%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU392+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 : n018.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 12:48:41 PM UTC 2026
% Result : Theorem 9.74s 2.28s
% Output : Refutation 10.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 29
% Syntax : Number of formulae : 289 ( 17 unt; 9 def)
% Number of atoms : 1488 ( 38 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 1970 ( 771 ~; 973 |; 151 &)
% ( 30 <=>; 43 =>; 0 <=; 2 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 10 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 474 ( 0 sgn 446 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,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(f28,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(f29,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_yellow19) ).
fof(f30,axiom,
! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( open_subset(X3,X0)
& in(X2,X3) )
=> in(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_waybel_7) ).
fof(f32,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(f33,axiom,
! [X0,X1] :
( ( top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f41,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f44,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& element(X1,the_carrier(X0)) )
=> ! [X2] :
( point_neighbourhood(X2,X0,X1)
=> element(X2,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
fof(f62,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f77,axiom,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> open_subset(interior(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_tops_1) ).
fof(f83,axiom,
! [X0,X1,X2] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& X0 = X3
& is_eventually_in(X1,X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).
fof(f122,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ! [X2] :
( in(X2,filter_of_net_str(X0,X1))
<=> ( is_eventually_in(X0,X1,X2)
& element(X2,powerset(the_carrier(X0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_yellow19) ).
fof(f123,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_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_yellow19) ).
fof(f124,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_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f123]) ).
fof(f125,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f126,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f128,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f129,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(interior(X0,X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_1) ).
fof(f130,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f131,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( open_subset(X1,X0)
& in(X2,X1) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f136,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ! [X2,X3] :
( subset(X2,X3)
=> ( ( is_eventually_in(X0,X1,X2)
=> is_eventually_in(X0,X1,X3) )
& ( is_often_in(X0,X1,X2)
=> is_often_in(X0,X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel_0) ).
fof(f185,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,[],[f27]) ).
fof(f186,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,[],[f185]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f187]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f190,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f189]) ).
fof(f191,plain,
! [X0] :
( ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( in(X3,X1)
| ~ open_subset(X3,X0)
| ~ in(X2,X3)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f192,plain,
! [X0] :
( ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( in(X3,X1)
| ~ open_subset(X3,X0)
| ~ in(X2,X3)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f191]) ).
fof(f194,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,[],[f32]) ).
fof(f195,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,[],[f194]) ).
fof(f196,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f33]) ).
fof(f197,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f196]) ).
fof(f202,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f204,plain,
! [X0,X1] :
( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(ennf_transformation,[],[f44]) ).
fof(f205,plain,
! [X0,X1] :
( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(flattening,[],[f204]) ).
fof(f217,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f62]) ).
fof(f218,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f217]) ).
fof(f240,plain,
! [X0,X1] :
( open_subset(interior(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f77]) ).
fof(f241,plain,
! [X0,X1] :
( open_subset(interior(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f240]) ).
fof(f245,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& X0 = X3
& is_eventually_in(X1,X2,X3) ) )
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(ennf_transformation,[],[f83]) ).
fof(f246,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& X0 = X3
& is_eventually_in(X1,X2,X3) ) )
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(flattening,[],[f245]) ).
fof(f281,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,filter_of_net_str(X0,X1))
<=> ( is_eventually_in(X0,X1,X2)
& element(X2,powerset(the_carrier(X0))) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f122]) ).
fof(f282,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,filter_of_net_str(X0,X1))
<=> ( is_eventually_in(X0,X1,X2)
& element(X2,powerset(the_carrier(X0))) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f281]) ).
fof(f283,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,lim_points_of_net(X0,X1))
<~> is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) )
& 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,[],[f124]) ).
fof(f284,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,lim_points_of_net(X0,X1))
<~> is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) )
& 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,[],[f283]) ).
fof(f285,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f125]) ).
fof(f286,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f126]) ).
fof(f287,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f286]) ).
fof(f289,plain,
! [X0] :
( ! [X1] :
( subset(interior(X0,X1),X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f129]) ).
fof(f290,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f130]) ).
fof(f291,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f290]) ).
fof(f292,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( point_neighbourhood(X1,X0,X2)
| ~ open_subset(X1,X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f131]) ).
fof(f293,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( point_neighbourhood(X1,X0,X2)
| ~ open_subset(X1,X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f292]) ).
fof(f298,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( ( ( is_eventually_in(X0,X1,X3)
| ~ is_eventually_in(X0,X1,X2) )
& ( is_often_in(X0,X1,X3)
| ~ is_often_in(X0,X1,X2) ) )
| ~ subset(X2,X3) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f136]) ).
fof(f299,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( ( ( is_eventually_in(X0,X1,X3)
| ~ is_eventually_in(X0,X1,X2) )
& ( is_often_in(X0,X1,X3)
| ~ is_often_in(X0,X1,X2) ) )
| ~ subset(X2,X3) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f298]) ).
fof(f302,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,[],[f186]) ).
fof(f303,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,[],[f302]) ).
fof(f304,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,[],[f303]) ).
fof(f305,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = lim_points_of_net(X0,X1)
| ( ( ( ~ is_eventually_in(X0,X1,sK2(X0,X1,X2))
& point_neighbourhood(sK2(X0,X1,X2),X0,sK1(X0,X1,X2)) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( ! [X5] :
( is_eventually_in(X0,X1,X5)
| ~ point_neighbourhood(X5,X0,sK1(X0,X1,X2)) )
| in(sK1(X0,X1,X2),X2) )
& element(sK1(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ( ~ is_eventually_in(X0,X1,sK3(X0,X1,X6))
& point_neighbourhood(sK3(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,[sK1,sK2,sK3]),skolemize(X3,sK1(X0,X1,X2)),skolemize(X4,sK2(X0,X1,X2)),skolemize(X7,sK3(X0,X1,X6))],[f304]) ).
fof(f306,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( point_neighbourhood(X2,X0,X1)
| ~ in(X1,interior(X0,X2)) )
& ( in(X1,interior(X0,X2))
| ~ point_neighbourhood(X2,X0,X1) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f188]) ).
fof(f307,plain,
! [X0] :
( ! [X1,X2] :
( ( is_a_convergence_point_of_set(X0,X1,X2)
| ? [X3] :
( ~ in(X3,X1)
& open_subset(X3,X0)
& in(X2,X3)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ open_subset(X3,X0)
| ~ in(X2,X3)
| ~ element(X3,powerset(the_carrier(X0))) )
| ~ is_a_convergence_point_of_set(X0,X1,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f192]) ).
fof(f308,plain,
! [X0] :
( ! [X1,X2] :
( ( is_a_convergence_point_of_set(X0,X1,X2)
| ? [X3] :
( ~ in(X3,X1)
& open_subset(X3,X0)
& in(X2,X3)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X4,X1)
| ~ open_subset(X4,X0)
| ~ in(X2,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ is_a_convergence_point_of_set(X0,X1,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(rectify,[],[f307]) ).
fof(f309,plain,
! [X0] :
( ! [X1,X2] :
( ( is_a_convergence_point_of_set(X0,X1,X2)
| ( ~ in(sK4(X0,X1,X2),X1)
& open_subset(sK4(X0,X1,X2),X0)
& in(X2,sK4(X0,X1,X2))
& element(sK4(X0,X1,X2),powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X4,X1)
| ~ open_subset(X4,X0)
| ~ in(X2,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ is_a_convergence_point_of_set(X0,X1,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f308]) ).
fof(f319,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| X0 != X3
| ~ is_eventually_in(X1,X2,X3) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& X0 = X3
& is_eventually_in(X1,X2,X3) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(nnf_transformation,[],[f246]) ).
fof(f320,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| X0 != X3
| ~ is_eventually_in(X1,X2,X3) ) )
& ( ? [X4] :
( element(X4,powerset(the_carrier(X1)))
& X0 = X4
& is_eventually_in(X1,X2,X4) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(rectify,[],[f319]) ).
