TSTP Solution File: SEU392+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU392+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:06:51 EDT 2023
% Result : Theorem 25.21s 4.23s
% Output : CNFRefutation 25.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 37
% Syntax : Number of formulae : 398 ( 39 unt; 0 def)
% Number of atoms : 2054 ( 98 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 2734 (1078 ~;1232 |; 331 &)
% ( 22 <=>; 68 =>; 0 <=; 3 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 4 con; 0-3 aty)
% Number of variables : 799 ( 16 sgn; 368 !; 58 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( empty(X1)
=> ( closed_subset(X1,X0)
& open_subset(X1,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tops_1) ).
fof(f27,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)))
=> ( 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) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_yellow_6) ).
fof(f28,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(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/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(f29,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_yellow19) ).
fof(f30,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( in(X2,X3)
& open_subset(X3,X0) )
=> in(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_waybel_7) ).
fof(f32,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/sandbox/benchmark/theBenchmark.p',dt_k11_yellow_6) ).
fof(f33,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f41,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f44,axiom,
! [X0,X1] :
( ( element(X1,the_carrier(X0))
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X2] :
( point_neighbourhood(X2,X0,X1)
=> element(X2,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
fof(f58,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& boundary_set(X1,X0)
& top_str(X0) )
=> ( boundary_set(interior(X0,X1),X0)
& v5_membered(interior(X0,X1))
& v4_membered(interior(X0,X1))
& v3_membered(interior(X0,X1))
& v2_membered(interior(X0,X1))
& v1_membered(interior(X0,X1))
& empty(interior(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_tops_1) ).
fof(f72,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f77,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> open_subset(interior(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_tops_1) ).
fof(f83,axiom,
! [X0,X1,X2] :
( ( net_str(X2,X1)
& ~ empty_carrier(X2)
& one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).
fof(f99,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f114,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tops_1) ).
fof(f122,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2] :
( in(X2,filter_of_net_str(X0,X1))
<=> ( element(X2,powerset(the_carrier(X0)))
& is_eventually_in(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_yellow19) ).
fof(f123,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_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_yellow19) ).
fof(f124,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_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) ) ) ) ),
inference(negated_conjecture,[],[f123]) ).
fof(f127,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f128,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',t44_tops_1) ).
fof(f130,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f131,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( in(X2,X1)
& open_subset(X1,X0) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f132,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f133,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f134,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f136,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2,X3] :
( subset(X2,X3)
=> ( ( is_often_in(X0,X1,X2)
=> is_often_in(X0,X1,X3) )
& ( is_eventually_in(X0,X1,X2)
=> is_eventually_in(X0,X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_waybel_0) ).
fof(f186,plain,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& boundary_set(X1,X0)
& top_str(X0) )
=> ( boundary_set(interior(X0,X1),X0)
& v4_membered(interior(X0,X1))
& v3_membered(interior(X0,X1))
& v2_membered(interior(X0,X1))
& v1_membered(interior(X0,X1))
& empty(interior(X0,X1)) ) ),
inference(pure_predicate_removal,[],[f58]) ).
fof(f187,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f114]) ).
fof(f192,plain,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& boundary_set(X1,X0)
& top_str(X0) )
=> ( boundary_set(interior(X0,X1),X0)
& v3_membered(interior(X0,X1))
& v2_membered(interior(X0,X1))
& v1_membered(interior(X0,X1))
& empty(interior(X0,X1)) ) ),
inference(pure_predicate_removal,[],[f186]) ).
fof(f193,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f187]) ).
fof(f195,plain,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& boundary_set(X1,X0)
& top_str(X0) )
=> ( boundary_set(interior(X0,X1),X0)
& v2_membered(interior(X0,X1))
& v1_membered(interior(X0,X1))
& empty(interior(X0,X1)) ) ),
inference(pure_predicate_removal,[],[f192]) ).
fof(f196,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f193]) ).
fof(f200,plain,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& boundary_set(X1,X0)
& top_str(X0) )
=> ( boundary_set(interior(X0,X1),X0)
& v1_membered(interior(X0,X1))
& empty(interior(X0,X1)) ) ),
inference(pure_predicate_removal,[],[f195]) ).
fof(f201,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f196]) ).
fof(f204,plain,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& boundary_set(X1,X0)
& top_str(X0) )
=> ( boundary_set(interior(X0,X1),X0)
& empty(interior(X0,X1)) ) ),
inference(pure_predicate_removal,[],[f200]) ).
fof(f205,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f201]) ).
fof(f208,plain,
empty(empty_set),
inference(pure_predicate_removal,[],[f72]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
& open_subset(X1,X0) )
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f232,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
& open_subset(X1,X0) )
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f231]) ).
fof(f260,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( lim_points_of_net(X0,X1) = X2
<=> ! [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))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f261,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( lim_points_of_net(X0,X1) = X2
<=> ! [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))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f260]) ).
fof(f262,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)) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f263,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)) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f262]) ).
fof(f264,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f265,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f264]) ).
fof(f266,plain,
! [X0] :
( ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( in(X3,X1)
| ~ in(X2,X3)
| ~ open_subset(X3,X0)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f267,plain,
! [X0] :
( ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( in(X3,X1)
| ~ in(X2,X3)
| ~ open_subset(X3,X0)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f266]) ).
fof(f269,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f270,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f269]) ).
fof(f271,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f272,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(flattening,[],[f271]) ).
fof(f277,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f279,plain,
! [X0,X1] :
( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1) )
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f280,plain,
! [X0,X1] :
( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1) )
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f279]) ).
fof(f286,plain,
! [X0,X1] :
( ( boundary_set(interior(X0,X1),X0)
& empty(interior(X0,X1)) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ boundary_set(X1,X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f204]) ).
fof(f287,plain,
! [X0,X1] :
( ( boundary_set(interior(X0,X1),X0)
& empty(interior(X0,X1)) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ boundary_set(X1,X0)
| ~ top_str(X0) ),
inference(flattening,[],[f286]) ).
fof(f315,plain,
! [X0,X1] :
( open_subset(interior(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f316,plain,
! [X0,X1] :
( open_subset(interior(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f315]) ).
fof(f319,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(ennf_transformation,[],[f83]) ).
fof(f320,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(flattening,[],[f319]) ).
fof(f344,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f205]) ).
fof(f345,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f344]) ).
