%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU386+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 : Sun Sep 27 08:46:09 AM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 70 ( 17 unt; 0 def)
% Number of atoms : 378 ( 9 equ)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 511 ( 203 ~; 231 |; 52 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 112 ( 0 sgn 39 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d18_yellow_6,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('theBenchmark.p',d18_yellow_6) ).
fof(d9_waybel_9,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('theBenchmark.p',d9_waybel_9) ).
fof(dt_k11_yellow_6,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('theBenchmark.p',dt_k11_yellow_6) ).
fof(dt_l1_pre_topc,axiom,
! [A] :
( top_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_pre_topc) ).
fof(t28_yellow_6,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('theBenchmark.p',t28_yellow_6) ).
fof(t29_waybel_9,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('theBenchmark.p',t29_waybel_9) ).
fof(t29_waybel_9_neg,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(assume_negation,[status(cth)],[t29_waybel_9]) ).
fof(nnf_44,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(fof_nnf,[status(thm)],[t29_waybel_9_neg]) ).
fof(sk_t29_waybel_9_neg,plain,
( ~ is_a_cluster_point_of_netstr(sK0,sK2,sK3)
& in(sK3,lim_points_of_net(sK0,sK2))
& element(sK3,the_carrier(sK0))
& net_str(sK2,sK0)
& directed_relstr(sK2)
& transitive_relstr(sK2)
& ~ empty_carrier(sK2)
& top_str(sK0)
& topological_space(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK2),skolemize(C,sK3)],[nnf_44]) ).
cnf(c_49,negated_conjecture,
topological_space(sK0),
inference(split_conjunct,[status(thm)],[sk_t29_waybel_9_neg]) ).
cnf(c_52,plain,
( 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(clausify,[status(thm)],[dt_k11_yellow_6]) ).
fof(nnf_8,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) )
& ( ! [X0] :
( is_often_in(A,B,X0)
| ~ point_neighbourhood(X0,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(fof_nnf,[status(thm)],[d9_waybel_9]) ).
fof(sk_d9_waybel_9_sk,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ~ is_often_in(A,B,sK1(A,B,C))
& point_neighbourhood(sK1(A,B,C),A,C) )
| is_a_cluster_point_of_netstr(A,B,C) )
& ( ! [X0] :
( is_often_in(A,B,X0)
| ~ point_neighbourhood(X0,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,[sK1]),skolemize(D,sK1(A,B,C))],[nnf_8]) ).
fof(sk_d9_waybel_9,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ is_often_in(VAR_0,VAR_1,sK1(VAR_0,VAR_1,VAR_2))
| is_a_cluster_point_of_netstr(VAR_0,VAR_1,VAR_2)
| ~ element(VAR_2,the_carrier(VAR_0))
| ~ net_str(VAR_1,VAR_0)
| empty_carrier(VAR_1)
| ~ top_str(VAR_0)
| ~ topological_space(VAR_0)
| empty_carrier(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( point_neighbourhood(sK1(VAR_0,VAR_1,VAR_2),VAR_0,VAR_2)
| is_a_cluster_point_of_netstr(VAR_0,VAR_1,VAR_2)
| ~ element(VAR_2,the_carrier(VAR_0))
| ~ net_str(VAR_1,VAR_0)
| empty_carrier(VAR_1)
| ~ top_str(VAR_0)
| ~ topological_space(VAR_0)
| empty_carrier(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( is_often_in(VAR_0,VAR_1,VAR_3)
| ~ point_neighbourhood(VAR_3,VAR_0,VAR_2)
| ~ is_a_cluster_point_of_netstr(VAR_0,VAR_1,VAR_2)
| ~ element(VAR_2,the_carrier(VAR_0))
| ~ net_str(VAR_1,VAR_0)
| empty_carrier(VAR_1)
| ~ top_str(VAR_0)
| ~ topological_space(VAR_0)
| empty_carrier(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d9_waybel_9_sk]) ).
cnf(c_53,plain,
( ~ is_often_in(A,B,sK1(A,B,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(split_conjunct,[status(thm)],[sk_d9_waybel_9]) ).
cnf(c_54,plain,
( point_neighbourhood(sK1(A,B,C),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(split_conjunct,[status(thm)],[sk_d9_waybel_9]) ).
cnf(c_62,plain,
( is_eventually_in(A,B,E)
| ~ point_neighbourhood(E,A,D)
| ~ in(D,C)
| ~ element(D,the_carrier(A))
| lim_points_of_net(A,B) != C
| ~ 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(clausify,[status(thm)],[d18_yellow_6]) ).
cnf(c_63,negated_conjecture,
transitive_relstr(sK2),
inference(split_conjunct,[status(thm)],[sk_t29_waybel_9_neg]) ).