fof(f321,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| X0 != X3
| ~ is_eventually_in(X1,X2,X3) ) )
& ( ( element(sK13(X0,X1,X2),powerset(the_carrier(X1)))
& sK13(X0,X1,X2) = X0
& is_eventually_in(X1,X2,sK13(X0,X1,X2)) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X4,sK13(X0,X1,X2))],[f320]) ).
fof(f358,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,filter_of_net_str(X0,X1))
| ~ is_eventually_in(X0,X1,X2)
| ~ element(X2,powerset(the_carrier(X0))) )
& ( ( is_eventually_in(X0,X1,X2)
& element(X2,powerset(the_carrier(X0))) )
| ~ in(X2,filter_of_net_str(X0,X1)) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f282]) ).
fof(f359,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,filter_of_net_str(X0,X1))
| ~ is_eventually_in(X0,X1,X2)
| ~ element(X2,powerset(the_carrier(X0))) )
& ( ( is_eventually_in(X0,X1,X2)
& element(X2,powerset(the_carrier(X0))) )
| ~ in(X2,filter_of_net_str(X0,X1)) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f358]) ).
fof(f360,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ in(X2,lim_points_of_net(X0,X1)) )
& ( is_a_convergence_point_of_set(X0,filter_of_net_str(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(nnf_transformation,[],[f284]) ).
fof(f361,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ in(X2,lim_points_of_net(X0,X1)) )
& ( is_a_convergence_point_of_set(X0,filter_of_net_str(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,[],[f360]) ).
fof(f362,plain,
( ( ~ is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51)
| ~ in(sK51,lim_points_of_net(sK49,sK50)) )
& ( is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51)
| in(sK51,lim_points_of_net(sK49,sK50)) )
& element(sK51,the_carrier(sK49))
& ~ empty_carrier(sK50)
& transitive_relstr(sK50)
& directed_relstr(sK50)
& net_str(sK50,sK49)
& ~ empty_carrier(sK49)
& topological_space(sK49)
& top_str(sK49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49,sK50,sK51]),skolemize(X0,sK49),skolemize(X1,sK50),skolemize(X2,sK51)],[f361]) ).
fof(f365,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f128]) ).
fof(f437,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,[],[f305]) ).
fof(f438,plain,
! [X2,X0,X1,X6] :
( in(X6,X2)
| point_neighbourhood(sK3(X0,X1,X6),X0,X6)
| ~ 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,[],[f305]) ).
fof(f439,plain,
! [X2,X0,X1,X6] :
( in(X6,X2)
| ~ is_eventually_in(X0,X1,sK3(X0,X1,X6))
| ~ 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,[],[f305]) ).
fof(f444,plain,
! [X2,X0,X1] :
( in(X1,interior(X0,X2))
| ~ point_neighbourhood(X2,X0,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f306]) ).
fof(f446,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f447,plain,
! [X2,X0,X1,X4] :
( ~ top_str(X0)
| ~ open_subset(X4,X0)
| ~ in(X2,X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ topological_space(X0)
| in(X4,X1) ),
inference(cnf_transformation,[],[f309]) ).
fof(f448,plain,
! [X2,X0,X1] :
( element(sK4(X0,X1,X2),powerset(the_carrier(X0)))
| is_a_convergence_point_of_set(X0,X1,X2)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f449,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| in(X2,sK4(X0,X1,X2))
| ~ topological_space(X0)
| is_a_convergence_point_of_set(X0,X1,X2) ),
inference(cnf_transformation,[],[f309]) ).
fof(f450,plain,
! [X2,X0,X1] :
( open_subset(sK4(X0,X1,X2),X0)
| is_a_convergence_point_of_set(X0,X1,X2)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f451,plain,
! [X2,X0,X1] :
( ~ in(sK4(X0,X1,X2),X1)
| is_a_convergence_point_of_set(X0,X1,X2)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f454,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,[],[f195]) ).
fof(f455,plain,
! [X0,X1] :
( ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f197]) ).
fof(f461,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f463,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ point_neighbourhood(X2,X0,X1)
| empty_carrier(X0)
| ~ topological_space(X0)
| element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0)) ),
inference(cnf_transformation,[],[f205]) ).
fof(f488,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f548,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(interior(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f241]) ).
fof(f583,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X1)
| ~ in(X0,a_2_1_yellow19(X1,X2))
| empty_carrier(X1)
| is_eventually_in(X1,X2,sK13(X0,X1,X2))
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(cnf_transformation,[],[f321]) ).
fof(f584,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X1)
| ~ in(X0,a_2_1_yellow19(X1,X2))
| empty_carrier(X1)
| sK13(X0,X1,X2) = X0
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(cnf_transformation,[],[f321]) ).
fof(f768,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| ~ is_eventually_in(X0,X1,X2)
| ~ element(X2,powerset(the_carrier(X0)))
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| in(X2,filter_of_net_str(X0,X1)) ),
inference(cnf_transformation,[],[f359]) ).
fof(f769,plain,
top_str(sK49),
inference(cnf_transformation,[],[f362]) ).
fof(f770,plain,
topological_space(sK49),
inference(cnf_transformation,[],[f362]) ).
fof(f771,plain,
~ empty_carrier(sK49),
inference(cnf_transformation,[],[f362]) ).
fof(f772,plain,
net_str(sK50,sK49),
inference(cnf_transformation,[],[f362]) ).
fof(f773,plain,
directed_relstr(sK50),
inference(cnf_transformation,[],[f362]) ).
fof(f774,plain,
transitive_relstr(sK50),
inference(cnf_transformation,[],[f362]) ).
fof(f775,plain,
~ empty_carrier(sK50),
inference(cnf_transformation,[],[f362]) ).
fof(f776,plain,
element(sK51,the_carrier(sK49)),
inference(cnf_transformation,[],[f362]) ).
fof(f777,plain,
( is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51)
| in(sK51,lim_points_of_net(sK49,sK50)) ),
inference(cnf_transformation,[],[f362]) ).
fof(f778,plain,
( ~ is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51)
| ~ in(sK51,lim_points_of_net(sK49,sK50)) ),
inference(cnf_transformation,[],[f362]) ).
fof(f779,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f285]) ).
fof(f780,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f287]) ).
fof(f783,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f365]) ).
fof(f784,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f365]) ).
fof(f785,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset(interior(X0,X1),X1) ),
inference(cnf_transformation,[],[f289]) ).
fof(f786,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| element(X0,X2)
| ~ element(X1,powerset(X2)) ),
inference(cnf_transformation,[],[f291]) ).
fof(f787,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ open_subset(X1,X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| empty_carrier(X0)
| ~ topological_space(X0)
| point_neighbourhood(X1,X0,X2) ),
inference(cnf_transformation,[],[f293]) ).
fof(f793,plain,
! [X2,X3,X0,X1] :
( ~ subset(X2,X3)
| ~ is_eventually_in(X0,X1,X2)
| is_eventually_in(X0,X1,X3)
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f794,plain,
! [X0,X1,X6] :
( in(X6,lim_points_of_net(X0,X1))
| ~ is_eventually_in(X0,X1,sK3(X0,X1,X6))
| ~ 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,[],[f439]) ).
fof(f795,plain,
! [X0,X1,X6] :
( in(X6,lim_points_of_net(X0,X1))
| point_neighbourhood(sK3(X0,X1,X6),X0,X6)
| ~ 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,[],[f438]) ).
fof(f796,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,[],[f437]) ).
fof(f799,definition,
( spl53_1
<=> in(sK51,lim_points_of_net(sK49,sK50)) ),
introduced(definition,[new_symbols(definition,[spl53_1])],[avatar_definition]) ).
fof(f800,plain,
( in(sK51,lim_points_of_net(sK49,sK50))
| ~ spl53_1 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f802,definition,
( spl53_2
<=> is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51) ),
introduced(definition,[new_symbols(definition,[spl53_2])],[avatar_definition]) ).
fof(f803,plain,
( is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51)
| ~ spl53_2 ),
inference(avatar_component_clause,[],[f802]) ).