fof(f355,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,filter_of_net_str(X0,X1))
<=> ( element(X2,powerset(the_carrier(X0)))
& is_eventually_in(X0,X1,X2) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f122]) ).
fof(f356,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,filter_of_net_str(X0,X1))
<=> ( element(X2,powerset(the_carrier(X0)))
& is_eventually_in(X0,X1,X2) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f355]) ).
fof(f357,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)) )
& net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f124]) ).
fof(f358,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)) )
& net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f357]) ).
fof(f362,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f127]) ).
fof(f363,plain,
! [X0] :
( ! [X1] :
( subset(interior(X0,X1),X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f129]) ).
fof(f364,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f130]) ).
fof(f365,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f364]) ).
fof(f366,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( point_neighbourhood(X1,X0,X2)
| ~ in(X2,X1)
| ~ open_subset(X1,X0)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f131]) ).
fof(f367,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( point_neighbourhood(X1,X0,X2)
| ~ in(X2,X1)
| ~ open_subset(X1,X0)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f366]) ).
fof(f368,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f132]) ).
fof(f369,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f133]) ).
fof(f370,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f134]) ).
fof(f372,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( ( ( is_often_in(X0,X1,X3)
| ~ is_often_in(X0,X1,X2) )
& ( is_eventually_in(X0,X1,X3)
| ~ is_eventually_in(X0,X1,X2) ) )
| ~ subset(X2,X3) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f136]) ).
fof(f373,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( ( ( is_often_in(X0,X1,X3)
| ~ is_often_in(X0,X1,X2) )
& ( is_eventually_in(X0,X1,X3)
| ~ is_eventually_in(X0,X1,X2) ) )
| ~ subset(X2,X3) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f372]) ).
fof(f379,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( lim_points_of_net(X0,X1) = X2
| ? [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))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f261]) ).
fof(f380,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( lim_points_of_net(X0,X1) = X2
| ? [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))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f379]) ).
fof(f381,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( lim_points_of_net(X0,X1) = X2
| ? [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))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(rectify,[],[f380]) ).
fof(f382,plain,
! [X0,X1,X2] :
( ? [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)) )
=> ( ( ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,sK2(X0,X1,X2)) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( ! [X5] :
( is_eventually_in(X0,X1,X5)
| ~ point_neighbourhood(X5,X0,sK2(X0,X1,X2)) )
| in(sK2(X0,X1,X2),X2) )
& element(sK2(X0,X1,X2),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f383,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,sK2(X0,X1,X2)) )
=> ( ~ is_eventually_in(X0,X1,sK3(X0,X1,X2))
& point_neighbourhood(sK3(X0,X1,X2),X0,sK2(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f384,plain,
! [X0,X1,X6] :
( ? [X7] :
( ~ is_eventually_in(X0,X1,X7)
& point_neighbourhood(X7,X0,X6) )
=> ( ~ is_eventually_in(X0,X1,sK4(X0,X1,X6))
& point_neighbourhood(sK4(X0,X1,X6),X0,X6) ) ),
introduced(choice_axiom,[]) ).
fof(f385,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( lim_points_of_net(X0,X1) = X2
| ( ( ( ~ is_eventually_in(X0,X1,sK3(X0,X1,X2))
& point_neighbourhood(sK3(X0,X1,X2),X0,sK2(X0,X1,X2)) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( ! [X5] :
( is_eventually_in(X0,X1,X5)
| ~ point_neighbourhood(X5,X0,sK2(X0,X1,X2)) )
| in(sK2(X0,X1,X2),X2) )
& element(sK2(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ( ~ is_eventually_in(X0,X1,sK4(X0,X1,X6))
& point_neighbourhood(sK4(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))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f381,f384,f383,f382]) ).
fof(f386,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)) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f263]) ).
fof(f387,plain,
! [X0] :
( ! [X1,X2] :
( ( is_a_convergence_point_of_set(X0,X1,X2)
| ? [X3] :
( ~ in(X3,X1)
& in(X2,X3)
& open_subset(X3,X0)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X2,X3)
| ~ open_subset(X3,X0)
| ~ element(X3,powerset(the_carrier(X0))) )
| ~ is_a_convergence_point_of_set(X0,X1,X2) ) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(nnf_transformation,[],[f267]) ).
fof(f388,plain,
! [X0] :
( ! [X1,X2] :
( ( is_a_convergence_point_of_set(X0,X1,X2)
| ? [X3] :
( ~ in(X3,X1)
& in(X2,X3)
& open_subset(X3,X0)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X4,X1)
| ~ in(X2,X4)
| ~ open_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ is_a_convergence_point_of_set(X0,X1,X2) ) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(rectify,[],[f387]) ).
fof(f389,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ in(X3,X1)
& in(X2,X3)
& open_subset(X3,X0)
& element(X3,powerset(the_carrier(X0))) )
=> ( ~ in(sK5(X0,X1,X2),X1)
& in(X2,sK5(X0,X1,X2))
& open_subset(sK5(X0,X1,X2),X0)
& element(sK5(X0,X1,X2),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f390,plain,
! [X0] :
( ! [X1,X2] :
( ( is_a_convergence_point_of_set(X0,X1,X2)
| ( ~ in(sK5(X0,X1,X2),X1)
& in(X2,sK5(X0,X1,X2))
& open_subset(sK5(X0,X1,X2),X0)
& element(sK5(X0,X1,X2),powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X4,X1)
| ~ in(X2,X4)
| ~ open_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ is_a_convergence_point_of_set(X0,X1,X2) ) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f388,f389]) ).
fof(f408,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ is_eventually_in(X1,X2,X3)
| X0 != X3
| ~ element(X3,powerset(the_carrier(X1))) ) )
& ( ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(nnf_transformation,[],[f320]) ).
fof(f409,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ is_eventually_in(X1,X2,X3)
| X0 != X3
| ~ element(X3,powerset(the_carrier(X1))) ) )
& ( ? [X4] :
( is_eventually_in(X1,X2,X4)
& X0 = X4
& element(X4,powerset(the_carrier(X1))) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(rectify,[],[f408]) ).
