%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU386+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 : Fri Sep 25 02:57:18 PM UTC 2026
% Result : Theorem 1.18s 1.35s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 99 ( 29 unt; 1 def)
% Number of atoms : 613 ( 24 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 838 ( 333 ~; 387 |; 86 &)
% ( 9 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 208 ( 0 sgn 191 !; 17 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [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] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [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] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(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] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [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] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [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] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [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] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f56,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ! [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) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f57,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ! [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) ) ) ) ) ) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [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) ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [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) ) ) ) ) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| element(lim_points_of_net(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f9]) ).
fof(f61,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| element(lim_points_of_net(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f60]) ).
fof(f63,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f77,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ! [X2] :
( ~ is_eventually_in(X0,X1,X2)
| is_often_in(X0,X1,X2) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f78,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ! [X2] :
( ~ is_eventually_in(X0,X1,X2)
| is_often_in(X0,X1,X2) ) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& ? [X2] :
( element(X2,the_carrier(X0))
& in(X2,lim_points_of_net(X0,X1))
& ~ is_a_cluster_point_of_netstr(X0,X1,X2) ) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f80,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& ? [X2] :
( element(X2,the_carrier(X0))
& in(X2,lim_points_of_net(X0,X1))
& ~ is_a_cluster_point_of_netstr(X0,X1,X2) ) ) ),
inference(flattening,[],[f79]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f42]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f84]) ).
fof(f90,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( ( lim_points_of_net(X0,X1) != X2
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ( ( ~ in(X3,X2)
| ! [X4] :
( ~ point_neighbourhood(X4,X0,X3)
| is_eventually_in(X0,X1,X4) ) )
& ( ? [X4] :
( point_neighbourhood(X4,X0,X3)
& ~ is_eventually_in(X0,X1,X4) )
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& ( in(X3,X2)
| ! [X4] :
( ~ point_neighbourhood(X4,X0,X3)
| is_eventually_in(X0,X1,X4) ) )
& ( ~ in(X3,X2)
| ? [X4] :
( point_neighbourhood(X4,X0,X3)
& ~ is_eventually_in(X0,X1,X4) ) ) )
| X2 = lim_points_of_net(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f91,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( ( lim_points_of_net(X0,X1) != X2
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ( ( ~ in(X3,X2)
| ! [X4] :
( ~ point_neighbourhood(X4,X0,X3)
| is_eventually_in(X0,X1,X4) ) )
& ( ? [X4] :
( point_neighbourhood(X4,X0,X3)
& ~ is_eventually_in(X0,X1,X4) )
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& ( in(X3,X2)
| ! [X4] :
( ~ point_neighbourhood(X4,X0,X3)
| is_eventually_in(X0,X1,X4) ) )
& ( ~ in(X3,X2)
| ? [X4] :
( point_neighbourhood(X4,X0,X3)
& ~ is_eventually_in(X0,X1,X4) ) ) )
| X2 = lim_points_of_net(X0,X1) ) ) ) ) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( ( lim_points_of_net(X0,X1) != X2
| ! [X6] :
( ~ element(X6,the_carrier(X0))
| ( ( ~ in(X6,X2)
| ! [X8] :
( ~ point_neighbourhood(X8,X0,X6)
| is_eventually_in(X0,X1,X8) ) )
& ( ? [X7] :
( point_neighbourhood(X7,X0,X6)
& ~ is_eventually_in(X0,X1,X7) )
| in(X6,X2) ) ) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& ( in(X3,X2)
| ! [X5] :
( ~ point_neighbourhood(X5,X0,X3)
| is_eventually_in(X0,X1,X5) ) )
& ( ~ in(X3,X2)
| ? [X4] :
( point_neighbourhood(X4,X0,X3)
& ~ is_eventually_in(X0,X1,X4) ) ) )
| X2 = lim_points_of_net(X0,X1) ) ) ) ) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( ( lim_points_of_net(X0,X1) != X2
| ! [X6] :
( ~ element(X6,the_carrier(X0))
| ( ( ~ in(X6,X2)
| ! [X8] :
( ~ point_neighbourhood(X8,X0,X6)
| is_eventually_in(X0,X1,X8) ) )
& ( ( point_neighbourhood(sK2(X0,X1,X6),X0,X6)
& ~ is_eventually_in(X0,X1,sK2(X0,X1,X6)) )
| in(X6,X2) ) ) ) )
& ( ( element(sK0(X0,X1,X2),the_carrier(X0))
& ( in(sK0(X0,X1,X2),X2)
| ! [X5] :
( ~ point_neighbourhood(X5,X0,sK0(X0,X1,X2))
| is_eventually_in(X0,X1,X5) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ( point_neighbourhood(sK1(X0,X1,X2),X0,sK0(X0,X1,X2))
& ~ is_eventually_in(X0,X1,sK1(X0,X1,X2)) ) ) )
| X2 = lim_points_of_net(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X4,sK1(X0,X1,X2)),skolemize(X7,sK2(X0,X1,X6))],[f92]) ).
