B)
& ~ empty_carrier(B) )
=> ! [C] :
( is_eventually_in(A,B,C)
=> is_often_in(A,B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,conjecture,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& directed_relstr(B)
& transitive_relstr(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(A))
=> ( in(C,lim_points_of_net(A,B))
=> is_a_cluster_point_of_netstr(A,B,C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
~ ! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& directed_relstr(B)
& transitive_relstr(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(A))
=> ( in(C,lim_points_of_net(A,B))
=> is_a_cluster_point_of_netstr(A,B,C) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f60,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( C = lim_points_of_net(A,B)
<=> ! [D] :
( ( in(D,C)
<=> ! [E] :
( is_eventually_in(A,B,E)
| ~ point_neighbourhood(E,A,D) ) )
| ~ element(D,the_carrier(A)) ) )
| ~ element(C,powerset(the_carrier(A))) )
| ~ net_str(B,A)
| ~ directed_relstr(B)
| ~ transitive_relstr(B)
| empty_carrier(B) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f61,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D] :
( ( ! [E] :
( is_eventually_in(A,B,E)
| ~ point_neighbourhood(E,A,D) )
| in(D,C) )
& ( ? [E] :
( ~ is_eventually_in(A,B,E)
& point_neighbourhood(E,A,D) )
| ~ in(D,C) )
& element(D,the_carrier(A)) )
| C = lim_points_of_net(A,B) )
& ( ! [D] :
( ( ( ? [E] :
( ~ is_eventually_in(A,B,E)
& point_neighbourhood(E,A,D) )
| in(D,C) )
& ( ! [E] :
( is_eventually_in(A,B,E)
| ~ point_neighbourhood(E,A,D) )
| ~ in(D,C) ) )
| ~ element(D,the_carrier(A)) )
| C != lim_points_of_net(A,B) ) )
| ~ element(C,powerset(the_carrier(A))) )
| ~ net_str(B,A)
| ~ directed_relstr(B)
| ~ transitive_relstr(B)
| empty_carrier(B) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ( ! [E] :
( is_eventually_in(A,B,E)
| ~ point_neighbourhood(E,A,sK1_skl(C,B,A)) )
| in(sK1_skl(C,B,A),C) )
& ( ( ~ is_eventually_in(A,B,sK2_skl(C,B,A))
& point_neighbourhood(sK2_skl(C,B,A),A,sK1_skl(C,B,A)) )
| ~ in(sK1_skl(C,B,A),C) )
& element(sK1_skl(C,B,A),the_carrier(A)) )
| C = lim_points_of_net(A,B) )
& ( ! [D] :
( ( ( ( ~ is_eventually_in(A,B,sK0_skl(D,C,B,A))
& point_neighbourhood(sK0_skl(D,C,B,A),A,D) )
| in(D,C) )
& ( ! [E] :
( is_eventually_in(A,B,E)
| ~ point_neighbourhood(E,A,D) )
| ~ in(D,C) ) )
| ~ element(D,the_carrier(A)) )
| C != lim_points_of_net(A,B) ) )
| ~ element(C,powerset(the_carrier(A))) )
| ~ net_str(B,A)
| ~ directed_relstr(B)
| ~ transitive_relstr(B)
| empty_carrier(B) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(E,sK0_skl(D,C,B,A)),skolemize(D,sK1_skl(C,B,A)),skolemize(E,sK2_skl(C,B,A))],[f61]) ).
fof(f63,plain,
! [X0,X1,X2,X3,X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3)
| ~ in(X3,X2)
| ~ element(X3,the_carrier(X0))
| X2 != lim_points_of_net(X0,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f70,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( is_a_cluster_point_of_netstr(A,B,C)
<=> ! [D] :
( is_often_in(A,B,D)
| ~ point_neighbourhood(D,A,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f71,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ is_often_in(A,B,D)
& point_neighbourhood(D,A,C) )
| is_a_cluster_point_of_netstr(A,B,C) )
& ( ! [D] :
( is_often_in(A,B,D)
| ~ point_neighbourhood(D,A,C) )
| ~ is_a_cluster_point_of_netstr(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ~ is_often_in(A,B,sK3_skl(C,B,A))
& point_neighbourhood(sK3_skl(C,B,A),A,C) )
| is_a_cluster_point_of_netstr(A,B,C) )
& ( ! [D] :
( is_often_in(A,B,D)
| ~ point_neighbourhood(D,A,C) )
| ~ is_a_cluster_point_of_netstr(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(D,sK3_skl(C,B,A))],[f71]) ).