fof(f410,plain,
! [X0,X1,X2] :
( ? [X4] :
( is_eventually_in(X1,X2,X4)
& X0 = X4
& element(X4,powerset(the_carrier(X1))) )
=> ( is_eventually_in(X1,X2,sK14(X0,X1,X2))
& sK14(X0,X1,X2) = X0
& element(sK14(X0,X1,X2),powerset(the_carrier(X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f411,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ is_eventually_in(X1,X2,X3)
| X0 != X3
| ~ element(X3,powerset(the_carrier(X1))) ) )
& ( ( is_eventually_in(X1,X2,sK14(X0,X1,X2))
& sK14(X0,X1,X2) = X0
& element(sK14(X0,X1,X2),powerset(the_carrier(X1))) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f409,f410]) ).
fof(f440,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK29(X0))
& element(sK29(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f441,plain,
! [X0] :
( empty(sK29(X0))
& element(sK29(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f99,f440]) ).
fof(f468,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( nowhere_dense(sK43(X0),X0)
& boundary_set(sK43(X0),X0)
& closed_subset(sK43(X0),X0)
& open_subset(sK43(X0),X0)
& empty(sK43(X0))
& element(sK43(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f469,plain,
! [X0] :
( ( nowhere_dense(sK43(X0),X0)
& boundary_set(sK43(X0),X0)
& closed_subset(sK43(X0),X0)
& open_subset(sK43(X0),X0)
& empty(sK43(X0))
& element(sK43(X0),powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f345,f468]) ).
fof(f481,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,filter_of_net_str(X0,X1))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ is_eventually_in(X0,X1,X2) )
& ( ( element(X2,powerset(the_carrier(X0)))
& is_eventually_in(X0,X1,X2) )
| ~ in(X2,filter_of_net_str(X0,X1)) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f356]) ).
fof(f482,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,filter_of_net_str(X0,X1))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ is_eventually_in(X0,X1,X2) )
& ( ( element(X2,powerset(the_carrier(X0)))
& is_eventually_in(X0,X1,X2) )
| ~ in(X2,filter_of_net_str(X0,X1)) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f481]) ).
fof(f483,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)) )
& net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(nnf_transformation,[],[f358]) ).
fof(f484,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)) )
& net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f483]) ).
fof(f485,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)) )
& net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,X1),X2)
| ~ in(X2,lim_points_of_net(sK49,X1)) )
& ( is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,X1),X2)
| in(X2,lim_points_of_net(sK49,X1)) )
& element(X2,the_carrier(sK49)) )
& net_str(X1,sK49)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
& top_str(sK49)
& topological_space(sK49)
& ~ empty_carrier(sK49) ) ),
introduced(choice_axiom,[]) ).
fof(f486,plain,
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,X1),X2)
| ~ in(X2,lim_points_of_net(sK49,X1)) )
& ( is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,X1),X2)
| in(X2,lim_points_of_net(sK49,X1)) )
& element(X2,the_carrier(sK49)) )
& net_str(X1,sK49)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),X2)
| ~ in(X2,lim_points_of_net(sK49,sK50)) )
& ( is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),X2)
| in(X2,lim_points_of_net(sK49,sK50)) )
& element(X2,the_carrier(sK49)) )
& net_str(sK50,sK49)
& directed_relstr(sK50)
& transitive_relstr(sK50)
& ~ empty_carrier(sK50) ) ),
introduced(choice_axiom,[]) ).
fof(f487,plain,
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),X2)
| ~ in(X2,lim_points_of_net(sK49,sK50)) )
& ( is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),X2)
| in(X2,lim_points_of_net(sK49,sK50)) )
& element(X2,the_carrier(sK49)) )
=> ( ( ~ 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)) ) ),
introduced(choice_axiom,[]) ).
fof(f488,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))
& net_str(sK50,sK49)
& directed_relstr(sK50)
& transitive_relstr(sK50)
& ~ empty_carrier(sK50)
& top_str(sK49)
& topological_space(sK49)
& ~ empty_carrier(sK49) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50,sK51])],[f484,f487,f486,f485]) ).
fof(f489,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f362]) ).
fof(f490,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK52(X0,X1),X1)
| ~ in(sK52(X0,X1),X0) )
& ( in(sK52(X0,X1),X1)
| in(sK52(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f491,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK52(X0,X1),X1)
| ~ in(sK52(X0,X1),X0) )
& ( in(sK52(X0,X1),X1)
| in(sK52(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f489,f490]) ).
fof(f492,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f128]) ).
fof(f524,plain,
! [X0,X1] :
( open_subset(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f557,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)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f385]) ).
fof(f558,plain,
! [X2,X0,X1,X6] :
( in(X6,X2)
| point_neighbourhood(sK4(X0,X1,X6),X0,X6)
| ~ element(X6,the_carrier(X0))
| lim_points_of_net(X0,X1) != X2
| ~ element(X2,powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f385]) ).
fof(f559,plain,
! [X2,X0,X1,X6] :
( in(X6,X2)
| ~ is_eventually_in(X0,X1,sK4(X0,X1,X6))
| ~ element(X6,the_carrier(X0))
| lim_points_of_net(X0,X1) != X2
| ~ element(X2,powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f385]) ).
fof(f564,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))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f386]) ).
fof(f565,plain,
! [X2,X0,X1] :
( point_neighbourhood(X2,X0,X1)
| ~ in(X1,interior(X0,X2))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f386]) ).
fof(f566,plain,
! [X0,X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f567,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X2,X4)
| ~ open_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f390]) ).
fof(f568,plain,
! [X2,X0,X1] :
( is_a_convergence_point_of_set(X0,X1,X2)
| element(sK5(X0,X1,X2),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f390]) ).
fof(f569,plain,
! [X2,X0,X1] :
( is_a_convergence_point_of_set(X0,X1,X2)
| open_subset(sK5(X0,X1,X2),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f390]) ).
fof(f570,plain,
! [X2,X0,X1] :
( is_a_convergence_point_of_set(X0,X1,X2)
| in(X2,sK5(X0,X1,X2))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f390]) ).
fof(f571,plain,
! [X2,X0,X1] :
( is_a_convergence_point_of_set(X0,X1,X2)
| ~ in(sK5(X0,X1,X2),X1)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f390]) ).
fof(f574,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f575,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f272]) ).
fof(f581,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f583,plain,
! [X2,X0,X1] :
( element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f594,plain,
! [X0,X1] :
( empty(interior(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ boundary_set(X1,X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f635,plain,
empty(empty_set),
inference(cnf_transformation,[],[f208]) ).