fof(f94,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [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) ) )
& ( ? [X3] :
( point_neighbourhood(X3,X0,X2)
& ~ is_often_in(X0,X1,X3) )
| is_a_cluster_point_of_netstr(X0,X1,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f95,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ is_a_cluster_point_of_netstr(X0,X1,X2)
| ! [X4] :
( ~ point_neighbourhood(X4,X0,X2)
| is_often_in(X0,X1,X4) ) )
& ( ? [X3] :
( point_neighbourhood(X3,X0,X2)
& ~ is_often_in(X0,X1,X3) )
| is_a_cluster_point_of_netstr(X0,X1,X2) ) ) ) ) ),
inference(rectify,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ is_a_cluster_point_of_netstr(X0,X1,X2)
| ! [X4] :
( ~ point_neighbourhood(X4,X0,X2)
| is_often_in(X0,X1,X4) ) )
& ( ( point_neighbourhood(sK3(X0,X1,X2),X0,X2)
& ~ is_often_in(X0,X1,sK3(X0,X1,X2)) )
| is_a_cluster_point_of_netstr(X0,X1,X2) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f95]) ).
fof(f110,plain,
( top_str(sK17)
& topological_space(sK17)
& ~ empty_carrier(sK17)
& net_str(sK18,sK17)
& directed_relstr(sK18)
& transitive_relstr(sK18)
& ~ empty_carrier(sK18)
& element(sK19,the_carrier(sK17))
& in(sK19,lim_points_of_net(sK17,sK18))
& ~ is_a_cluster_point_of_netstr(sK17,sK18,sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19)],[f80]) ).
fof(f117,plain,
! [X2,X0,X1,X8,X6] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ element(X2,powerset(the_carrier(X0)))
| lim_points_of_net(X0,X1) != X2
| ~ element(X6,the_carrier(X0))
| ~ in(X6,X2)
| ~ point_neighbourhood(X8,X0,X6)
| is_eventually_in(X0,X1,X8) ),
inference(cnf_transformation,[],[f93]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X0))
| point_neighbourhood(sK3(X0,X1,X2),X0,X2)
| is_a_cluster_point_of_netstr(X0,X1,X2) ),
inference(cnf_transformation,[],[f96]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X0))
| ~ is_often_in(X0,X1,sK3(X0,X1,X2))
| is_a_cluster_point_of_netstr(X0,X1,X2) ),
inference(cnf_transformation,[],[f96]) ).
fof(f127,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| element(lim_points_of_net(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f129,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ is_eventually_in(X0,X1,X2)
| is_often_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f161,plain,
top_str(sK17),
inference(cnf_transformation,[],[f110]) ).
fof(f162,plain,
topological_space(sK17),
inference(cnf_transformation,[],[f110]) ).
fof(f163,plain,
~ empty_carrier(sK17),
inference(cnf_transformation,[],[f110]) ).
fof(f164,plain,
net_str(sK18,sK17),
inference(cnf_transformation,[],[f110]) ).
fof(f165,plain,
directed_relstr(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f166,plain,
transitive_relstr(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f167,plain,
~ empty_carrier(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f168,plain,
element(sK19,the_carrier(sK17)),
inference(cnf_transformation,[],[f110]) ).
fof(f169,plain,
in(sK19,lim_points_of_net(sK17,sK18)),
inference(cnf_transformation,[],[f110]) ).
fof(f170,plain,
~ is_a_cluster_point_of_netstr(sK17,sK18,sK19),
inference(cnf_transformation,[],[f110]) ).
