%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU386+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Tue Sep 29 12:48:39 PM UTC 2026
% Result : Theorem 2.94s 1.26s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 7
% Syntax : Number of formulae : 77 ( 12 unt; 0 def)
% Number of atoms : 571 ( 12 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 821 ( 327 ~; 376 |; 86 &)
% ( 9 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 169 ( 152 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( X2 = lim_points_of_net(X0,X1)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X2)
<=> ! [X4] :
( point_neighbourhood(X4,X0,X3)
=> is_eventually_in(X0,X1,X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_yellow_6) ).
fof(f8,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( is_a_cluster_point_of_netstr(X0,X1,X2)
<=> ! [X3] :
( point_neighbourhood(X3,X0,X2)
=> is_often_in(X0,X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_waybel_9) ).
fof(f9,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> element(lim_points_of_net(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_yellow_6) ).
fof(f13,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f37,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
=> is_often_in(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_yellow_6) ).
fof(f38,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,X1))
=> is_a_cluster_point_of_netstr(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_waybel_9) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,X1))
=> is_a_cluster_point_of_netstr(X0,X1,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f47,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ is_a_cluster_point_of_netstr(X0,X1,X2)
& in(X2,lim_points_of_net(X0,X1))
& element(X2,the_carrier(X0)) )
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f48,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ is_a_cluster_point_of_netstr(X0,X1,X2)
& in(X2,lim_points_of_net(X0,X1))
& element(X2,the_carrier(X0)) )
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f47]) ).
fof(f51,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f52,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f51]) ).
fof(f61,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f62,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_a_cluster_point_of_netstr(X0,X1,X2)
<=> ! [X3] :
( is_often_in(X0,X1,X3)
| ~ point_neighbourhood(X3,X0,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_a_cluster_point_of_netstr(X0,X1,X2)
<=> ! [X3] :
( is_often_in(X0,X1,X3)
| ~ point_neighbourhood(X3,X0,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f65]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_often_in(X0,X1,X2)
| ~ is_eventually_in(X0,X1,X2) )
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_often_in(X0,X1,X2)
| ~ is_eventually_in(X0,X1,X2) )
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = lim_points_of_net(X0,X1)
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) ) )
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = lim_points_of_net(X0,X1)
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) ) )
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f73]) ).
fof(f76,plain,
( ~ is_a_cluster_point_of_netstr(sK0,sK1,sK2)
& in(sK2,lim_points_of_net(sK0,sK1))
& element(sK2,the_carrier(sK0))
& ~ empty_carrier(sK1)
& transitive_relstr(sK1)
& directed_relstr(sK1)
& net_str(sK1,sK0)
& ~ empty_carrier(sK0)
& topological_space(sK0)
& top_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f48]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( is_a_cluster_point_of_netstr(X0,X1,X2)
| ? [X3] :
( ~ is_often_in(X0,X1,X3)
& point_neighbourhood(X3,X0,X2) ) )
& ( ! [X3] :
( is_often_in(X0,X1,X3)
| ~ point_neighbourhood(X3,X0,X2) )
| ~ is_a_cluster_point_of_netstr(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f66]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( is_a_cluster_point_of_netstr(X0,X1,X2)
| ? [X3] :
( ~ is_often_in(X0,X1,X3)
& point_neighbourhood(X3,X0,X2) ) )
& ( ! [X4] :
( is_often_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X2) )
| ~ is_a_cluster_point_of_netstr(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( is_a_cluster_point_of_netstr(X0,X1,X2)
| ( ~ is_often_in(X0,X1,sK7(X0,X1,X2))
& point_neighbourhood(sK7(X0,X1,X2),X0,X2) ) )
& ( ! [X4] :
( is_often_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X2) )
| ~ is_a_cluster_point_of_netstr(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f82]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = lim_points_of_net(X0,X1)
| ? [X3] :
( ( ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,X3) )
| ~ in(X3,X2) )
& ( ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) )
| in(X3,X2) )