fof(f640,plain,
! [X0,X1] :
( open_subset(interior(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f673,plain,
! [X2,X0,X1] :
( element(sK14(X0,X1,X2),powerset(the_carrier(X1)))
| ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f411]) ).
fof(f674,plain,
! [X2,X0,X1] :
( sK14(X0,X1,X2) = X0
| ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f411]) ).
fof(f749,plain,
! [X0] : element(sK29(X0),powerset(X0)),
inference(cnf_transformation,[],[f441]) ).
fof(f750,plain,
! [X0] : empty(sK29(X0)),
inference(cnf_transformation,[],[f441]) ).
fof(f798,plain,
! [X0] :
( element(sK43(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f469]) ).
fof(f799,plain,
! [X0] :
( empty(sK43(X0))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f469]) ).
fof(f800,plain,
! [X0] :
( open_subset(sK43(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f469]) ).
fof(f802,plain,
! [X0] :
( boundary_set(sK43(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f469]) ).
fof(f817,plain,
! [X2,X0,X1] :
( is_eventually_in(X0,X1,X2)
| ~ in(X2,filter_of_net_str(X0,X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f482]) ).
fof(f819,plain,
! [X2,X0,X1] :
( in(X2,filter_of_net_str(X0,X1))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f482]) ).
fof(f820,plain,
~ empty_carrier(sK49),
inference(cnf_transformation,[],[f488]) ).
fof(f821,plain,
topological_space(sK49),
inference(cnf_transformation,[],[f488]) ).
fof(f822,plain,
top_str(sK49),
inference(cnf_transformation,[],[f488]) ).
fof(f823,plain,
~ empty_carrier(sK50),
inference(cnf_transformation,[],[f488]) ).
fof(f824,plain,
transitive_relstr(sK50),
inference(cnf_transformation,[],[f488]) ).
fof(f825,plain,
directed_relstr(sK50),
inference(cnf_transformation,[],[f488]) ).
fof(f826,plain,
net_str(sK50,sK49),
inference(cnf_transformation,[],[f488]) ).
fof(f827,plain,
element(sK51,the_carrier(sK49)),
inference(cnf_transformation,[],[f488]) ).
fof(f828,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,[],[f488]) ).
fof(f829,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,[],[f488]) ).
fof(f832,plain,
! [X0,X1] :
( X0 = X1
| in(sK52(X0,X1),X1)
| in(sK52(X0,X1),X0) ),
inference(cnf_transformation,[],[f491]) ).
fof(f834,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f492]) ).
fof(f835,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f492]) ).
fof(f836,plain,
! [X0,X1] :
( subset(interior(X0,X1),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f837,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f365]) ).
fof(f838,plain,
! [X2,X0,X1] :
( point_neighbourhood(X1,X0,X2)
| ~ in(X2,X1)
| ~ open_subset(X1,X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f839,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f368]) ).
fof(f840,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f841,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f370]) ).
fof(f843,plain,
! [X2,X3,X0,X1] :
( is_eventually_in(X0,X1,X3)
| ~ is_eventually_in(X0,X1,X2)
| ~ subset(X2,X3)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f845,plain,
! [X0,X1,X6] :
( in(X6,lim_points_of_net(X0,X1))
| ~ is_eventually_in(X0,X1,sK4(X0,X1,X6))
| ~ element(X6,the_carrier(X0))
| ~ element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(equality_resolution,[],[f559]) ).
fof(f846,plain,
! [X0,X1,X6] :
( in(X6,lim_points_of_net(X0,X1))
| point_neighbourhood(sK4(X0,X1,X6),X0,X6)
| ~ element(X6,the_carrier(X0))
| ~ element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(equality_resolution,[],[f558]) ).
fof(f847,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)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(equality_resolution,[],[f557]) ).
cnf(c_70,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ empty(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| open_subset(X0,X1) ),
inference(cnf_transformation,[],[f524]) ).
cnf(c_95,plain,
( ~ is_eventually_in(X0,X1,sK4(X0,X1,X2))
| ~ element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ transitive_relstr(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ directed_relstr(X1)
| in(X2,lim_points_of_net(X0,X1))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f845]) ).
cnf(c_96,plain,
( ~ element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ transitive_relstr(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ directed_relstr(X1)
| point_neighbourhood(sK4(X0,X1,X2),X0,X2)
| in(X2,lim_points_of_net(X0,X1))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f846]) ).
cnf(c_97,plain,
( ~ element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ in(X2,lim_points_of_net(X0,X1))
| ~ point_neighbourhood(X3,X0,X2)
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ transitive_relstr(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ directed_relstr(X1)
| is_eventually_in(X0,X1,X3)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f847]) ).
cnf(c_98,plain,
( ~ in(X0,interior(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| point_neighbourhood(X2,X1,X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f565]) ).
cnf(c_99,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ point_neighbourhood(X0,X1,X2)
| ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X2,interior(X1,X0))
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f564]) ).
cnf(c_100,plain,
( ~ net_str(X0,X1)
| ~ one_sorted_str(X1)
| filter_of_net_str(X1,X0) = a_2_1_yellow19(X1,X0)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f566]) ).
cnf(c_101,plain,
( ~ in(sK5(X0,X1,X2),X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| is_a_convergence_point_of_set(X0,X1,X2) ),
inference(cnf_transformation,[],[f571]) ).
cnf(c_102,plain,
( ~ top_str(X0)
| ~ topological_space(X0)
| in(X1,sK5(X0,X2,X1))
| is_a_convergence_point_of_set(X0,X2,X1) ),
inference(cnf_transformation,[],[f570]) ).
cnf(c_103,plain,
( ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(sK5(X0,X1,X2),X0)
| is_a_convergence_point_of_set(X0,X1,X2) ),
inference(cnf_transformation,[],[f569]) ).
cnf(c_104,plain,
( ~ top_str(X0)
| ~ topological_space(X0)
| element(sK5(X0,X1,X2),powerset(the_carrier(X0)))
| is_a_convergence_point_of_set(X0,X1,X2) ),
inference(cnf_transformation,[],[f568]) ).
cnf(c_105,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ is_a_convergence_point_of_set(X1,X2,X3)
| ~ in(X3,X0)
| ~ open_subset(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X0,X2) ),
inference(cnf_transformation,[],[f567]) ).