fof(f173,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f180,plain,
! [X0,X1,X8,X6] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ element(X6,the_carrier(X0))
| ~ in(X6,lim_points_of_net(X0,X1))
| ~ point_neighbourhood(X8,X0,X6)
| is_eventually_in(X0,X1,X8) ),
inference(equality_resolution,[],[f117]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| is_eventually_in(X0,X1,X3)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X0)
| ~ element(X2,the_carrier(X0))
| ~ point_neighbourhood(X3,X0,X2)
| ~ in(X2,lim_points_of_net(X0,X1))
| ~ element(lim_points_of_net(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| is_a_cluster_point_of_netstr(X0,X1,X2)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ net_str(X1,X0)
| ~ element(X2,the_carrier(X0))
| ~ is_often_in(X0,X1,sK3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| is_a_cluster_point_of_netstr(X1,X2,X0)
| point_neighbourhood(sK3(X1,X2,X0),X1,X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ net_str(X2,X1)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| element(lim_points_of_net(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_67,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| is_often_in(X0,X1,X2)
| ~ one_sorted_str(X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X0)
| ~ is_eventually_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_99,negated_conjecture,
~ is_a_cluster_point_of_netstr(sK17,sK18,sK19),
inference(cnf_transformation,[],[f170]) ).
tcf(c_100,negated_conjecture,
in(sK19,lim_points_of_net(sK17,sK18)),
inference(cnf_transformation,[],[f169]) ).
tcf(c_101,negated_conjecture,
element(sK19,the_carrier(sK17)),
inference(cnf_transformation,[],[f168]) ).
tcf(c_102,negated_conjecture,
~ empty_carrier(sK18),
inference(cnf_transformation,[],[f167]) ).
tcf(c_103,negated_conjecture,
transitive_relstr(sK18),
inference(cnf_transformation,[],[f166]) ).
tcf(c_104,negated_conjecture,
directed_relstr(sK18),
inference(cnf_transformation,[],[f165]) ).
tcf(c_105,negated_conjecture,
net_str(sK18,sK17),
inference(cnf_transformation,[],[f164]) ).
tcf(c_106,negated_conjecture,
~ empty_carrier(sK17),
inference(cnf_transformation,[],[f163]) ).
tcf(c_107,negated_conjecture,
topological_space(sK17),
inference(cnf_transformation,[],[f162]) ).
tcf(c_108,negated_conjecture,
top_str(sK17),
inference(cnf_transformation,[],[f161]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_124,plain,
( one_sorted_str(sK17)
| ~ top_str(sK17) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| is_eventually_in(X0,X1,X3)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X0)
| ~ point_neighbourhood(X3,X0,X2)
| ~ in(X2,lim_points_of_net(X0,X1))
| ~ element(lim_points_of_net(X0,X1),powerset(the_carrier(X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_61,c_111]) ).
tcf(c_396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| is_eventually_in(X1,X2,X3)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| ~ net_str(X2,X1)
| ~ point_neighbourhood(X3,X1,X0)
| ~ in(X0,lim_points_of_net(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_334,c_65]) ).
tcf(c_1148,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ net_str(X1,X0)
| ~ element(X2,the_carrier(X0))
| ~ is_often_in(X0,X1,sK3(X0,X1,X2))
| ( X2 != sK19 )
| ( X1 != sK18 )
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_99]) ).
tcf(c_1149,plain,
( empty_carrier(sK18)
| empty_carrier(sK17)
| ~ top_str(sK17)
| ~ topological_space(sK17)
| ~ net_str(sK18,sK17)
| ~ element(sK19,the_carrier(sK17))
| ~ is_often_in(sK17,sK18,sK3(sK17,sK18,sK19)) ),
inference(unflattening,[status(thm)],[c_1148]) ).
tcf(c_1150,plain,
~ is_often_in(sK17,sK18,sK3(sK17,sK18,sK19)),
inference(global_subsumption_just,[status(thm)],[c_1149,c_108,c_107,c_106,c_105,c_102,c_101,c_1149]) ).
tcf(c_1185,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| point_neighbourhood(sK3(X1,X2,X0),X1,X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ net_str(X2,X1)
| ~ element(X0,the_carrier(X1))
| ( X2 != sK18 )
| ( X1 != sK17 )
| ( X0 != sK19 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_99]) ).
tcf(c_1186,plain,
( empty_carrier(sK18)
| empty_carrier(sK17)
| point_neighbourhood(sK3(sK17,sK18,sK19),sK17,sK19)
| ~ top_str(sK17)
| ~ topological_space(sK17)
| ~ net_str(sK18,sK17)
| ~ element(sK19,the_carrier(sK17)) ),
inference(unflattening,[status(thm)],[c_1185]) ).
tcf(c_1187,plain,
point_neighbourhood(sK3(sK17,sK18,sK19),sK17,sK19),
inference(global_subsumption_just,[status(thm)],[c_1186,c_108,c_107,c_106,c_105,c_102,c_101,c_1186]) ).