fof(f804,plain,
( spl53_1
| spl53_2 ),
inference(avatar_split_clause,[],[f777,f802,f799]) ).
fof(f805,plain,
( ~ in(sK51,lim_points_of_net(sK49,sK50))
| spl53_1 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f806,plain,
( ~ is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51)
| spl53_2 ),
inference(avatar_component_clause,[],[f802]) ).
fof(f807,plain,
( ~ spl53_1
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f778,f802,f799]) ).
fof(f808,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ point_neighbourhood(X2,X0,X1)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ topological_space(X0)
| in(X1,interior(X0,X2)) ),
inference(forward_subsumption_resolution,[],[f444,f463]) ).
fof(f809,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,[],[f796,f786]) ).
fof(f810,plain,
! [X0,X1,X6] :
( point_neighbourhood(sK3(X0,X1,X6),X0,X6)
| in(X6,lim_points_of_net(X0,X1))
| ~ element(X6,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,[],[f795,f454]) ).
fof(f811,plain,
! [X0,X1,X6] :
( ~ is_eventually_in(X0,X1,sK3(X0,X1,X6))
| in(X6,lim_points_of_net(X0,X1))
| ~ element(X6,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,[],[f794,f454]) ).
fof(f815,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,[],[f809,f454]) ).
fof(f816,plain,
! [X0,X1] :
( in(X0,sK4(sK49,X1,X0))
| ~ topological_space(sK49)
| is_a_convergence_point_of_set(sK49,X1,X0) ),
inference(resolution,[],[f769,f449]) ).
fof(f817,plain,
! [X0,X1] :
( in(X0,sK4(sK49,X1,X0))
| is_a_convergence_point_of_set(sK49,X1,X0) ),
inference(forward_subsumption_resolution,[],[f816,f770]) ).
fof(f818,plain,
! [X2,X0,X1] :
( ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| ~ is_a_convergence_point_of_set(sK49,X2,X1)
| ~ topological_space(sK49)
| in(X0,X2) ),
inference(resolution,[],[f447,f769]) ).
fof(f819,plain,
! [X2,X0,X1] :
( ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| ~ is_a_convergence_point_of_set(sK49,X2,X1)
| in(X0,X2) ),
inference(forward_subsumption_resolution,[],[f818,f770]) ).
fof(f820,plain,
one_sorted_str(sK49),
inference(resolution,[],[f461,f769]) ).
fof(f821,plain,
! [X0,X1] :
( ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK49))
| ~ element(X0,powerset(the_carrier(sK49)))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| point_neighbourhood(X0,sK49,X1) ),
inference(resolution,[],[f787,f769]) ).
fof(f822,plain,
! [X0,X1] :
( ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| point_neighbourhood(X0,sK49,X1) ),
inference(forward_subsumption_resolution,[],[f821,f786]) ).
fof(f823,plain,
! [X0,X1] :
( ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| ~ topological_space(sK49)
| point_neighbourhood(X0,sK49,X1) ),
inference(forward_subsumption_resolution,[],[f822,f771]) ).
fof(f824,plain,
! [X0,X1] :
( ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| point_neighbourhood(X0,sK49,X1) ),
inference(forward_subsumption_resolution,[],[f823,f770]) ).
fof(f825,plain,
! [X2,X0,X1] :
( ~ in(X0,sK4(sK49,X1,X2))
| ~ element(sK4(sK49,X1,X2),powerset(the_carrier(sK49)))
| point_neighbourhood(sK4(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(resolution,[],[f824,f450]) ).
fof(f826,plain,
! [X2,X0,X1] :
( ~ in(X0,sK4(sK49,X1,X2))
| ~ element(sK4(sK49,X1,X2),powerset(the_carrier(sK49)))
| point_neighbourhood(sK4(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f825,f770]) ).
fof(f827,plain,
! [X2,X0,X1] :
( ~ element(sK4(sK49,X1,X2),powerset(the_carrier(sK49)))
| ~ in(X0,sK4(sK49,X1,X2))
| point_neighbourhood(sK4(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2) ),
inference(forward_subsumption_resolution,[],[f826,f769]) ).
fof(f828,plain,
! [X0,X1] :
( ~ in(X0,a_2_1_yellow19(sK49,X1))
| empty_carrier(sK49)
| is_eventually_in(sK49,X1,sK13(X0,sK49,X1))
| empty_carrier(X1)
| ~ net_str(X1,sK49) ),
inference(resolution,[],[f820,f583]) ).
fof(f829,plain,
! [X0,X1] :
( ~ in(X0,a_2_1_yellow19(sK49,X1))
| empty_carrier(sK49)
| sK13(X0,sK49,X1) = X0
| empty_carrier(X1)
| ~ net_str(X1,sK49) ),
inference(resolution,[],[f820,f584]) ).
fof(f830,plain,
! [X0,X1] :
( ~ is_eventually_in(sK49,X0,X1)
| ~ element(X1,powerset(the_carrier(sK49)))
| empty_carrier(X0)
| ~ net_str(X0,sK49)
| empty_carrier(sK49)
| in(X1,filter_of_net_str(sK49,X0)) ),
inference(resolution,[],[f820,f768]) ).
fof(f832,plain,
! [X0] :
( empty_carrier(X0)
| ~ net_str(X0,sK49)
| empty_carrier(sK49)
| filter_of_net_str(sK49,X0) = a_2_1_yellow19(sK49,X0) ),
inference(resolution,[],[f820,f446]) ).
fof(f833,plain,
! [X0] :
( ~ net_str(X0,sK49)
| empty_carrier(X0)
| filter_of_net_str(sK49,X0) = a_2_1_yellow19(sK49,X0) ),
inference(forward_subsumption_resolution,[],[f832,f771]) ).
fof(f835,plain,
! [X0,X1] :
( ~ is_eventually_in(sK49,X0,X1)
| ~ element(X1,powerset(the_carrier(sK49)))
| empty_carrier(X0)
| ~ net_str(X0,sK49)
| in(X1,filter_of_net_str(sK49,X0)) ),
inference(forward_subsumption_resolution,[],[f830,f771]) ).
fof(f836,plain,
! [X0,X1] :
( ~ net_str(X1,sK49)
| sK13(X0,sK49,X1) = X0
| empty_carrier(X1)
| ~ in(X0,a_2_1_yellow19(sK49,X1)) ),
inference(forward_subsumption_resolution,[],[f829,f771]) ).
fof(f837,plain,
! [X0,X1] :
( ~ net_str(X1,sK49)
| is_eventually_in(sK49,X1,sK13(X0,sK49,X1))
| empty_carrier(X1)
| ~ in(X0,a_2_1_yellow19(sK49,X1)) ),
inference(forward_subsumption_resolution,[],[f828,f771]) ).
fof(f838,plain,
( empty_carrier(sK50)
| filter_of_net_str(sK49,sK50) = a_2_1_yellow19(sK49,sK50) ),
inference(resolution,[],[f833,f772]) ).
fof(f839,plain,
filter_of_net_str(sK49,sK50) = a_2_1_yellow19(sK49,sK50),
inference(forward_subsumption_resolution,[],[f838,f775]) ).
fof(f840,plain,
! [X0] :
( sK13(X0,sK49,sK50) = X0
| empty_carrier(sK50)
| ~ in(X0,a_2_1_yellow19(sK49,sK50)) ),
inference(resolution,[],[f836,f772]) ).
fof(f841,plain,
! [X0] :
( sK13(X0,sK49,sK50) = X0
| ~ in(X0,a_2_1_yellow19(sK49,sK50)) ),
inference(forward_subsumption_resolution,[],[f840,f775]) ).
fof(f842,plain,
! [X0] :
( ~ in(X0,filter_of_net_str(sK49,sK50))
| sK13(X0,sK49,sK50) = X0 ),
inference(forward_demodulation,[],[f841,f839]) ).
fof(f843,plain,
! [X0] :
( is_eventually_in(sK49,sK50,sK13(X0,sK49,sK50))
| empty_carrier(sK50)
| ~ in(X0,a_2_1_yellow19(sK49,sK50)) ),
inference(resolution,[],[f837,f772]) ).