cnf(c_64,negated_conjecture,
( element(lim_points_of_net(sK0,A),powerset(the_carrier(sK0)))
| ~ net_str(A,sK0)
| ~ directed_relstr(A)
| ~ transitive_relstr(A)
| empty_carrier(A)
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_49,c_52]) ).
cnf(c_71,negated_conjecture,
( is_eventually_in(sK0,A,D)
| ~ point_neighbourhood(D,sK0,C)
| ~ in(C,B)
| ~ element(C,the_carrier(sK0))
| lim_points_of_net(sK0,A) != B
| ~ element(B,powerset(the_carrier(sK0)))
| ~ net_str(A,sK0)
| ~ directed_relstr(A)
| ~ transitive_relstr(A)
| empty_carrier(A)
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_49,c_62]) ).
cnf(c_72,plain,
( 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(clausify,[status(thm)],[t28_yellow_6]) ).
cnf(c_80,negated_conjecture,
( is_often_in(A,sK2,B)
| ~ is_eventually_in(A,sK2,B)
| ~ net_str(sK2,A)
| ~ directed_relstr(sK2)
| empty_carrier(sK2)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(resolve,[status(thm)],[c_72,c_63]) ).
cnf(c_81,negated_conjecture,
( is_eventually_in(sK0,sK2,C)
| ~ point_neighbourhood(C,sK0,B)
| ~ in(B,A)
| ~ element(B,the_carrier(sK0))
| lim_points_of_net(sK0,sK2) != A
| ~ element(A,powerset(the_carrier(sK0)))
| ~ net_str(sK2,sK0)
| ~ directed_relstr(sK2)
| empty_carrier(sK2)
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_63,c_71]) ).
cnf(c_88,negated_conjecture,
( element(lim_points_of_net(sK0,sK2),powerset(the_carrier(sK0)))
| ~ net_str(sK2,sK0)
| ~ directed_relstr(sK2)
| empty_carrier(sK2)
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_63,c_64]) ).
cnf(c_92,plain,
( one_sorted_str(A)
| ~ top_str(A) ),
inference(clausify,[status(thm)],[dt_l1_pre_topc]) ).
cnf(c_121,negated_conjecture,
~ empty_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t29_waybel_9_neg]) ).
cnf(c_122,negated_conjecture,
top_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t29_waybel_9_neg]) ).
cnf(c_123,negated_conjecture,
~ empty_carrier(sK2),
inference(split_conjunct,[status(thm)],[sk_t29_waybel_9_neg]) ).
cnf(c_124,negated_conjecture,
directed_relstr(sK2),
inference(split_conjunct,[status(thm)],[sk_t29_waybel_9_neg]) ).
cnf(c_125,negated_conjecture,
net_str(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t29_waybel_9_neg]) ).
cnf(c_126,negated_conjecture,
element(sK3,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t29_waybel_9_neg]) ).
cnf(c_127,negated_conjecture,
in(sK3,lim_points_of_net(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_t29_waybel_9_neg]) ).
cnf(c_128,negated_conjecture,
~ is_a_cluster_point_of_netstr(sK0,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t29_waybel_9_neg]) ).
cnf(c_133,negated_conjecture,
( ~ is_often_in(sK0,A,sK1(sK0,A,B))
| is_a_cluster_point_of_netstr(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ net_str(A,sK0)
| empty_carrier(A)
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_49,c_53]) ).
cnf(c_841,negated_conjecture,
( ~ is_often_in(sK0,A,sK1(sK0,A,B))
| is_a_cluster_point_of_netstr(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ net_str(A,sK0)
| empty_carrier(A)
| ~ top_str(sK0) ),
inference(resolve,[status(thm)],[c_121,c_133]) ).
cnf(c_134,negated_conjecture,
( ~ is_often_in(sK0,A,sK1(sK0,A,B))
| is_a_cluster_point_of_netstr(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ net_str(A,sK0)
| empty_carrier(A) ),
inference(resolve,[status(thm)],[c_122,c_841]) ).
cnf(c_135,negated_conjecture,
( point_neighbourhood(sK1(sK0,A,B),sK0,B)
| is_a_cluster_point_of_netstr(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ net_str(A,sK0)
| empty_carrier(A)
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_49,c_54]) ).
cnf(c_842,negated_conjecture,
( point_neighbourhood(sK1(sK0,A,B),sK0,B)
| is_a_cluster_point_of_netstr(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ net_str(A,sK0)
| empty_carrier(A)
| ~ top_str(sK0) ),
inference(resolve,[status(thm)],[c_121,c_135]) ).
cnf(c_136,negated_conjecture,
( point_neighbourhood(sK1(sK0,A,B),sK0,B)
| is_a_cluster_point_of_netstr(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ net_str(A,sK0)
| empty_carrier(A) ),
inference(resolve,[status(thm)],[c_122,c_842]) ).