tcf(c_1260,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| is_often_in(X1,X0,X2)
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ net_str(X0,X1)
| ~ is_eventually_in(X1,X0,X2)
| ( X0 != sK18 ) ),
inference(resolution_lifted,[status(thm)],[c_98,c_103]) ).
tcf(c_1261,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK18)
| empty_carrier(X0)
| is_often_in(X0,sK18,X1)
| ~ directed_relstr(sK18)
| ~ one_sorted_str(X0)
| ~ net_str(sK18,X0)
| ~ is_eventually_in(X0,sK18,X1) ),
inference(unflattening,[status(thm)],[c_1260]) ).
tcf(c_1263,plain,
! [X0: $i,X1: $i] :
( ~ one_sorted_str(X0)
| ~ net_str(sK18,X0)
| ~ is_eventually_in(X0,sK18,X1)
| is_often_in(X0,sK18,X1)
| empty_carrier(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1261,c_104,c_102,c_1261]) ).
tcf(c_1264,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X0)
| is_often_in(X0,sK18,X1)
| ~ one_sorted_str(X0)
| ~ net_str(sK18,X0)
| ~ is_eventually_in(X0,sK18,X1) ),
inference(renaming,[status(thm)],[c_1263]) ).
tcf(c_1341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X2)
| empty_carrier(X0)
| is_eventually_in(X2,X0,X3)
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ directed_relstr(X0)
| ~ net_str(X0,X2)
| ~ point_neighbourhood(X3,X2,X1)
| ~ in(X1,lim_points_of_net(X2,X0))
| ( X0 != sK18 ) ),
inference(resolution_lifted,[status(thm)],[c_396,c_103]) ).
tcf(c_1342,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(sK18)
| empty_carrier(X1)
| is_eventually_in(X1,sK18,X2)
| ~ directed_relstr(sK18)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ net_str(sK18,X1)
| ~ point_neighbourhood(X2,X1,X0)
| ~ in(X0,lim_points_of_net(X1,sK18)) ),
inference(unflattening,[status(thm)],[c_1341]) ).
tcf(c_1344,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ top_str(X1)
| ~ topological_space(X1)
| ~ net_str(sK18,X1)
| ~ point_neighbourhood(X2,X1,X0)
| ~ in(X0,lim_points_of_net(X1,sK18))
| is_eventually_in(X1,sK18,X2)
| empty_carrier(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1342,c_104,c_102,c_1342]) ).
tcf(c_1345,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| is_eventually_in(X1,sK18,X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ net_str(sK18,X1)
| ~ point_neighbourhood(X2,X1,X0)
| ~ in(X0,lim_points_of_net(X1,sK18)) ),
inference(renaming,[status(thm)],[c_1344]) ).
tcf(c_1569,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| is_eventually_in(X0,sK18,X2)
| ~ top_str(X0)
| ~ net_str(sK18,X0)
| ~ point_neighbourhood(X2,X0,X1)
| ~ in(X1,lim_points_of_net(X0,sK18))
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_1345,c_107]) ).
tcf(c_1570,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK17)
| is_eventually_in(sK17,sK18,X1)
| ~ top_str(sK17)
| ~ net_str(sK18,sK17)
| ~ point_neighbourhood(X1,sK17,X0)
| ~ in(X0,lim_points_of_net(sK17,sK18)) ),
inference(unflattening,[status(thm)],[c_1569]) ).
tcf(c_1572,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,lim_points_of_net(sK17,sK18))
| ~ point_neighbourhood(X1,sK17,X0)
| is_eventually_in(sK17,sK18,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1570,c_108,c_106,c_105,c_1570]) ).
tcf(c_1573,plain,
! [X0: $i,X1: $i] :
( is_eventually_in(sK17,sK18,X1)
| ~ point_neighbourhood(X1,sK17,X0)
| ~ in(X0,lim_points_of_net(sK17,sK18)) ),
inference(renaming,[status(thm)],[c_1572]) ).
tcf(c_2008,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X0)
| is_often_in(X0,sK18,X1)
| ~ one_sorted_str(X0)
| ~ is_eventually_in(X0,sK18,X1)
| ( sK18 != sK18 )
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_105,c_1264]) ).
tcf(c_2009,plain,
! [X0: $i] :
( empty_carrier(sK17)
| is_often_in(sK17,sK18,X0)
| ~ one_sorted_str(sK17)
| ~ is_eventually_in(sK17,sK18,X0) ),
inference(unflattening,[status(thm)],[c_2008]) ).