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,X3) ) )
& ( ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) )
| ~ in(X3,X2) ) )
| ~ element(X3,the_carrier(X0)) )
| lim_points_of_net(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f74]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = lim_points_of_net(X0,X1)
| ? [X3] :
( ( ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,X3) )
| ~ in(X3,X2) )
& ( ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) )
| in(X3,X2) )
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,X3) ) )
& ( ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) )
| ~ in(X3,X2) ) )
| ~ element(X3,the_carrier(X0)) )
| lim_points_of_net(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = lim_points_of_net(X0,X1)
| ? [X3] :
( ( ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,X3) )
| ~ in(X3,X2) )
& ( ! [X5] :
( is_eventually_in(X0,X1,X5)
| ~ point_neighbourhood(X5,X0,X3) )
| in(X3,X2) )
& element(X3,the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ? [X7] :
( ~ is_eventually_in(X0,X1,X7)
& point_neighbourhood(X7,X0,X6) ) )
& ( ! [X8] :
( is_eventually_in(X0,X1,X8)
| ~ point_neighbourhood(X8,X0,X6) )
| ~ in(X6,X2) ) )
| ~ element(X6,the_carrier(X0)) )
| lim_points_of_net(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = lim_points_of_net(X0,X1)
| ( ( ( ~ is_eventually_in(X0,X1,sK14(X0,X1,X2))
& point_neighbourhood(sK14(X0,X1,X2),X0,sK13(X0,X1,X2)) )
| ~ in(sK13(X0,X1,X2),X2) )
& ( ! [X5] :
( is_eventually_in(X0,X1,X5)
| ~ point_neighbourhood(X5,X0,sK13(X0,X1,X2)) )
| in(sK13(X0,X1,X2),X2) )
& element(sK13(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ( ~ is_eventually_in(X0,X1,sK15(X0,X1,X6))
& point_neighbourhood(sK15(X0,X1,X6),X0,X6) ) )
& ( ! [X8] :
( is_eventually_in(X0,X1,X8)
| ~ point_neighbourhood(X8,X0,X6) )
| ~ in(X6,X2) ) )
| ~ element(X6,the_carrier(X0)) )
| lim_points_of_net(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X3,sK13(X0,X1,X2)),skolemize(X4,sK14(X0,X1,X2)),skolemize(X7,sK15(X0,X1,X6))],[f91]) ).
fof(f93,plain,
top_str(sK0),
inference(cnf_transformation,[],[f76]) ).
fof(f94,plain,
topological_space(sK0),
inference(cnf_transformation,[],[f76]) ).
fof(f95,plain,
~ empty_carrier(sK0),
inference(cnf_transformation,[],[f76]) ).
fof(f96,plain,
net_str(sK1,sK0),
inference(cnf_transformation,[],[f76]) ).
fof(f97,plain,
directed_relstr(sK1),
inference(cnf_transformation,[],[f76]) ).
fof(f98,plain,
transitive_relstr(sK1),
inference(cnf_transformation,[],[f76]) ).
fof(f99,plain,
~ empty_carrier(sK1),
inference(cnf_transformation,[],[f76]) ).
fof(f100,plain,
element(sK2,the_carrier(sK0)),
inference(cnf_transformation,[],[f76]) ).
fof(f101,plain,
in(sK2,lim_points_of_net(sK0,sK1)),
inference(cnf_transformation,[],[f76]) ).
fof(f102,plain,
~ is_a_cluster_point_of_netstr(sK0,sK1,sK2),
inference(cnf_transformation,[],[f76]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f112,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f115,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f118,plain,
! [X2,X0,X1] :
( point_neighbourhood(sK7(X0,X1,X2),X0,X2)
| is_a_cluster_point_of_netstr(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ is_often_in(X0,X1,sK7(X0,X1,X2))
| is_a_cluster_point_of_netstr(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f127,plain,
! [X2,X0,X1] :
( is_often_in(X0,X1,X2)
| ~ is_eventually_in(X0,X1,X2)
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f128,plain,
! [X2,X0,X1,X8,X6] :
( is_eventually_in(X0,X1,X8)
| ~ point_neighbourhood(X8,X0,X6)
| ~ in(X6,X2)
| ~ element(X6,the_carrier(X0))
| lim_points_of_net(X0,X1) != X2
| ~ element(X2,powerset(the_carrier(X0)))
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f138,plain,
! [X0,X1,X8,X6] :
( is_eventually_in(X0,X1,X8)
| ~ point_neighbourhood(X8,X0,X6)
| ~ in(X6,lim_points_of_net(X0,X1))
| ~ element(X6,the_carrier(X0))
| ~ element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(equality_resolution,[],[f128]) ).
fof(f182,plain,
! [X2,X0,X1] :
( is_a_cluster_point_of_netstr(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ is_eventually_in(X0,X1,sK7(X0,X1,X2))
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f119,f127]) ).
fof(f183,plain,
! [X2,X0,X1] :
( is_a_cluster_point_of_netstr(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ is_eventually_in(X0,X1,sK7(X0,X1,X2))
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ one_sorted_str(X0) ),
inference(duplicate_literal_removal,[],[f182]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ is_eventually_in(X0,X1,sK7(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| is_a_cluster_point_of_netstr(X0,X1,X2)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1) ),
inference(forward_subsumption_resolution,[],[f183,f115]) ).