fof(f844,plain,
! [X0] :
( is_eventually_in(sK49,sK50,sK13(X0,sK49,sK50))
| ~ in(X0,a_2_1_yellow19(sK49,sK50)) ),
inference(forward_subsumption_resolution,[],[f843,f775]) ).
fof(f845,plain,
! [X0] :
( ~ in(X0,filter_of_net_str(sK49,sK50))
| is_eventually_in(sK49,sK50,sK13(X0,sK49,sK50)) ),
inference(forward_demodulation,[],[f844,f839]) ).
fof(f849,plain,
! [X0,X1] :
( ~ point_neighbourhood(X0,sK49,X1)
| ~ element(X1,the_carrier(sK49))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| in(X1,interior(sK49,X0)) ),
inference(resolution,[],[f808,f769]) ).
fof(f850,plain,
! [X0,X1] :
( ~ point_neighbourhood(X0,sK49,X1)
| ~ element(X1,the_carrier(sK49))
| ~ topological_space(sK49)
| in(X1,interior(sK49,X0)) ),
inference(forward_subsumption_resolution,[],[f849,f771]) ).
fof(f851,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,X1)
| in(X1,interior(sK49,X0)) ),
inference(forward_subsumption_resolution,[],[f850,f770]) ).
fof(f852,plain,
! [X0] :
( in(sK51,interior(sK49,X0))
| ~ point_neighbourhood(X0,sK49,sK51) ),
inference(resolution,[],[f851,f776]) ).
fof(f869,plain,
! [X0,X1] :
( ~ point_neighbourhood(X0,sK49,X1)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| element(X0,powerset(the_carrier(sK49)))
| ~ element(X1,the_carrier(sK49)) ),
inference(resolution,[],[f463,f769]) ).
fof(f870,plain,
! [X0,X1] :
( ~ point_neighbourhood(X0,sK49,X1)
| ~ topological_space(sK49)
| element(X0,powerset(the_carrier(sK49)))
| ~ element(X1,the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[],[f869,f771]) ).
fof(f871,plain,
! [X0,X1] :
( ~ point_neighbourhood(X0,sK49,X1)
| element(X0,powerset(the_carrier(sK49)))
| ~ element(X1,the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[],[f870,f770]) ).
fof(f872,plain,
! [X0,X1] :
( element(sK3(sK49,X0,X1),powerset(the_carrier(sK49)))
| ~ element(X1,the_carrier(sK49))
| in(X1,lim_points_of_net(sK49,X0))
| ~ element(X1,the_carrier(sK49))
| empty_carrier(X0)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| ~ net_str(X0,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(resolution,[],[f871,f810]) ).
fof(f873,plain,
! [X0,X1] :
( element(sK3(sK49,X0,X1),powerset(the_carrier(sK49)))
| ~ element(X1,the_carrier(sK49))
| in(X1,lim_points_of_net(sK49,X0))
| empty_carrier(X0)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| ~ net_str(X0,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(duplicate_literal_removal,[],[f872]) ).
fof(f874,plain,
! [X0,X1] :
( element(sK3(sK49,X0,X1),powerset(the_carrier(sK49)))
| ~ element(X1,the_carrier(sK49))
| in(X1,lim_points_of_net(sK49,X0))
| empty_carrier(X0)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| ~ net_str(X0,sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f873,f771]) ).
fof(f875,plain,
! [X0,X1] :
( element(sK3(sK49,X0,X1),powerset(the_carrier(sK49)))
| ~ element(X1,the_carrier(sK49))
| in(X1,lim_points_of_net(sK49,X0))
| empty_carrier(X0)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| ~ net_str(X0,sK49)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f874,f770]) ).
fof(f876,plain,
! [X0,X1] :
( element(sK3(sK49,X0,X1),powerset(the_carrier(sK49)))
| ~ element(X1,the_carrier(sK49))
| in(X1,lim_points_of_net(sK49,X0))
| empty_carrier(X0)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| ~ net_str(X0,sK49) ),
inference(forward_subsumption_resolution,[],[f875,f769]) ).
fof(f877,plain,
! [X2,X0,X1] :
( ~ element(sK4(sK49,X2,X0),powerset(X1))
| element(X0,X1)
| is_a_convergence_point_of_set(sK49,X2,X0) ),
inference(resolution,[],[f786,f817]) ).
fof(f879,plain,
! [X0] :
( subset(interior(sK49,X0),X0)
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(resolution,[],[f785,f769]) ).
fof(f880,plain,
! [X2,X0,X1] :
( ~ is_eventually_in(X1,X2,interior(sK49,X0))
| ~ element(X0,powerset(the_carrier(sK49)))
| is_eventually_in(X1,X2,X0)
| empty_carrier(X2)
| ~ net_str(X2,X1)
| empty_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(resolution,[],[f879,f793]) ).
fof(f881,plain,
! [X2,X0,X1] :
( ~ in(X0,sK4(sK49,X1,X2))
| point_neighbourhood(sK4(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2)
| is_a_convergence_point_of_set(sK49,X1,X2)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(resolution,[],[f827,f448]) ).
fof(f882,plain,
! [X2,X0,X1] :
( ~ in(X0,sK4(sK49,X1,X2))
| point_neighbourhood(sK4(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(duplicate_literal_removal,[],[f881]) ).
fof(f883,plain,
! [X2,X0,X1] :
( ~ in(X0,sK4(sK49,X1,X2))
| point_neighbourhood(sK4(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f882,f770]) ).
fof(f884,plain,
! [X2,X0,X1] :
( ~ in(X0,sK4(sK49,X1,X2))
| point_neighbourhood(sK4(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2) ),
inference(forward_subsumption_resolution,[],[f883,f769]) ).
fof(f887,plain,
! [X0,X1] :
( point_neighbourhood(sK4(sK49,X0,X1),sK49,X1)
| is_a_convergence_point_of_set(sK49,X0,X1)
| is_a_convergence_point_of_set(sK49,X0,X1) ),
inference(resolution,[],[f884,f817]) ).
fof(f888,plain,
! [X0,X1] :
( point_neighbourhood(sK4(sK49,X0,X1),sK49,X1)
| is_a_convergence_point_of_set(sK49,X0,X1) ),
inference(duplicate_literal_removal,[],[f887]) ).
fof(f890,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(sK49))
| element(sK4(sK49,X0,X1),powerset(the_carrier(sK49)))
| is_a_convergence_point_of_set(sK49,X0,X1) ),
inference(resolution,[],[f888,f871]) ).
fof(f902,plain,
! [X0,X1] :
( ~ net_str(X1,sK49)
| in(X0,lim_points_of_net(sK49,X1))
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ element(X0,the_carrier(sK49))
| subset(sK3(sK49,X1,X0),the_carrier(sK49)) ),
inference(resolution,[],[f876,f783]) ).
fof(f915,definition,
( spl53_3
<=> empty(the_carrier(sK49)) ),
introduced(definition,[new_symbols(definition,[spl53_3])],[avatar_definition]) ).
fof(f916,plain,
( empty(the_carrier(sK49))
| ~ spl53_3 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f927,plain,
( empty_carrier(sK49)
| ~ one_sorted_str(sK49)
| ~ spl53_3 ),
inference(resolution,[],[f916,f488]) ).
fof(f929,plain,
( ~ one_sorted_str(sK49)
| ~ spl53_3 ),
inference(forward_subsumption_resolution,[],[f927,f771]) ).
fof(f930,plain,
( $false
| ~ spl53_3 ),
inference(forward_subsumption_resolution,[],[f929,f820]) ).
fof(f931,plain,
~ spl53_3,
inference(avatar_contradiction_clause,[],[f930]) ).
fof(f947,plain,
! [X0] :
( element(interior(sK49,X0),powerset(the_carrier(sK49)))
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(resolution,[],[f455,f769]) ).