cnf(c_108,plain,
( ~ net_str(X0,X1)
| ~ transitive_relstr(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ directed_relstr(X0)
| element(lim_points_of_net(X1,X0),powerset(the_carrier(X1)))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f574]) ).
cnf(c_109,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| element(interior(X1,X0),powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f575]) ).
cnf(c_115,plain,
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f581]) ).
cnf(c_117,plain,
( ~ point_neighbourhood(X0,X1,X2)
| ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(X0,powerset(the_carrier(X1)))
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f583]) ).
cnf(c_129,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ boundary_set(X0,X1)
| ~ top_str(X1)
| empty(interior(X1,X0)) ),
inference(cnf_transformation,[],[f594]) ).
cnf(c_169,plain,
empty(empty_set),
inference(cnf_transformation,[],[f635]) ).
cnf(c_174,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| open_subset(interior(X1,X0),X1) ),
inference(cnf_transformation,[],[f640]) ).
cnf(c_209,plain,
( ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| sK14(X0,X1,X2) = X0
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(cnf_transformation,[],[f674]) ).
cnf(c_210,plain,
( ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| element(sK14(X0,X1,X2),powerset(the_carrier(X1)))
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(cnf_transformation,[],[f673]) ).
cnf(c_283,plain,
empty(sK29(X0)),
inference(cnf_transformation,[],[f750]) ).
cnf(c_284,plain,
element(sK29(X0),powerset(X0)),
inference(cnf_transformation,[],[f749]) ).
cnf(c_333,plain,
( ~ top_str(X0)
| ~ topological_space(X0)
| boundary_set(sK43(X0),X0) ),
inference(cnf_transformation,[],[f802]) ).
cnf(c_335,plain,
( ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(sK43(X0),X0) ),
inference(cnf_transformation,[],[f800]) ).
cnf(c_336,plain,
( ~ top_str(X0)
| ~ topological_space(X0)
| empty(sK43(X0)) ),
inference(cnf_transformation,[],[f799]) ).
cnf(c_337,plain,
( ~ top_str(X0)
| ~ topological_space(X0)
| element(sK43(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f798]) ).
cnf(c_351,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ is_eventually_in(X1,X2,X0)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| in(X0,filter_of_net_str(X1,X2))
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(cnf_transformation,[],[f819]) ).
cnf(c_353,plain,
( ~ in(X0,filter_of_net_str(X1,X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| is_eventually_in(X1,X2,X0)
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(cnf_transformation,[],[f817]) ).
cnf(c_354,negated_conjecture,
( ~ 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,[],[f829]) ).
cnf(c_355,negated_conjecture,
( 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,[],[f828]) ).
cnf(c_356,negated_conjecture,
element(sK51,the_carrier(sK49)),
inference(cnf_transformation,[],[f827]) ).
cnf(c_357,negated_conjecture,
net_str(sK50,sK49),
inference(cnf_transformation,[],[f826]) ).
cnf(c_358,negated_conjecture,
directed_relstr(sK50),
inference(cnf_transformation,[],[f825]) ).
cnf(c_359,negated_conjecture,
transitive_relstr(sK50),
inference(cnf_transformation,[],[f824]) ).
cnf(c_360,negated_conjecture,
~ empty_carrier(sK50),
inference(cnf_transformation,[],[f823]) ).
cnf(c_361,negated_conjecture,
top_str(sK49),
inference(cnf_transformation,[],[f822]) ).
cnf(c_362,negated_conjecture,
topological_space(sK49),
inference(cnf_transformation,[],[f821]) ).
cnf(c_363,negated_conjecture,
~ empty_carrier(sK49),
inference(cnf_transformation,[],[f820]) ).
cnf(c_367,plain,
( X0 = X1
| in(sK52(X0,X1),X0)
| in(sK52(X0,X1),X1) ),
inference(cnf_transformation,[],[f832]) ).
cnf(c_368,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f835]) ).
cnf(c_369,plain,
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f834]) ).
cnf(c_370,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| subset(interior(X1,X0),X0) ),
inference(cnf_transformation,[],[f836]) ).
cnf(c_371,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[],[f837]) ).
cnf(c_372,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ element(X2,the_carrier(X1))
| ~ in(X2,X0)
| ~ open_subset(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| point_neighbourhood(X0,X1,X2)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f838]) ).
cnf(c_373,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f839]) ).
cnf(c_374,plain,
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[],[f840]) ).
cnf(c_375,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f841]) ).
cnf(c_378,plain,
( ~ is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| ~ subset(X2,X3)
| ~ one_sorted_str(X0)
| is_eventually_in(X0,X1,X3)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f843]) ).
cnf(c_567,plain,
( ~ point_neighbourhood(X0,X1,X2)
| ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X2,interior(X1,X0))
| empty_carrier(X1) ),
inference(global_subsumption_just,[status(thm)],[c_99,c_117,c_99]) ).
cnf(c_570,plain,
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_369]) ).
cnf(c_571,plain,
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_570]) ).
cnf(c_572,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_368]) ).
cnf(c_578,plain,
( ~ in(sK51,lim_points_of_net(sK49,sK50))
| ~ is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51) ),
inference(prop_impl_just,[status(thm)],[c_354]) ).
cnf(c_579,plain,
( ~ is_a_convergence_point_of_set(sK49,filter_of_net_str(sK49,sK50),sK51)
| ~ in(sK51,lim_points_of_net(sK49,sK50)) ),
inference(renaming,[status(thm)],[c_578]) ).
cnf(c_658,plain,
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_115]) ).
cnf(c_1090,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| element(X0,X2) ),
inference(bin_hyper_res,[status(thm)],[c_371,c_572]) ).
cnf(c_1091,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| ~ empty(X2) ),
inference(bin_hyper_res,[status(thm)],[c_373,c_572]) ).
cnf(c_2456,plain,
( ~ in(X0,lim_points_of_net(X1,X2))
| ~ point_neighbourhood(X3,X1,X0)
| ~ element(X0,the_carrier(X1))
| ~ net_str(X2,X1)
| ~ transitive_relstr(X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ directed_relstr(X2)
| is_eventually_in(X1,X2,X3)
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_97,c_108]) ).
cnf(c_2457,plain,
( ~ element(X0,the_carrier(X1))
| ~ net_str(X2,X1)
| ~ transitive_relstr(X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ directed_relstr(X2)
| point_neighbourhood(sK4(X1,X2,X0),X1,X0)
| in(X0,lim_points_of_net(X1,X2))
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_96,c_108]) ).