cnf(c_843,negated_conjecture,
( element(lim_points_of_net(sK0,sK2),powerset(the_carrier(sK0)))
| ~ net_str(sK2,sK0)
| ~ directed_relstr(sK2)
| empty_carrier(sK2)
| ~ top_str(sK0) ),
inference(resolve,[status(thm)],[c_121,c_88]) ).
cnf(c_844,negated_conjecture,
( element(lim_points_of_net(sK0,sK2),powerset(the_carrier(sK0)))
| ~ net_str(sK2,sK0)
| ~ directed_relstr(sK2)
| empty_carrier(sK2) ),
inference(resolve,[status(thm)],[c_122,c_843]) ).
cnf(c_845,negated_conjecture,
( element(lim_points_of_net(sK0,sK2),powerset(the_carrier(sK0)))
| ~ net_str(sK2,sK0)
| ~ directed_relstr(sK2) ),
inference(resolve,[status(thm)],[c_123,c_844]) ).
cnf(c_846,negated_conjecture,
( element(lim_points_of_net(sK0,sK2),powerset(the_carrier(sK0)))
| ~ net_str(sK2,sK0) ),
inference(resolve,[status(thm)],[c_124,c_845]) ).
cnf(c_143,negated_conjecture,
element(lim_points_of_net(sK0,sK2),powerset(the_carrier(sK0))),
inference(resolve,[status(thm)],[c_125,c_846]) ).
cnf(c_847,negated_conjecture,
( is_eventually_in(sK0,sK2,C)
| ~ point_neighbourhood(C,sK0,B)
| ~ in(B,A)
| ~ element(B,the_carrier(sK0))
| lim_points_of_net(sK0,sK2) != A
| ~ element(A,powerset(the_carrier(sK0)))
| ~ net_str(sK2,sK0)
| ~ directed_relstr(sK2)
| empty_carrier(sK2)
| ~ top_str(sK0) ),
inference(resolve,[status(thm)],[c_121,c_81]) ).
cnf(c_848,negated_conjecture,
( is_eventually_in(sK0,sK2,C)
| ~ point_neighbourhood(C,sK0,B)
| ~ in(B,A)
| ~ element(B,the_carrier(sK0))
| lim_points_of_net(sK0,sK2) != A
| ~ element(A,powerset(the_carrier(sK0)))
| ~ net_str(sK2,sK0)
| ~ directed_relstr(sK2)
| empty_carrier(sK2) ),
inference(resolve,[status(thm)],[c_122,c_847]) ).
cnf(c_849,negated_conjecture,
( is_eventually_in(sK0,sK2,C)
| ~ point_neighbourhood(C,sK0,B)
| ~ in(B,A)
| ~ element(B,the_carrier(sK0))
| lim_points_of_net(sK0,sK2) != A
| ~ element(A,powerset(the_carrier(sK0)))
| ~ net_str(sK2,sK0)
| ~ directed_relstr(sK2) ),
inference(resolve,[status(thm)],[c_123,c_848]) ).
cnf(c_850,negated_conjecture,
( is_eventually_in(sK0,sK2,C)
| ~ point_neighbourhood(C,sK0,B)
| ~ in(B,A)
| ~ element(B,the_carrier(sK0))
| lim_points_of_net(sK0,sK2) != A
| ~ element(A,powerset(the_carrier(sK0)))
| ~ net_str(sK2,sK0) ),
inference(resolve,[status(thm)],[c_124,c_849]) ).
cnf(c_150,negated_conjecture,
( is_eventually_in(sK0,sK2,C)
| ~ point_neighbourhood(C,sK0,B)
| ~ in(B,A)
| ~ element(B,the_carrier(sK0))
| lim_points_of_net(sK0,sK2) != A
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_125,c_850]) ).
cnf(c_851,negated_conjecture,
( is_often_in(A,sK2,B)
| ~ is_eventually_in(A,sK2,B)
| ~ net_str(sK2,A)
| ~ directed_relstr(sK2)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(resolve,[status(thm)],[c_123,c_80]) ).
cnf(c_151,negated_conjecture,
( is_often_in(A,sK2,B)
| ~ is_eventually_in(A,sK2,B)
| ~ net_str(sK2,A)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(resolve,[status(thm)],[c_124,c_851]) ).
cnf(c_180,plain,
one_sorted_str(sK0),
inference(resolve,[status(thm)],[c_122,c_92]) ).
cnf(c_852,negated_conjecture,
( ~ is_often_in(sK0,sK2,sK1(sK0,sK2,A))
| is_a_cluster_point_of_netstr(sK0,sK2,A)
| ~ element(A,the_carrier(sK0))
| ~ net_str(sK2,sK0) ),
inference(resolve,[status(thm)],[c_134,c_123]) ).