fof(f961,plain,
! [X0,X1] :
( element(X0,the_carrier(sK49))
| is_a_convergence_point_of_set(sK49,X1,X0)
| is_a_convergence_point_of_set(sK49,X1,X0)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(resolution,[],[f877,f448]) ).
fof(f963,plain,
! [X0,X1] :
( element(X0,the_carrier(sK49))
| is_a_convergence_point_of_set(sK49,X1,X0)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(duplicate_literal_removal,[],[f961]) ).
fof(f964,plain,
! [X0,X1] :
( element(X0,the_carrier(sK49))
| is_a_convergence_point_of_set(sK49,X1,X0)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f963,f770]) ).
fof(f965,plain,
! [X0,X1] :
( element(X0,the_carrier(sK49))
| is_a_convergence_point_of_set(sK49,X1,X0) ),
inference(forward_subsumption_resolution,[],[f964,f769]) ).
fof(f967,plain,
! [X0,X1] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| in(X1,the_carrier(sK49))
| empty(the_carrier(sK49)) ),
inference(resolution,[],[f965,f780]) ).
fof(f969,definition,
( spl53_5
<=> ! [X0,X1] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| in(X1,the_carrier(sK49)) ) ),
introduced(definition,[new_symbols(definition,[spl53_5])],[avatar_definition]) ).
fof(f970,plain,
( ! [X0,X1] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| in(X1,the_carrier(sK49)) )
| ~ spl53_5 ),
inference(avatar_component_clause,[],[f969]) ).
fof(f971,plain,
( spl53_3
| spl53_5 ),
inference(avatar_split_clause,[],[f967,f969,f915]) ).
fof(f1108,plain,
! [X0] :
( ~ topological_space(sK49)
| open_subset(interior(sK49,X0),sK49)
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(resolution,[],[f548,f769]) ).
fof(f1109,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK49)))
| open_subset(interior(sK49,X0),sK49) ),
inference(forward_subsumption_resolution,[],[f1108,f770]) ).
fof(f1179,plain,
! [X0,X1] :
( element(sK4(sK49,X0,X1),powerset(the_carrier(sK49)))
| is_a_convergence_point_of_set(sK49,X0,X1)
| ~ in(X1,the_carrier(sK49)) ),
inference(resolution,[],[f890,f779]) ).
fof(f1182,plain,
( ! [X0,X1] :
( element(sK4(sK49,X0,X1),powerset(the_carrier(sK49)))
| is_a_convergence_point_of_set(sK49,X0,X1) )
| ~ spl53_5 ),
inference(forward_subsumption_resolution,[],[f1179,f970]) ).
fof(f1431,plain,
( ! [X0] :
( ~ point_neighbourhood(X0,sK49,sK51)
| is_eventually_in(sK49,sK50,X0)
| empty_carrier(sK50)
| ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) )
| ~ spl53_1 ),
inference(resolution,[],[f800,f815]) ).
fof(f1434,plain,
( ! [X0] :
( ~ point_neighbourhood(X0,sK49,sK51)
| is_eventually_in(sK49,sK50,X0)
| ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) )
| ~ spl53_1 ),
inference(forward_subsumption_resolution,[],[f1431,f775]) ).
fof(f1435,plain,
( ! [X0] :
( ~ point_neighbourhood(X0,sK49,sK51)
| is_eventually_in(sK49,sK50,X0)
| ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) )
| ~ spl53_1 ),
inference(forward_subsumption_resolution,[],[f1434,f774]) ).
fof(f1436,plain,
( ! [X0] :
( ~ point_neighbourhood(X0,sK49,sK51)
| is_eventually_in(sK49,sK50,X0)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) )
| ~ spl53_1 ),
inference(forward_subsumption_resolution,[],[f1435,f773]) ).
fof(f1437,plain,
( ! [X0] :
( ~ point_neighbourhood(X0,sK49,sK51)
| is_eventually_in(sK49,sK50,X0)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) )
| ~ spl53_1 ),
inference(forward_subsumption_resolution,[],[f1436,f772]) ).
fof(f1438,plain,
( ! [X0] :
( ~ point_neighbourhood(X0,sK49,sK51)
| is_eventually_in(sK49,sK50,X0)
| ~ topological_space(sK49)
| ~ top_str(sK49) )
| ~ spl53_1 ),
inference(forward_subsumption_resolution,[],[f1437,f771]) ).
fof(f1439,plain,
( ! [X0] :
( ~ point_neighbourhood(X0,sK49,sK51)
| is_eventually_in(sK49,sK50,X0)
| ~ top_str(sK49) )
| ~ spl53_1 ),
inference(forward_subsumption_resolution,[],[f1438,f770]) ).
fof(f1440,plain,
( ! [X0] :
( ~ point_neighbourhood(X0,sK49,sK51)
| is_eventually_in(sK49,sK50,X0) )
| ~ spl53_1 ),
inference(forward_subsumption_resolution,[],[f1439,f769]) ).
fof(f1459,plain,
( ! [X0] :
( is_eventually_in(sK49,sK50,sK4(sK49,X0,sK51))
| is_a_convergence_point_of_set(sK49,X0,sK51) )
| ~ spl53_1 ),
inference(resolution,[],[f1440,f888]) ).
fof(f1678,plain,
( ! [X0] :
( is_a_convergence_point_of_set(sK49,X0,sK51)
| ~ element(sK4(sK49,X0,sK51),powerset(the_carrier(sK49)))
| empty_carrier(sK50)
| ~ net_str(sK50,sK49)
| in(sK4(sK49,X0,sK51),filter_of_net_str(sK49,sK50)) )
| ~ spl53_1 ),
inference(resolution,[],[f1459,f835]) ).
fof(f1683,plain,
( ! [X0] :
( is_a_convergence_point_of_set(sK49,X0,sK51)
| empty_carrier(sK50)
| ~ net_str(sK50,sK49)
| in(sK4(sK49,X0,sK51),filter_of_net_str(sK49,sK50)) )
| ~ spl53_1
| ~ spl53_5 ),
inference(forward_subsumption_resolution,[],[f1678,f1182]) ).
fof(f1685,plain,
( ! [X0] :
( is_a_convergence_point_of_set(sK49,X0,sK51)
| ~ net_str(sK50,sK49)
| in(sK4(sK49,X0,sK51),filter_of_net_str(sK49,sK50)) )
| ~ spl53_1
| ~ spl53_5 ),
inference(forward_subsumption_resolution,[],[f1683,f775]) ).
fof(f1687,plain,
( ! [X0] :
( in(sK4(sK49,X0,sK51),filter_of_net_str(sK49,sK50))
| is_a_convergence_point_of_set(sK49,X0,sK51) )
| ~ spl53_1
| ~ spl53_5 ),
inference(forward_subsumption_resolution,[],[f1685,f772]) ).
fof(f1695,plain,
( is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51)
| is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| ~ spl53_1
| ~ spl53_5 ),
inference(resolution,[],[f1687,f451]) ).
fof(f1697,plain,
( is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| ~ spl53_1
| ~ spl53_5 ),
inference(duplicate_literal_removal,[],[f1695]) ).
fof(f1698,plain,
( ~ topological_space(sK49)
| ~ top_str(sK49)
| ~ spl53_1
| spl53_2
| ~ spl53_5 ),
inference(forward_subsumption_resolution,[],[f1697,f806]) ).
fof(f1699,plain,
( ~ top_str(sK49)
| ~ spl53_1
| spl53_2
| ~ spl53_5 ),
inference(forward_subsumption_resolution,[],[f1698,f770]) ).
fof(f1700,plain,
( $false
| ~ spl53_1
| spl53_2
| ~ spl53_5 ),
inference(forward_subsumption_resolution,[],[f1699,f769]) ).
fof(f1701,plain,
( ~ spl53_1
| spl53_2
| ~ spl53_5 ),
inference(avatar_contradiction_clause,[],[f1700]) ).
fof(f2114,plain,
! [X0] :
( in(X0,lim_points_of_net(sK49,sK50))
| empty_carrier(sK50)
| ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ element(X0,the_carrier(sK49))
| subset(sK3(sK49,sK50,X0),the_carrier(sK49)) ),
inference(resolution,[],[f902,f772]) ).