cnf(c_2458,plain,
( ~ is_eventually_in(X0,X1,sK4(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ transitive_relstr(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ directed_relstr(X1)
| in(X2,lim_points_of_net(X0,X1))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_95,c_108]) ).
cnf(c_4444,plain,
( X0 != X1
| X2 != X3
| ~ element(X0,powerset(X2))
| ~ in(X4,X1)
| element(X4,X3) ),
inference(resolution_lifted,[status(thm)],[c_571,c_1090]) ).
cnf(c_4445,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(unflattening,[status(thm)],[c_4444]) ).
cnf(c_4515,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X2,X0)
| ~ open_subset(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| point_neighbourhood(X0,X1,X2)
| empty_carrier(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_372,c_4445]) ).
cnf(c_4616,plain,
( filter_of_net_str(sK49,sK50) != X1
| X0 != sK49
| X2 != sK51
| ~ in(sK51,lim_points_of_net(sK49,sK50))
| ~ top_str(X0)
| ~ topological_space(X0)
| element(sK5(X0,X1,X2),powerset(the_carrier(X0))) ),
inference(resolution_lifted,[status(thm)],[c_104,c_579]) ).
cnf(c_4617,plain,
( ~ in(sK51,lim_points_of_net(sK49,sK50))
| ~ top_str(sK49)
| ~ topological_space(sK49)
| element(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),powerset(the_carrier(sK49))) ),
inference(unflattening,[status(thm)],[c_4616]) ).
cnf(c_4618,plain,
( ~ in(sK51,lim_points_of_net(sK49,sK50))
| element(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),powerset(the_carrier(sK49))) ),
inference(global_subsumption_just,[status(thm)],[c_4617,c_362,c_361,c_4617]) ).
cnf(c_4626,plain,
( filter_of_net_str(sK49,sK50) != X1
| X0 != sK49
| X2 != sK51
| ~ in(sK51,lim_points_of_net(sK49,sK50))
| ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(sK5(X0,X1,X2),X0) ),
inference(resolution_lifted,[status(thm)],[c_103,c_579]) ).
cnf(c_4627,plain,
( ~ in(sK51,lim_points_of_net(sK49,sK50))
| ~ top_str(sK49)
| ~ topological_space(sK49)
| open_subset(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),sK49) ),
inference(unflattening,[status(thm)],[c_4626]) ).
cnf(c_4628,plain,
( ~ in(sK51,lim_points_of_net(sK49,sK50))
| open_subset(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),sK49) ),
inference(global_subsumption_just,[status(thm)],[c_4627,c_362,c_361,c_4627]) ).
cnf(c_4636,plain,
( filter_of_net_str(sK49,sK50) != X1
| X0 != sK49
| X2 != sK51
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK51,lim_points_of_net(sK49,sK50))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution_lifted,[status(thm)],[c_101,c_579]) ).
cnf(c_4637,plain,
( ~ in(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),filter_of_net_str(sK49,sK50))
| ~ in(sK51,lim_points_of_net(sK49,sK50))
| ~ top_str(sK49)
| ~ topological_space(sK49) ),
inference(unflattening,[status(thm)],[c_4636]) ).
cnf(c_4638,plain,
( ~ in(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),filter_of_net_str(sK49,sK50))
| ~ in(sK51,lim_points_of_net(sK49,sK50)) ),
inference(global_subsumption_just,[status(thm)],[c_4637,c_362,c_361,c_4637]) ).
cnf(c_4669,plain,
( filter_of_net_str(sK49,sK50) != X2
| X0 != sK49
| X1 != sK51
| ~ in(sK51,lim_points_of_net(sK49,sK50))
| ~ top_str(X0)
| ~ topological_space(X0)
| in(X1,sK5(X0,X2,X1)) ),
inference(resolution_lifted,[status(thm)],[c_102,c_579]) ).
cnf(c_4670,plain,
( ~ in(sK51,lim_points_of_net(sK49,sK50))
| ~ top_str(sK49)
| ~ topological_space(sK49)
| in(sK51,sK5(sK49,filter_of_net_str(sK49,sK50),sK51)) ),
inference(unflattening,[status(thm)],[c_4669]) ).
cnf(c_4671,plain,
( ~ in(sK51,lim_points_of_net(sK49,sK50))
| in(sK51,sK5(sK49,filter_of_net_str(sK49,sK50),sK51)) ),
inference(global_subsumption_just,[status(thm)],[c_4670,c_362,c_361,c_4670]) ).
cnf(c_5671,plain,
( X0 != sK49
| ~ is_eventually_in(X0,X1,sK4(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ transitive_relstr(X1)
| ~ top_str(X0)
| ~ directed_relstr(X1)
| in(X2,lim_points_of_net(X0,X1))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_2458,c_362]) ).
cnf(c_5672,plain,
( ~ is_eventually_in(sK49,X0,sK4(sK49,X0,X1))
| ~ element(X1,the_carrier(sK49))
| ~ net_str(X0,sK49)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| ~ top_str(sK49)
| in(X1,lim_points_of_net(sK49,X0))
| empty_carrier(X0)
| empty_carrier(sK49) ),
inference(unflattening,[status(thm)],[c_5671]) ).
cnf(c_5674,plain,
( empty_carrier(X0)
| in(X1,lim_points_of_net(sK49,X0))
| ~ is_eventually_in(sK49,X0,sK4(sK49,X0,X1))
| ~ element(X1,the_carrier(sK49))
| ~ net_str(X0,sK49)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0) ),
inference(global_subsumption_just,[status(thm)],[c_5672,c_361,c_363,c_5672]) ).
cnf(c_5675,plain,
( ~ is_eventually_in(sK49,X0,sK4(sK49,X0,X1))
| ~ element(X1,the_carrier(sK49))
| ~ net_str(X0,sK49)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| in(X1,lim_points_of_net(sK49,X0))
| empty_carrier(X0) ),
inference(renaming,[status(thm)],[c_5674]) ).
cnf(c_5719,plain,
( X0 != sK49
| ~ top_str(X0)
| element(sK43(X0),powerset(the_carrier(X0))) ),
inference(resolution_lifted,[status(thm)],[c_337,c_362]) ).