fof(f218,plain,
! [X0,X1,X8,X6] :
( is_eventually_in(X0,X1,X8)
| ~ point_neighbourhood(X8,X0,X6)
| ~ in(X6,lim_points_of_net(X0,X1))
| ~ element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(forward_subsumption_resolution,[],[f138,f105]) ).
fof(f219,plain,
! [X0,X1,X8,X6] :
( ~ in(X6,lim_points_of_net(X0,X1))
| ~ point_neighbourhood(X8,X0,X6)
| is_eventually_in(X0,X1,X8)
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(forward_subsumption_resolution,[],[f218,f112]) ).
fof(f221,plain,
! [X0] :
( ~ point_neighbourhood(X0,sK0,sK2)
| is_eventually_in(sK0,sK1,X0)
| empty_carrier(sK1)
| ~ transitive_relstr(sK1)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(resolution,[],[f219,f101]) ).
fof(f223,plain,
! [X0] :
( ~ point_neighbourhood(X0,sK0,sK2)
| is_eventually_in(sK0,sK1,X0)
| ~ transitive_relstr(sK1)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f221,f99]) ).
fof(f224,plain,
! [X0] :
( ~ point_neighbourhood(X0,sK0,sK2)
| is_eventually_in(sK0,sK1,X0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f223,f98]) ).
fof(f225,plain,
! [X0] :
( ~ point_neighbourhood(X0,sK0,sK2)
| is_eventually_in(sK0,sK1,X0)
| ~ net_str(sK1,sK0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f224,f97]) ).
fof(f226,plain,
! [X0] :
( ~ point_neighbourhood(X0,sK0,sK2)
| is_eventually_in(sK0,sK1,X0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f225,f96]) ).
fof(f227,plain,
! [X0] :
( ~ point_neighbourhood(X0,sK0,sK2)
| is_eventually_in(sK0,sK1,X0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f226,f95]) ).
fof(f228,plain,
! [X0] :
( ~ point_neighbourhood(X0,sK0,sK2)
| is_eventually_in(sK0,sK1,X0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f227,f94]) ).
fof(f229,plain,
! [X0] :
( is_eventually_in(sK0,sK1,X0)
| ~ point_neighbourhood(X0,sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f228,f93]) ).
fof(f302,plain,
! [X0] :
( ~ element(X0,the_carrier(sK0))
| empty_carrier(sK1)
| ~ net_str(sK1,sK0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0)
| is_a_cluster_point_of_netstr(sK0,sK1,X0)
| ~ transitive_relstr(sK1)
| ~ directed_relstr(sK1)
| ~ point_neighbourhood(sK7(sK0,sK1,X0),sK0,sK2) ),
inference(resolution,[],[f184,f229]) ).
fof(f303,plain,
! [X0] :
( ~ element(X0,the_carrier(sK0))
| ~ net_str(sK1,sK0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0)
| is_a_cluster_point_of_netstr(sK0,sK1,X0)
| ~ transitive_relstr(sK1)
| ~ directed_relstr(sK1)
| ~ point_neighbourhood(sK7(sK0,sK1,X0),sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f302,f99]) ).
fof(f304,plain,
! [X0] :
( ~ element(X0,the_carrier(sK0))
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0)
| is_a_cluster_point_of_netstr(sK0,sK1,X0)
| ~ transitive_relstr(sK1)
| ~ directed_relstr(sK1)
| ~ point_neighbourhood(sK7(sK0,sK1,X0),sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f303,f96]) ).
fof(f305,plain,
! [X0] :
( ~ element(X0,the_carrier(sK0))
| ~ topological_space(sK0)
| ~ top_str(sK0)
| is_a_cluster_point_of_netstr(sK0,sK1,X0)
| ~ transitive_relstr(sK1)
| ~ directed_relstr(sK1)
| ~ point_neighbourhood(sK7(sK0,sK1,X0),sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f304,f95]) ).
fof(f306,plain,
! [X0] :
( ~ element(X0,the_carrier(sK0))
| ~ top_str(sK0)
| is_a_cluster_point_of_netstr(sK0,sK1,X0)
| ~ transitive_relstr(sK1)
| ~ directed_relstr(sK1)
| ~ point_neighbourhood(sK7(sK0,sK1,X0),sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f305,f94]) ).
fof(f307,plain,
! [X0] :
( ~ element(X0,the_carrier(sK0))
| is_a_cluster_point_of_netstr(sK0,sK1,X0)
| ~ transitive_relstr(sK1)
| ~ directed_relstr(sK1)
| ~ point_neighbourhood(sK7(sK0,sK1,X0),sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f306,f93]) ).