fof(f2115,plain,
! [X0] :
( in(X0,lim_points_of_net(sK49,sK50))
| ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ element(X0,the_carrier(sK49))
| subset(sK3(sK49,sK50,X0),the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[],[f2114,f775]) ).
fof(f2116,plain,
! [X0] :
( in(X0,lim_points_of_net(sK49,sK50))
| ~ directed_relstr(sK50)
| ~ element(X0,the_carrier(sK49))
| subset(sK3(sK49,sK50,X0),the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[],[f2115,f774]) ).
fof(f2117,plain,
! [X0] :
( subset(sK3(sK49,sK50,X0),the_carrier(sK49))
| ~ element(X0,the_carrier(sK49))
| in(X0,lim_points_of_net(sK49,sK50)) ),
inference(forward_subsumption_resolution,[],[f2116,f773]) ).
fof(f2118,plain,
! [X0] :
( ~ element(X0,the_carrier(sK49))
| in(X0,lim_points_of_net(sK49,sK50))
| element(sK3(sK49,sK50,X0),powerset(the_carrier(sK49))) ),
inference(resolution,[],[f2117,f784]) ).
fof(f2125,plain,
( in(sK51,lim_points_of_net(sK49,sK50))
| element(sK3(sK49,sK50,sK51),powerset(the_carrier(sK49))) ),
inference(resolution,[],[f2118,f776]) ).
fof(f2126,plain,
( element(sK3(sK49,sK50,sK51),powerset(the_carrier(sK49)))
| spl53_1 ),
inference(forward_subsumption_resolution,[],[f2125,f805]) ).
fof(f2130,plain,
( open_subset(interior(sK49,sK3(sK49,sK50,sK51)),sK49)
| spl53_1 ),
inference(resolution,[],[f2126,f1109]) ).
fof(f2274,plain,
( ! [X0,X1] :
( ~ in(X0,interior(sK49,sK3(sK49,sK50,sK51)))
| ~ element(interior(sK49,sK3(sK49,sK50,sK51)),powerset(the_carrier(sK49)))
| ~ is_a_convergence_point_of_set(sK49,X1,X0)
| in(interior(sK49,sK3(sK49,sK50,sK51)),X1) )
| spl53_1 ),
inference(resolution,[],[f2130,f819]) ).
fof(f2558,definition,
( spl53_96
<=> element(interior(sK49,sK3(sK49,sK50,sK51)),powerset(the_carrier(sK49))) ),
introduced(definition,[new_symbols(definition,[spl53_96])],[avatar_definition]) ).
fof(f2559,plain,
( ~ element(interior(sK49,sK3(sK49,sK50,sK51)),powerset(the_carrier(sK49)))
| spl53_96 ),
inference(avatar_component_clause,[],[f2558]) ).
fof(f2565,definition,
( spl53_98
<=> ! [X0,X1] :
( ~ in(X0,interior(sK49,sK3(sK49,sK50,sK51)))
| in(interior(sK49,sK3(sK49,sK50,sK51)),X1)
| ~ is_a_convergence_point_of_set(sK49,X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl53_98])],[avatar_definition]) ).
fof(f2566,plain,
( ! [X0,X1] :
( ~ is_a_convergence_point_of_set(sK49,X1,X0)
| in(interior(sK49,sK3(sK49,sK50,sK51)),X1)
| ~ in(X0,interior(sK49,sK3(sK49,sK50,sK51))) )
| ~ spl53_98 ),
inference(avatar_component_clause,[],[f2565]) ).
fof(f2567,plain,
( ~ spl53_96
| spl53_98
| spl53_1 ),
inference(avatar_split_clause,[],[f2274,f799,f2565,f2558]) ).
fof(f2660,plain,
( ~ element(sK3(sK49,sK50,sK51),powerset(the_carrier(sK49)))
| spl53_96 ),
inference(resolution,[],[f2559,f947]) ).
fof(f2664,plain,
( $false
| spl53_1
| spl53_96 ),
inference(forward_subsumption_resolution,[],[f2660,f2126]) ).
fof(f2665,plain,
( spl53_1
| spl53_96 ),
inference(avatar_contradiction_clause,[],[f2664]) ).
fof(f2676,definition,
( spl53_111
<=> is_eventually_in(sK49,sK50,interior(sK49,sK3(sK49,sK50,sK51))) ),
introduced(definition,[new_symbols(definition,[spl53_111])],[avatar_definition]) ).
fof(f2677,plain,
( is_eventually_in(sK49,sK50,interior(sK49,sK3(sK49,sK50,sK51)))
| ~ spl53_111 ),
inference(avatar_component_clause,[],[f2676]) ).
fof(f2986,plain,
( in(interior(sK49,sK3(sK49,sK50,sK51)),filter_of_net_str(sK49,sK50))
| ~ in(sK51,interior(sK49,sK3(sK49,sK50,sK51)))
| ~ spl53_2
| ~ spl53_98 ),
inference(resolution,[],[f2566,f803]) ).
fof(f3000,definition,
( spl53_129
<=> in(sK51,interior(sK49,sK3(sK49,sK50,sK51))) ),
introduced(definition,[new_symbols(definition,[spl53_129])],[avatar_definition]) ).
fof(f3001,plain,
( ~ in(sK51,interior(sK49,sK3(sK49,sK50,sK51)))
| spl53_129 ),
inference(avatar_component_clause,[],[f3000]) ).
fof(f3029,plain,
( ~ element(sK3(sK49,sK50,sK51),powerset(the_carrier(sK49)))
| is_eventually_in(sK49,sK50,sK3(sK49,sK50,sK51))
| empty_carrier(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ one_sorted_str(sK49)
| ~ spl53_111 ),
inference(resolution,[],[f2677,f880]) ).
fof(f3032,plain,
( is_eventually_in(sK49,sK50,sK3(sK49,sK50,sK51))
| empty_carrier(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ one_sorted_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3029,f2126]) ).
fof(f3035,plain,
( is_eventually_in(sK49,sK50,sK3(sK49,sK50,sK51))
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ one_sorted_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3032,f775]) ).
fof(f3038,plain,
( is_eventually_in(sK49,sK50,sK3(sK49,sK50,sK51))
| empty_carrier(sK49)
| ~ one_sorted_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3035,f772]) ).
fof(f3041,plain,
( is_eventually_in(sK49,sK50,sK3(sK49,sK50,sK51))
| ~ one_sorted_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3038,f771]) ).
fof(f3044,plain,
( is_eventually_in(sK49,sK50,sK3(sK49,sK50,sK51))
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3041,f820]) ).
fof(f3092,plain,
( in(sK51,lim_points_of_net(sK49,sK50))
| ~ element(sK51,the_carrier(sK49))
| empty_carrier(sK50)
| ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(resolution,[],[f3044,f811]) ).
fof(f3096,plain,
( ~ element(sK51,the_carrier(sK49))
| empty_carrier(sK50)
| ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3092,f805]) ).
fof(f3099,plain,
( empty_carrier(sK50)
| ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3096,f776]) ).
fof(f3102,plain,
( ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3099,f775]) ).
fof(f3105,plain,
( ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3102,f774]) ).
fof(f3107,plain,
( ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3105,f773]) ).
fof(f3109,plain,
( empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3107,f772]) ).
fof(f3110,plain,
( ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3109,f771]) ).
fof(f3111,plain,
( ~ top_str(sK49)
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3110,f770]) ).
fof(f3112,plain,
( $false
| spl53_1
| ~ spl53_111 ),
inference(forward_subsumption_resolution,[],[f3111,f769]) ).
fof(f3113,plain,
( spl53_1
| ~ spl53_111 ),
inference(avatar_contradiction_clause,[],[f3112]) ).
fof(f3122,plain,
( ~ point_neighbourhood(sK3(sK49,sK50,sK51),sK49,sK51)
| spl53_129 ),
inference(resolution,[],[f3001,f852]) ).