cnf(c_5720,plain,
( ~ top_str(sK49)
| element(sK43(sK49),powerset(the_carrier(sK49))) ),
inference(unflattening,[status(thm)],[c_5719]) ).
cnf(c_5721,plain,
element(sK43(sK49),powerset(the_carrier(sK49))),
inference(global_subsumption_just,[status(thm)],[c_5720,c_361,c_5720]) ).
cnf(c_5726,plain,
( X0 != sK49
| ~ top_str(X0)
| empty(sK43(X0)) ),
inference(resolution_lifted,[status(thm)],[c_336,c_362]) ).
cnf(c_5727,plain,
( ~ top_str(sK49)
| empty(sK43(sK49)) ),
inference(unflattening,[status(thm)],[c_5726]) ).
cnf(c_5728,plain,
empty(sK43(sK49)),
inference(global_subsumption_just,[status(thm)],[c_5727,c_361,c_5727]) ).
cnf(c_5733,plain,
( X0 != sK49
| ~ top_str(X0)
| open_subset(sK43(X0),X0) ),
inference(resolution_lifted,[status(thm)],[c_335,c_362]) ).
cnf(c_5734,plain,
( ~ top_str(sK49)
| open_subset(sK43(sK49),sK49) ),
inference(unflattening,[status(thm)],[c_5733]) ).
cnf(c_5735,plain,
open_subset(sK43(sK49),sK49),
inference(global_subsumption_just,[status(thm)],[c_5734,c_361,c_5734]) ).
cnf(c_5740,plain,
( X0 != sK49
| ~ top_str(X0)
| boundary_set(sK43(X0),X0) ),
inference(resolution_lifted,[status(thm)],[c_333,c_362]) ).
cnf(c_5741,plain,
( ~ top_str(sK49)
| boundary_set(sK43(sK49),sK49) ),
inference(unflattening,[status(thm)],[c_5740]) ).
cnf(c_5742,plain,
boundary_set(sK43(sK49),sK49),
inference(global_subsumption_just,[status(thm)],[c_5741,c_361,c_5741]) ).
cnf(c_5803,plain,
( X0 != sK49
| ~ top_str(X0)
| element(sK5(X0,X1,X2),powerset(the_carrier(X0)))
| is_a_convergence_point_of_set(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_104,c_362]) ).
cnf(c_5804,plain,
( ~ top_str(sK49)
| element(sK5(sK49,X0,X1),powerset(the_carrier(sK49)))
| is_a_convergence_point_of_set(sK49,X0,X1) ),
inference(unflattening,[status(thm)],[c_5803]) ).
cnf(c_5827,plain,
( X0 != sK49
| ~ top_str(X0)
| in(X1,sK5(X0,X2,X1))
| is_a_convergence_point_of_set(X0,X2,X1) ),
inference(resolution_lifted,[status(thm)],[c_102,c_362]) ).
cnf(c_5828,plain,
( ~ top_str(sK49)
| in(X0,sK5(sK49,X1,X0))
| is_a_convergence_point_of_set(sK49,X1,X0) ),
inference(unflattening,[status(thm)],[c_5827]) ).
cnf(c_5911,plain,
( X0 != sK49
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,X1)
| ~ open_subset(X1,X0)
| ~ top_str(X0)
| point_neighbourhood(X1,X0,X2)
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_4515,c_362]) ).
cnf(c_5912,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ in(X1,X0)
| ~ open_subset(X0,sK49)
| ~ top_str(sK49)
| point_neighbourhood(X0,sK49,X1)
| empty_carrier(sK49) ),
inference(unflattening,[status(thm)],[c_5911]) ).
cnf(c_5913,plain,
( point_neighbourhood(X0,sK49,X1)
| ~ element(X0,powerset(the_carrier(sK49)))
| ~ in(X1,X0)
| ~ open_subset(X0,sK49) ),
inference(global_subsumption_just,[status(thm)],[c_5912,c_361,c_363,c_5912]) ).
cnf(c_5914,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ in(X1,X0)
| ~ open_subset(X0,sK49)
| point_neighbourhood(X0,sK49,X1) ),
inference(renaming,[status(thm)],[c_5913]) ).
cnf(c_5927,plain,
( X0 != sK49
| ~ element(X1,the_carrier(X0))
| ~ net_str(X2,X0)
| ~ transitive_relstr(X2)
| ~ top_str(X0)
| ~ directed_relstr(X2)
| point_neighbourhood(sK4(X0,X2,X1),X0,X1)
| in(X1,lim_points_of_net(X0,X2))
| empty_carrier(X0)
| empty_carrier(X2) ),
inference(resolution_lifted,[status(thm)],[c_2457,c_362]) ).
cnf(c_5928,plain,
( ~ element(X0,the_carrier(sK49))
| ~ net_str(X1,sK49)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ top_str(sK49)
| point_neighbourhood(sK4(sK49,X1,X0),sK49,X0)
| in(X0,lim_points_of_net(sK49,X1))
| empty_carrier(X1)
| empty_carrier(sK49) ),
inference(unflattening,[status(thm)],[c_5927]) ).
cnf(c_5930,plain,
( empty_carrier(X1)
| in(X0,lim_points_of_net(sK49,X1))
| point_neighbourhood(sK4(sK49,X1,X0),sK49,X0)
| ~ element(X0,the_carrier(sK49))
| ~ net_str(X1,sK49)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1) ),
inference(global_subsumption_just,[status(thm)],[c_5928,c_361,c_363,c_5928]) ).
cnf(c_5931,plain,
( ~ element(X0,the_carrier(sK49))
| ~ net_str(X1,sK49)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| point_neighbourhood(sK4(sK49,X1,X0),sK49,X0)
| in(X0,lim_points_of_net(sK49,X1))
| empty_carrier(X1) ),
inference(renaming,[status(thm)],[c_5930]) ).
cnf(c_5954,plain,
( X0 != sK49
| ~ in(X1,lim_points_of_net(X0,X2))
| ~ point_neighbourhood(X3,X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ net_str(X2,X0)
| ~ transitive_relstr(X2)
| ~ top_str(X0)
| ~ directed_relstr(X2)
| is_eventually_in(X0,X2,X3)
| empty_carrier(X0)
| empty_carrier(X2) ),
inference(resolution_lifted,[status(thm)],[c_2456,c_362]) ).