fof(f74,plain,
! [X0,X1,X2] :
( point_neighbourhood(sK3_skl(X2,X1,X0),X0,X2)
| is_a_cluster_point_of_netstr(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ is_often_in(X0,X1,sK3_skl(X2,X1,X0))
| is_a_cluster_point_of_netstr(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f76,plain,
! [A,B] :
( element(lim_points_of_net(A,B),powerset(the_carrier(A)))
| ~ net_str(B,A)
| ~ directed_relstr(B)
| ~ transitive_relstr(B)
| empty_carrier(B)
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f77,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
! [A] :
( one_sorted_str(A)
| ~ top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f81,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f136,plain,
! [A] :
( ! [B] :
( ! [C] :
( is_often_in(A,B,C)
| ~ is_eventually_in(A,B,C) )
| ~ net_str(B,A)
| ~ directed_relstr(B)
| ~ transitive_relstr(B)
| empty_carrier(B) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f137,plain,
! [X0,X1,X2] :
( is_often_in(X0,X1,X2)
| ~ is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ is_a_cluster_point_of_netstr(A,B,C)
& in(C,lim_points_of_net(A,B))
& element(C,the_carrier(A)) )
& net_str(B,A)
& directed_relstr(B)
& transitive_relstr(B)
& ~ empty_carrier(B) )
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f139,plain,
( ~ is_a_cluster_point_of_netstr(sK17_skl,sK18_skl,sK19_skl)
& in(sK19_skl,lim_points_of_net(sK17_skl,sK18_skl))
& element(sK19_skl,the_carrier(sK17_skl))
& net_str(sK18_skl,sK17_skl)
& directed_relstr(sK18_skl)
& transitive_relstr(sK18_skl)
& ~ empty_carrier(sK18_skl)
& top_str(sK17_skl)
& topological_space(sK17_skl)
& ~ empty_carrier(sK17_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(A,sK17_skl),skolemize(B,sK18_skl),skolemize(C,sK19_skl)],[f138]) ).
fof(f140,plain,
~ empty_carrier(sK17_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
topological_space(sK17_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f142,plain,
top_str(sK17_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,plain,
~ empty_carrier(sK18_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f144,plain,
transitive_relstr(sK18_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f145,plain,
directed_relstr(sK18_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f146,plain,
net_str(sK18_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f147,plain,
element(sK19_skl,the_carrier(sK17_skl)),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f148,plain,
in(sK19_skl,lim_points_of_net(sK17_skl,sK18_skl)),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f149,plain,
~ is_a_cluster_point_of_netstr(sK17_skl,sK18_skl,sK19_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f170,plain,
! [X0,X1,X2,X3] :
( is_eventually_in(X0,X1,X3)
| ~ point_neighbourhood(X3,X0,X2)
| ~ in(X2,lim_points_of_net(X0,X1))
| ~ element(X2,the_carrier(X0))
| ~ element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f175,plain,
! [X0,X1,X2,X3] :
( is_eventually_in(X0,X1,X3)
| ~ point_neighbourhood(X3,X0,X2)
| ~ in(X2,lim_points_of_net(X0,X1))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f170,f77]) ).
fof(f181,definition,
( sQ1_spl
<=> empty_carrier(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ1_spl
| empty_carrier(sK18_skl) ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
( sQ2_spl
<=> directed_relstr(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( sQ2_spl
| ~ directed_relstr(sK18_skl) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f188,definition,
( sQ3_spl
<=> transitive_relstr(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( sQ3_spl
| ~ transitive_relstr(sK18_skl) ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f192,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f182,f143]) ).
fof(f193,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f195,definition,
( sQ4_spl
<=> empty_carrier(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ4_spl
| empty_carrier(sK17_skl) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,definition,
( sQ5_spl
<=> top_str(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ5_spl
| ~ top_str(sK17_skl) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,definition,
( sQ6_spl
<=> net_str(sK18_skl,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( sQ6_spl
| ~ net_str(sK18_skl,sK17_skl) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f212,definition,
( sQ9_spl
<=> topological_space(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( sQ9_spl
| ~ topological_space(sK17_skl) ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f216,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f145]) ).
fof(f217,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f218,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f144]) ).
fof(f219,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f218]) ).
fof(f220,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f146]) ).
fof(f221,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f222,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f200,f142]) ).
fof(f223,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f222]) ).
fof(f224,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f140]) ).
fof(f225,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f224]) ).
fof(f235,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f141]) ).
fof(f236,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f267,definition,
( sQ16_spl
<=> one_sorted_str(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ16_spl
| ~ one_sorted_str(sK17_skl) ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f280,plain,
! [X0] :
( is_eventually_in(sK17_skl,sK18_skl,X0)
| ~ point_neighbourhood(X0,sK17_skl,sK19_skl)
| ~ element(sK19_skl,the_carrier(sK17_skl))
| ~ net_str(sK18_skl,sK17_skl)
| ~ directed_relstr(sK18_skl)
| ~ transitive_relstr(sK18_skl)
| empty_carrier(sK18_skl)
| ~ top_str(sK17_skl)
| ~ topological_space(sK17_skl)
| empty_carrier(sK17_skl) ),
inference(resolution,[status(thm)],[f148,f175]) ).