fof(f3129,plain,
( in(sK51,lim_points_of_net(sK49,sK50))
| ~ element(sK51,the_carrier(sK49))
| empty_carrier(sK50)
| ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_129 ),
inference(resolution,[],[f3122,f810]) ).
fof(f3131,plain,
( ~ element(sK51,the_carrier(sK49))
| empty_carrier(sK50)
| ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| spl53_129 ),
inference(forward_subsumption_resolution,[],[f3129,f805]) ).
fof(f3132,plain,
( empty_carrier(sK50)
| ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| spl53_129 ),
inference(forward_subsumption_resolution,[],[f3131,f776]) ).
fof(f3133,plain,
( ~ transitive_relstr(sK50)
| ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| spl53_129 ),
inference(forward_subsumption_resolution,[],[f3132,f775]) ).
fof(f3134,plain,
( ~ directed_relstr(sK50)
| ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| spl53_129 ),
inference(forward_subsumption_resolution,[],[f3133,f774]) ).
fof(f3135,plain,
( ~ net_str(sK50,sK49)
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| spl53_129 ),
inference(forward_subsumption_resolution,[],[f3134,f773]) ).
fof(f3136,plain,
( empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| spl53_129 ),
inference(forward_subsumption_resolution,[],[f3135,f772]) ).
fof(f3137,plain,
( ~ topological_space(sK49)
| ~ top_str(sK49)
| spl53_1
| spl53_129 ),
inference(forward_subsumption_resolution,[],[f3136,f771]) ).
fof(f3138,plain,
( ~ top_str(sK49)
| spl53_1
| spl53_129 ),
inference(forward_subsumption_resolution,[],[f3137,f770]) ).
fof(f3139,plain,
( $false
| spl53_1
| spl53_129 ),
inference(forward_subsumption_resolution,[],[f3138,f769]) ).
fof(f3140,plain,
( spl53_1
| spl53_129 ),
inference(avatar_contradiction_clause,[],[f3139]) ).
fof(f3142,definition,
( spl53_140
<=> in(interior(sK49,sK3(sK49,sK50,sK51)),filter_of_net_str(sK49,sK50)) ),
introduced(definition,[new_symbols(definition,[spl53_140])],[avatar_definition]) ).
fof(f3143,plain,
( in(interior(sK49,sK3(sK49,sK50,sK51)),filter_of_net_str(sK49,sK50))
| ~ spl53_140 ),
inference(avatar_component_clause,[],[f3142]) ).
fof(f3144,plain,
( ~ spl53_129
| spl53_140
| ~ spl53_2
| ~ spl53_98 ),
inference(avatar_split_clause,[],[f2986,f2565,f802,f3142,f3000]) ).
fof(f3145,plain,
( is_eventually_in(sK49,sK50,sK13(interior(sK49,sK3(sK49,sK50,sK51)),sK49,sK50))
| ~ spl53_140 ),
inference(resolution,[],[f3143,f845]) ).
fof(f3146,plain,
( interior(sK49,sK3(sK49,sK50,sK51)) = sK13(interior(sK49,sK3(sK49,sK50,sK51)),sK49,sK50)
| ~ spl53_140 ),
inference(resolution,[],[f3143,f842]) ).
fof(f3151,plain,
( is_eventually_in(sK49,sK50,interior(sK49,sK3(sK49,sK50,sK51)))
| ~ spl53_140 ),
inference(forward_demodulation,[],[f3145,f3146]) ).
fof(f3153,plain,
( spl53_111
| ~ spl53_140 ),
inference(avatar_split_clause,[],[f3151,f3142,f2676]) ).
cnf(s1,plain,
( spl53_1
| spl53_2 ),
inference(sat_conversion,[],[f804]) ).
cnf(s2,plain,
( ~ spl53_1
| ~ spl53_2 ),
inference(sat_conversion,[],[f807]) ).
cnf(s5,plain,
~ spl53_3,
inference(sat_conversion,[],[f931]) ).
cnf(s6,plain,
( spl53_3
| spl53_5 ),
inference(sat_conversion,[],[f971]) ).
cnf(s49,plain,
( ~ spl53_1
| spl53_2
| ~ spl53_5 ),
inference(sat_conversion,[],[f1701]) ).
cnf(s105,plain,
( spl53_1
| ~ spl53_96
| spl53_98 ),
inference(sat_conversion,[],[f2567]) ).
cnf(s116,plain,
( spl53_1
| spl53_96 ),
inference(sat_conversion,[],[f2665]) ).
cnf(s162,plain,
( spl53_1
| ~ spl53_111 ),
inference(sat_conversion,[],[f3113]) ).
cnf(s165,plain,
( spl53_1
| spl53_129 ),
inference(sat_conversion,[],[f3140]) ).
cnf(s166,plain,
( ~ spl53_2
| ~ spl53_98
| ~ spl53_129
| spl53_140 ),
inference(sat_conversion,[],[f3144]) ).
cnf(s167,plain,
( spl53_111
| ~ spl53_140 ),
inference(sat_conversion,[],[f3153]) ).
cnf(s174,plain,
spl53_5,
inference(rat,[],[s6,s5]) ).
cnf(s176,plain,
spl53_1,
inference(rat,[],[s166,s105,s167,s1,s116,s162,s165]) ).
cnf(s177,plain,
spl53_2,
inference(rat,[],[s49,s174,s176]) ).
cnf(s178,plain,
$false,
inference(rat,[],[s2,s177,s176]) ).
fof(f3154,plain,
$false,
inference(avatar_sat_refutation,[],[s178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU392+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n018.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 : Mon Sep 28 05:07:10 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 9.74/2.28 % (3003522)Detected formulas, will run a generic FOF schedule.
% 9.74/2.28 % (3003527)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=4285661038:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.74/2.28 % (3003531)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=471865621:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.74/2.28 % (3003529)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=3439137442:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.74/2.28 % (3003528)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=1519966275:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.74/2.28 % (3003530)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3632005714:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.74/2.28 % (3003532)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2563579716:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.74/2.28 % (3003533)dis-21_1_sil=8000:lcm=predicate:random_seed=3708451405: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)
% 9.74/2.28 % (3003530)Refutation not found, incomplete strategy
% 9.74/2.28 % (3003530)------------------------------
% 9.74/2.28 % (3003530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003530)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003530)Termination reason: Refutation not found, incomplete strategy
% 9.74/2.28 % (3003530)Time elapsed: 0.004 s
% 9.74/2.28 % (3003530)Peak memory usage: 89 MB
% 9.74/2.28 % (3003530)Instructions burned: 4 (million)
% 9.74/2.28 % (3003531)Instruction limit reached!
% 9.74/2.28 % (3003531)------------------------------
% 9.74/2.28 % (3003531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003531)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003531)Termination reason: Instruction limit
% 9.74/2.28 % (3003531)Termination phase: Saturation
% 9.74/2.28 % (3003531)Time elapsed: 0.070 s
% 9.74/2.28 % (3003531)Peak memory usage: 89 MB
% 9.74/2.28 % (3003531)Instructions burned: 119 (million)
% 9.74/2.28 % (3003533)Instruction limit reached!
% 9.74/2.28 % (3003533)------------------------------
% 9.74/2.28 % (3003533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003533)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003533)Termination reason: Instruction limit
% 9.74/2.28 % (3003533)Termination phase: Saturation
% 9.74/2.28 % (3003533)Time elapsed: 0.077 s
% 9.74/2.28 % (3003533)Peak memory usage: 93 MB
% 9.74/2.28 % (3003533)Instructions burned: 129 (million)
% 9.74/2.28 % (3003532)Instruction limit reached!