tcf(c_2011,plain,
! [X0: $i] :
( ~ is_eventually_in(sK17,sK18,X0)
| is_often_in(sK17,sK18,X0) ),
inference(global_subsumption_just,[status(thm)],[c_2009,c_108,c_106,c_124,c_2009]) ).
tcf(c_2012,plain,
! [X0: $i] :
( is_often_in(sK17,sK18,X0)
| ~ is_eventually_in(sK17,sK18,X0) ),
inference(renaming,[status(thm)],[c_2011]) ).
tcf(c_3264,definition,
iPr_def_14 = sK3(sK17,sK18,sK19),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_3266,plain,
! [X0: $i] :
( is_often_in(sK17,sK18,X0)
| ~ is_eventually_in(sK17,sK18,X0) ),
inference(demodulation,[status(thm)],[c_2012]) ).
tcf(c_3279,plain,
! [X0: $i,X1: $i] :
( is_eventually_in(sK17,sK18,X0)
| ~ in(X1,iPr_def_12)
| ~ point_neighbourhood(X0,sK17,X1) ),
inference(demodulation,[status(thm)],[c_1573]) ).
tcf(c_3283,plain,
point_neighbourhood(iPr_def_14,sK17,sK19),
inference(demodulation,[status(thm)],[c_1187,c_3264]) ).
tcf(c_3284,plain,
~ is_often_in(sK17,sK18,iPr_def_14),
inference(demodulation,[status(thm)],[c_1150]) ).
tcf(c_3288,negated_conjecture,
in(sK19,iPr_def_12),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_4080,plain,
( is_eventually_in(sK17,sK18,iPr_def_14)
| ~ in(sK19,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3283,c_3279]) ).
tcf(c_4081,plain,
is_eventually_in(sK17,sK18,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_4080,c_3288]) ).
tcf(c_4086,plain,
is_often_in(sK17,sK18,iPr_def_14),
inference(superposition,[status(thm)],[c_4081,c_3266]) ).
tcf(c_4087,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4086,c_3284]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU386+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Thu Sep 24 13:57:52 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.46
% 0.17/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.46
% 0.17/0.46 % Detected problem language: tptp
% 0.17/0.48 % Proving...
% 1.18/1.35 % SZS status Started for theBenchmark.p
% 1.18/1.35 % SZS status Theorem for theBenchmark.p
% 1.18/1.35
% 1.18/1.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.18/1.35
% 1.18/1.35 % ------ iProver source info
% 1.18/1.35
% 1.18/1.35 % git: date: 2026-07-19 20:42:38 +0200
% 1.18/1.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.18/1.35 % git: non_committed_changes: false
% 1.18/1.35
% 1.18/1.35 % ------ Parsing...
% 1.18/1.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.18/1.35
% 1.18/1.35 % ------ Preprocessing... sup_sim: 0 sf_s rm: 16 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 12 0s sf_e pe_s pe_e %
% 1.18/1.35
% 1.18/1.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.18/1.35
% 1.18/1.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.18/1.35 % ------ Proving...
% 1.18/1.35 % ------ Problem Properties
% 1.18/1.35
% 1.18/1.35 %
% 1.18/1.35 % clauses 57
% 1.18/1.35 % conjectures 4
% 1.18/1.35 % EPR 27
% 1.18/1.35 % Horn 45
% 1.18/1.35 % unary 26
% 1.18/1.35 % binary 11
% 1.18/1.35 % lits 120
% 1.18/1.35 % lits eq 12
% 1.18/1.35 % fd_pure 0
% 1.18/1.35 % fd_pseudo 0
% 1.18/1.35 % fd_cond 5
% 1.18/1.35 % fd_pseudo_cond 1
% 1.18/1.35 % AC symbols 0
% 1.18/1.35
% 1.18/1.35 % ------ Schedule dynamic 5 is on
% 1.18/1.35
% 1.18/1.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.18/1.35
% 1.18/1.35
% 1.18/1.35 % ------
% 1.18/1.35 % Current options:
% 1.18/1.35 % ------
% 1.18/1.35
% 1.18/1.35
% 1.18/1.35 %
% 1.18/1.35
% 1.18/1.35 % ------ Proving...
% 1.18/1.35 %
% 1.18/1.35
% 1.18/1.35 % SZS status Theorem for theBenchmark.p
% 1.18/1.35
% 1.18/1.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.18/1.35
% 1.18/1.35
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