cnf(c_853,negated_conjecture,
( ~ is_often_in(sK0,sK2,sK1(sK0,sK2,A))
| is_a_cluster_point_of_netstr(sK0,sK2,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_852,c_125]) ).
cnf(c_854,negated_conjecture,
( ~ is_often_in(sK0,sK2,sK1(sK0,sK2,sK3))
| is_a_cluster_point_of_netstr(sK0,sK2,sK3) ),
inference(resolve,[status(thm)],[c_853,c_126]) ).
cnf(c_191,negated_conjecture,
~ is_often_in(sK0,sK2,sK1(sK0,sK2,sK3)),
inference(resolve,[status(thm)],[c_854,c_128]) ).
cnf(c_855,negated_conjecture,
( point_neighbourhood(sK1(sK0,sK2,A),sK0,A)
| is_a_cluster_point_of_netstr(sK0,sK2,A)
| ~ element(A,the_carrier(sK0))
| empty_carrier(sK2) ),
inference(resolve,[status(thm)],[c_136,c_125]) ).
cnf(c_192,negated_conjecture,
( point_neighbourhood(sK1(sK0,sK2,A),sK0,A)
| is_a_cluster_point_of_netstr(sK0,sK2,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_123,c_855]) ).
cnf(c_856,negated_conjecture,
( is_often_in(sK0,sK2,A)
| ~ is_eventually_in(sK0,sK2,A)
| ~ net_str(sK2,sK0)
| ~ one_sorted_str(sK0) ),
inference(resolve,[status(thm)],[c_151,c_121]) ).
cnf(c_857,negated_conjecture,
( is_often_in(sK0,sK2,A)
| ~ is_eventually_in(sK0,sK2,A)
| ~ net_str(sK2,sK0) ),
inference(resolve,[status(thm)],[c_856,c_180]) ).
cnf(c_858,negated_conjecture,
( is_often_in(sK0,sK2,A)
| ~ is_eventually_in(sK0,sK2,A) ),
inference(resolve,[status(thm)],[c_857,c_125]) ).
cnf(c_432,negated_conjecture,
~ is_eventually_in(sK0,sK2,sK1(sK0,sK2,sK3)),
inference(resolve,[status(thm)],[c_858,c_191]) ).
cnf(c_859,negated_conjecture,
( point_neighbourhood(sK1(sK0,sK2,sK3),sK0,sK3)
| is_a_cluster_point_of_netstr(sK0,sK2,sK3) ),
inference(resolve,[status(thm)],[c_192,c_126]) ).
cnf(c_433,negated_conjecture,
point_neighbourhood(sK1(sK0,sK2,sK3),sK0,sK3),
inference(resolve,[status(thm)],[c_128,c_859]) ).
cnf(c_860,plain,
( is_eventually_in(sK0,sK2,B)
| ~ point_neighbourhood(B,sK0,A)
| ~ in(A,lim_points_of_net(sK0,sK2))
| ~ element(A,the_carrier(sK0))
| ~ element(lim_points_of_net(sK0,sK2),powerset(the_carrier(sK0))) ),
inference(xxres,[status(thm)],[c_150]) ).
cnf(c_861,negated_conjecture,
( is_eventually_in(sK0,sK2,A)
| ~ point_neighbourhood(A,sK0,sK3)
| ~ in(sK3,lim_points_of_net(sK0,sK2))
| ~ element(lim_points_of_net(sK0,sK2),powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_860,c_126]) ).
cnf(c_862,negated_conjecture,
( is_eventually_in(sK0,sK2,A)
| ~ point_neighbourhood(A,sK0,sK3)
| ~ element(lim_points_of_net(sK0,sK2),powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_861,c_127]) ).
cnf(c_863,negated_conjecture,
( is_eventually_in(sK0,sK2,sK1(sK0,sK2,sK3))
| ~ element(lim_points_of_net(sK0,sK2),powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_862,c_433]) ).
cnf(c_864,negated_conjecture,
~ element(lim_points_of_net(sK0,sK2),powerset(the_carrier(sK0))),
inference(resolve,[status(thm)],[c_863,c_432]) ).
cnf(c_840,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_143,c_864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU386+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 09:23:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2438348 was started by sandbox2 on n013,
% 0.10/0.38 % Sat Sep 26 09:23:27 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.45
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45
% 0.10/0.45 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.10/0.45 % Length of proof is 40.
% 0.10/0.45 % Level of proof is 6.
% 0.10/0.45 % Maximum clause weight is 51.000.
% 0.10/0.45 % Given clauses 299.
% 0.10/0.45
% 0.10/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------