% 9.74/2.28 % (3003532)------------------------------
% 9.74/2.28 % (3003532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003532)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003532)Termination reason: Instruction limit
% 9.74/2.28 % (3003532)Termination phase: Saturation
% 9.74/2.28 % (3003532)Time elapsed: 0.100 s
% 9.74/2.28 % (3003532)Peak memory usage: 90 MB
% 9.74/2.28 % (3003532)Instructions burned: 140 (million)
% 9.74/2.28 % (3003542)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3551056953:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.74/2.28 % (3003541)lrs+10_1_sil=8000:sp=occurrence:random_seed=920419645:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.74/2.28 % (3003542)Refutation not found, incomplete strategy
% 9.74/2.28 % (3003542)------------------------------
% 9.74/2.28 % (3003542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003542)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003542)Termination reason: Refutation not found, incomplete strategy
% 9.74/2.28 % (3003542)Time elapsed: 0.005 s
% 9.74/2.28 % (3003542)Peak memory usage: 89 MB
% 9.74/2.28 % (3003542)Instructions burned: 5 (million)
% 9.74/2.28 % (3003543)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1454319836:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.74/2.28 % (3003530)------------------------------
% 9.74/2.28 % (3003530)------------------------------
% 9.74/2.28 % (3003543)Instruction limit reached!
% 9.74/2.28 % (3003543)------------------------------
% 9.74/2.28 % (3003543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003543)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003543)Termination reason: Instruction limit
% 9.74/2.28 % (3003543)Termination phase: Saturation
% 9.74/2.28 % (3003543)Time elapsed: 0.140 s
% 9.74/2.28 % (3003543)Peak memory usage: 93 MB
% 9.74/2.28 % (3003543)Instructions burned: 327 (million)
% 9.74/2.28 % (3003541)Instruction limit reached!
% 9.74/2.28 % (3003541)------------------------------
% 9.74/2.28 % (3003541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003541)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003541)Termination reason: Instruction limit
% 9.74/2.28 % (3003541)Termination phase: Saturation
% 9.74/2.28 % (3003541)Time elapsed: 0.181 s
% 9.74/2.28 % (3003541)Peak memory usage: 92 MB
% 9.74/2.28 % (3003541)Instructions burned: 287 (million)
% 9.74/2.28 % (3003547)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3143868884:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 9.74/2.28 % (3003542)------------------------------
% 9.74/2.28 % (3003542)------------------------------
% 9.74/2.28 % (3003548)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3846931035:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 9.74/2.28 % (3003548)Refutation not found, incomplete strategy
% 9.74/2.28 % (3003548)------------------------------
% 9.74/2.28 % (3003548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003548)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003548)Termination reason: Refutation not found, incomplete strategy
% 9.74/2.28 % (3003548)Time elapsed: 0.004 s
% 9.74/2.28 % (3003548)Peak memory usage: 89 MB
% 9.74/2.28 % (3003548)Instructions burned: 11 (million)
% 9.74/2.28 % (3003550)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4167707547:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.74/2.28 % (3003547)Instruction limit reached!
% 9.74/2.28 % (3003547)------------------------------
% 9.74/2.28 % (3003547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003547)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003547)Termination reason: Instruction limit
% 9.74/2.28 % (3003547)Termination phase: Saturation
% 9.74/2.28 % (3003547)Time elapsed: 0.155 s
% 9.74/2.28 % (3003547)Peak memory usage: 92 MB
% 9.74/2.28 % (3003547)Instructions burned: 249 (million)
% 9.74/2.28 % (3003551)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3898170483:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 9.74/2.28 % (3003548)------------------------------
% 9.74/2.28 % (3003548)------------------------------
% 9.74/2.28 % (3003551)Instruction limit reached!
% 9.74/2.28 % (3003551)------------------------------
% 9.74/2.28 % (3003551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003551)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003551)Termination reason: Instruction limit
% 9.74/2.28 % (3003551)Termination phase: Saturation
% 9.74/2.28 % (3003551)Time elapsed: 0.076 s
% 9.74/2.28 % (3003551)Peak memory usage: 91 MB
% 9.74/2.28 % (3003551)Instructions burned: 114 (million)
% 9.74/2.28 % (3003554)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1771012856:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 9.74/2.28 % (3003556)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3556086432:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 9.74/2.28 % (3003556)Instruction limit reached!
% 9.74/2.28 % (3003556)------------------------------
% 9.74/2.28 % (3003556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003556)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003556)Termination reason: Instruction limit
% 9.74/2.28 % (3003556)Termination phase: Saturation
% 9.74/2.28 % (3003556)Time elapsed: 0.039 s
% 9.74/2.28 % (3003556)Peak memory usage: 89 MB
% 9.74/2.28 % (3003556)Instructions burned: 114 (million)
% 9.74/2.28 % (3003554)Instruction limit reached!
% 9.74/2.28 % (3003554)------------------------------
% 9.74/2.28 % (3003554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003554)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003554)Termination reason: Instruction limit
% 9.74/2.28 % (3003554)Termination phase: Saturation
% 9.74/2.28 % (3003554)Time elapsed: 0.069 s
% 9.74/2.28 % (3003554)Peak memory usage: 89 MB
% 9.74/2.28 % (3003554)Instructions burned: 128 (million)
% 9.74/2.28 % (3003557)lrs+10_1_sil=8000:sp=occurrence:random_seed=969492210:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 9.74/2.28 % (3003560)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3798574022:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 9.74/2.28 % (3003560)Refutation not found, incomplete strategy
% 9.74/2.28 % (3003560)------------------------------
% 9.74/2.28 % (3003560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003560)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003560)Termination reason: Refutation not found, incomplete strategy
% 9.74/2.28 % (3003560)Time elapsed: 0.005 s
% 9.74/2.28 % (3003560)Peak memory usage: 89 MB
% 9.74/2.28 % (3003560)Instructions burned: 14 (million)
% 9.74/2.28 % (3003561)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2300498443:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 9.74/2.28 % (3003560)------------------------------
% 9.74/2.28 % (3003560)------------------------------
% 9.74/2.28 % (3003528)First to succeed.
% 9.74/2.28 % (3003528)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3003522"
% 9.74/2.28 % (3003565)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2013745683:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 9.74/2.28 % (3003565)Instruction limit reached!
% 9.74/2.28 % (3003565)------------------------------
% 9.74/2.28 % (3003565)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003565)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003565)Termination reason: Instruction limit
% 9.74/2.28 % (3003565)Termination phase: Saturation
% 9.74/2.28 % (3003565)Time elapsed: 0.044 s
% 9.74/2.28 % (3003565)Peak memory usage: 92 MB
% 9.74/2.28 % (3003565)Instructions burned: 138 (million)
% 9.74/2.28 % (3003567)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3932180664:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 9.74/2.28 % (3003567)Refutation not found, incomplete strategy
% 9.74/2.28 % (3003567)------------------------------
% 9.74/2.28 % (3003567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.28 % (3003567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.28 % (3003567)CaDiCaL version: 2.1.3
% 9.74/2.28 % (3003567)Termination reason: Refutation not found, incomplete strategy
% 9.74/2.28 % (3003567)Time elapsed: 0.005 s
% 9.74/2.28 % (3003567)Peak memory usage: 89 MB
% 9.74/2.28 % (3003567)Instructions burned: 14 (million)
% 9.74/2.28 % (3003528)Refutation found. Thanks to Tanya!
% 9.74/2.28 % SZS status Theorem for theBenchmark
% 9.74/2.28 % SZS output start Proof for theBenchmark
% See solution above
% 10.56/2.47 % (3003528)------------------------------
% 10.56/2.47 % (3003528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.47 % (3003528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.47 % (3003528)CaDiCaL version: 2.1.3
% 10.56/2.47 % (3003528)Termination reason: Refutation
% 10.56/2.47 % (3003528)Time elapsed: 0.987 s
% 10.56/2.47 % (3003528)Peak memory usage: 135 MB
% 10.56/2.47 % (3003528)Instructions burned: 1417 (million)
% 10.56/2.47 % (3003528)------------------------------
% 10.56/2.47 % (3003528)------------------------------
% 10.56/2.47 % (3003522)Success in time 1.415 s
% 10.56/2.47 % Vampire exiting
%------------------------------------------------------------------------------