fof(f308,plain,
! [X0] :
( ~ element(X0,the_carrier(sK0))
| is_a_cluster_point_of_netstr(sK0,sK1,X0)
| ~ directed_relstr(sK1)
| ~ point_neighbourhood(sK7(sK0,sK1,X0),sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f307,f98]) ).
fof(f309,plain,
! [X0] :
( ~ point_neighbourhood(sK7(sK0,sK1,X0),sK0,sK2)
| is_a_cluster_point_of_netstr(sK0,sK1,X0)
| ~ element(X0,the_carrier(sK0)) ),
inference(forward_subsumption_resolution,[],[f308,f97]) ).
fof(f310,plain,
( is_a_cluster_point_of_netstr(sK0,sK1,sK2)
| ~ element(sK2,the_carrier(sK0))
| is_a_cluster_point_of_netstr(sK0,sK1,sK2)
| ~ element(sK2,the_carrier(sK0))
| empty_carrier(sK1)
| ~ net_str(sK1,sK0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(resolution,[],[f309,f118]) ).
fof(f311,plain,
( is_a_cluster_point_of_netstr(sK0,sK1,sK2)
| ~ element(sK2,the_carrier(sK0))
| empty_carrier(sK1)
| ~ net_str(sK1,sK0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(duplicate_literal_removal,[],[f310]) ).
fof(f312,plain,
( ~ element(sK2,the_carrier(sK0))
| empty_carrier(sK1)
| ~ net_str(sK1,sK0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f311,f102]) ).
fof(f313,plain,
( empty_carrier(sK1)
| ~ net_str(sK1,sK0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f312,f100]) ).
fof(f314,plain,
( ~ net_str(sK1,sK0)
| empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f313,f99]) ).
fof(f315,plain,
( empty_carrier(sK0)
| ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f314,f96]) ).
fof(f316,plain,
( ~ topological_space(sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f315,f95]) ).
fof(f317,plain,
~ top_str(sK0),
inference(forward_subsumption_resolution,[],[f316,f94]) ).
fof(f318,plain,
$false,
inference(forward_subsumption_resolution,[],[f317,f93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU386+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 05:03:23 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.94/1.26 % (4164796)Detected formulas, will run a generic FOF schedule.
% 2.94/1.26 % (4164802)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3779929752:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.94/1.26 % (4164803)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1863126328:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.94/1.26 % (4164804)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2233507703:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.94/1.26 % (4164805)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2919602570:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.94/1.26 % (4164801)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2132402369:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.94/1.26 % (4164804)Refutation not found, incomplete strategy
% 2.94/1.26 % (4164804)------------------------------
% 2.94/1.26 % (4164804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.26 % (4164804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.26 % (4164804)CaDiCaL version: 2.1.3
% 2.94/1.26 % (4164804)Termination reason: Refutation not found, incomplete strategy
% 2.94/1.26 % (4164804)Time elapsed: 0.003 s
% 2.94/1.26 % (4164804)Peak memory usage: 88 MB
% 2.94/1.26 % (4164804)Instructions burned: 2 (million)
% 2.94/1.26 % (4164805)First to succeed.
% 2.94/1.26 % (4164807)dis-21_1_sil=8000:lcm=predicate:random_seed=906268869:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.94/1.26 % (4164805)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4164796"
% 2.94/1.26 % (4164806)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2308255167:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.94/1.26 % (4164807)Also succeeded, but the first one will report.
% 2.94/1.26 % (4164806)Also succeeded, but the first one will report.
% 2.94/1.26 % (4164804)------------------------------
% 2.94/1.26 % (4164804)------------------------------
% 2.94/1.26 % (4164805)Refutation found. Thanks to Tanya!
% 2.94/1.26 % SZS status Theorem for theBenchmark
% 2.94/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.35 % (4164805)------------------------------
% 3.42/1.35 % (4164805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.35 % (4164805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.35 % (4164805)CaDiCaL version: 2.1.3
% 3.42/1.35 % (4164805)Termination reason: Refutation
% 3.42/1.35 % (4164805)Time elapsed: 0.010 s
% 3.42/1.35 % (4164805)Peak memory usage: 88 MB
% 3.42/1.35 % (4164805)Instructions burned: 15 (million)
% 3.42/1.35 % (4164805)------------------------------
% 3.42/1.35 % (4164805)------------------------------
% 3.42/1.35 % (4164796)Success in time 0.417 s
% 3.42/1.35 % Vampire exiting
%------------------------------------------------------------------------------