fof(f282,definition,
( sQ20_spl
<=> element(sK19_skl,the_carrier(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( sQ20_spl
| ~ element(sK19_skl,the_carrier(sK17_skl)) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,definition,
! [X0] :
( sQ21_spl
<=> ( is_eventually_in(sK17_skl,sK18_skl,X0)
| ~ point_neighbourhood(X0,sK17_skl,sK19_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f286,plain,
! [X0] :
( ~ sQ21_spl
| is_eventually_in(sK17_skl,sK18_skl,X0)
| ~ point_neighbourhood(X0,sK17_skl,sK19_skl) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,plain,
( sQ21_spl
| ~ sQ20_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ1_spl
| ~ sQ5_spl
| ~ sQ9_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f280,f195,f212,f198,f181,f188,f184,f201,f282,f285]) ).
fof(f289,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f147]) ).
fof(f290,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f289]) ).
fof(f291,plain,
( ~ is_often_in(sK17_skl,sK18_skl,sK3_skl(sK19_skl,sK18_skl,sK17_skl))
| ~ element(sK19_skl,the_carrier(sK17_skl))
| ~ net_str(sK18_skl,sK17_skl)
| empty_carrier(sK18_skl)
| ~ top_str(sK17_skl)
| ~ topological_space(sK17_skl)
| empty_carrier(sK17_skl) ),
inference(resolution,[status(thm)],[f149,f75]) ).
fof(f292,definition,
( sQ22_spl
<=> is_often_in(sK17_skl,sK18_skl,sK3_skl(sK19_skl,sK18_skl,sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( sQ22_spl
| ~ is_often_in(sK17_skl,sK18_skl,sK3_skl(sK19_skl,sK18_skl,sK17_skl)) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,plain,
( ~ sQ22_spl
| ~ sQ20_spl
| ~ sQ6_spl
| sQ1_spl
| ~ sQ5_spl
| ~ sQ9_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f291,f195,f212,f198,f181,f201,f282,f292]) ).
fof(f338,definition,
( sQ32_spl
<=> is_a_cluster_point_of_netstr(sK17_skl,sK18_skl,sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( ~ sQ32_spl
| is_a_cluster_point_of_netstr(sK17_skl,sK18_skl,sK19_skl) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f342,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f149]) ).
fof(f343,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f342]) ).
fof(f453,plain,
( sQ22_spl
| ~ is_eventually_in(sK17_skl,sK18_skl,sK3_skl(sK19_skl,sK18_skl,sK17_skl))
| ~ net_str(sK18_skl,sK17_skl)
| ~ directed_relstr(sK18_skl)
| ~ transitive_relstr(sK18_skl)
| empty_carrier(sK18_skl)
| ~ one_sorted_str(sK17_skl)
| empty_carrier(sK17_skl) ),
inference(resolution,[status(thm)],[f294,f137]) ).
fof(f455,definition,
( sQ53_spl
<=> is_eventually_in(sK17_skl,sK18_skl,sK3_skl(sK19_skl,sK18_skl,sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ53_spl
| ~ is_eventually_in(sK17_skl,sK18_skl,sK3_skl(sK19_skl,sK18_skl,sK17_skl)) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,plain,
( sQ22_spl
| ~ sQ53_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ1_spl
| ~ sQ16_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f453,f195,f267,f181,f188,f184,f201,f455,f292]) ).
fof(f471,plain,
( ~ sQ21_spl
| sQ53_spl
| ~ point_neighbourhood(sK3_skl(sK19_skl,sK18_skl,sK17_skl),sK17_skl,sK19_skl) ),
inference(resolution,[status(thm)],[f457,f286]) ).
fof(f475,plain,
( ~ sQ21_spl
| sQ53_spl
| is_a_cluster_point_of_netstr(sK17_skl,sK18_skl,sK19_skl)
| ~ element(sK19_skl,the_carrier(sK17_skl))
| ~ net_str(sK18_skl,sK17_skl)
| empty_carrier(sK18_skl)
| ~ top_str(sK17_skl)
| ~ topological_space(sK17_skl)
| empty_carrier(sK17_skl) ),
inference(resolution,[status(thm)],[f471,f74]) ).
fof(f476,plain,
( ~ sQ21_spl
| sQ53_spl
| sQ32_spl
| ~ sQ20_spl
| ~ sQ6_spl
| sQ1_spl
| ~ sQ5_spl
| ~ sQ9_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f475,f195,f212,f198,f181,f201,f282,f338,f455,f285]) ).
fof(f577,plain,
( sQ16_spl
| ~ top_str(sK17_skl) ),
inference(resolution,[status(thm)],[f81,f269]) ).
fof(f578,plain,
( sQ16_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f577,f198,f267]) ).
fof(f579,plain,
$false,
inference(sat_refutation,[status(thm)],[f193,f217,f219,f221,f223,f225,f236,f288,f290,f295,f343,f458,f476,f578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU386+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n016.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 06:22:52 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 0.26/0.55 % Refutation found
% 0.26/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.26/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.57 % Elapsed time: 0.118187 seconds
% 0.26/0.57 % CPU time: 0.515116 seconds
% 0.26/0.57 % Total memory used: 89.974 MB
% 0.26/0.57 % Net memory used: 89.645 MB
%------------------------------------------------------------------------------