cnf(c_5955,plain,
( ~ in(X0,lim_points_of_net(sK49,X1))
| ~ point_neighbourhood(X2,sK49,X0)
| ~ element(X0,the_carrier(sK49))
| ~ net_str(X1,sK49)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ top_str(sK49)
| is_eventually_in(sK49,X1,X2)
| empty_carrier(X1)
| empty_carrier(sK49) ),
inference(unflattening,[status(thm)],[c_5954]) ).
cnf(c_5957,plain,
( empty_carrier(X1)
| is_eventually_in(sK49,X1,X2)
| ~ in(X0,lim_points_of_net(sK49,X1))
| ~ point_neighbourhood(X2,sK49,X0)
| ~ element(X0,the_carrier(sK49))
| ~ net_str(X1,sK49)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1) ),
inference(global_subsumption_just,[status(thm)],[c_5955,c_361,c_363,c_5955]) ).
cnf(c_5958,plain,
( ~ in(X0,lim_points_of_net(sK49,X1))
| ~ point_neighbourhood(X2,sK49,X0)
| ~ element(X0,the_carrier(sK49))
| ~ net_str(X1,sK49)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| is_eventually_in(sK49,X1,X2)
| empty_carrier(X1) ),
inference(renaming,[status(thm)],[c_5957]) ).
cnf(c_5984,plain,
( X0 != sK49
| ~ point_neighbourhood(X1,X0,X2)
| ~ element(X2,the_carrier(X0))
| ~ top_str(X0)
| in(X2,interior(X0,X1))
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_567,c_362]) ).
cnf(c_5985,plain,
( ~ point_neighbourhood(X0,sK49,X1)
| ~ element(X1,the_carrier(sK49))
| ~ top_str(sK49)
| in(X1,interior(sK49,X0))
| empty_carrier(sK49) ),
inference(unflattening,[status(thm)],[c_5984]) ).
cnf(c_5987,plain,
( in(X1,interior(sK49,X0))
| ~ point_neighbourhood(X0,sK49,X1)
| ~ element(X1,the_carrier(sK49)) ),
inference(global_subsumption_just,[status(thm)],[c_5985,c_361,c_363,c_5985]) ).
cnf(c_5988,plain,
( ~ point_neighbourhood(X0,sK49,X1)
| ~ element(X1,the_carrier(sK49))
| in(X1,interior(sK49,X0)) ),
inference(renaming,[status(thm)],[c_5987]) ).
cnf(c_5999,plain,
( X0 != sK49
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| open_subset(interior(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_174,c_362]) ).
cnf(c_6000,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ top_str(sK49)
| open_subset(interior(sK49,X0),sK49) ),
inference(unflattening,[status(thm)],[c_5999]) ).
cnf(c_6023,plain,
( X0 != sK49
| ~ point_neighbourhood(X1,X0,X2)
| ~ element(X2,the_carrier(X0))
| ~ top_str(X0)
| element(X1,powerset(the_carrier(X0)))
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_117,c_362]) ).
cnf(c_6024,plain,
( ~ point_neighbourhood(X0,sK49,X1)
| ~ element(X1,the_carrier(sK49))
| ~ top_str(sK49)
| element(X0,powerset(the_carrier(sK49)))
| empty_carrier(sK49) ),
inference(unflattening,[status(thm)],[c_6023]) ).
cnf(c_6026,plain,
( element(X0,powerset(the_carrier(sK49)))
| ~ point_neighbourhood(X0,sK49,X1)
| ~ element(X1,the_carrier(sK49)) ),
inference(global_subsumption_just,[status(thm)],[c_6024,c_361,c_363,c_6024]) ).
cnf(c_6027,plain,
( ~ point_neighbourhood(X0,sK49,X1)
| ~ element(X1,the_carrier(sK49))
| element(X0,powerset(the_carrier(sK49))) ),
inference(renaming,[status(thm)],[c_6026]) ).
cnf(c_6059,plain,
( X0 != sK49
| ~ element(X1,powerset(the_carrier(X0)))
| ~ is_a_convergence_point_of_set(X0,X2,X3)
| ~ in(X3,X1)
| ~ open_subset(X1,X0)
| ~ top_str(X0)
| in(X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_105,c_362]) ).
cnf(c_6060,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ is_a_convergence_point_of_set(sK49,X1,X2)
| ~ in(X2,X0)
| ~ open_subset(X0,sK49)
| ~ top_str(sK49)
| in(X0,X1) ),
inference(unflattening,[status(thm)],[c_6059]) ).
cnf(c_6061,plain,
( ~ open_subset(X0,sK49)
| ~ in(X2,X0)
| ~ is_a_convergence_point_of_set(sK49,X1,X2)
| ~ element(X0,powerset(the_carrier(sK49)))
| in(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_6060,c_361,c_6060]) ).
cnf(c_6062,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ is_a_convergence_point_of_set(sK49,X1,X2)
| ~ in(X2,X0)
| ~ open_subset(X0,sK49)
| in(X0,X1) ),
inference(renaming,[status(thm)],[c_6061]) ).
cnf(c_6078,plain,
( X0 != sK49
| ~ in(X1,interior(X0,X2))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| point_neighbourhood(X2,X0,X1)
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_98,c_362]) ).
cnf(c_6079,plain,
( ~ in(X0,interior(sK49,X1))
| ~ element(X1,powerset(the_carrier(sK49)))
| ~ element(X0,the_carrier(sK49))
| ~ top_str(sK49)
| point_neighbourhood(X1,sK49,X0)
| empty_carrier(sK49) ),
inference(unflattening,[status(thm)],[c_6078]) ).
cnf(c_6081,plain,
( point_neighbourhood(X1,sK49,X0)
| ~ in(X0,interior(sK49,X1))
| ~ element(X1,powerset(the_carrier(sK49)))
| ~ element(X0,the_carrier(sK49)) ),
inference(global_subsumption_just,[status(thm)],[c_6079,c_361,c_363,c_6079]) ).
cnf(c_6082,plain,
( ~ in(X0,interior(sK49,X1))
| ~ element(X1,powerset(the_carrier(sK49)))
| ~ element(X0,the_carrier(sK49))
| point_neighbourhood(X1,sK49,X0) ),
inference(renaming,[status(thm)],[c_6081]) ).
cnf(c_6156,plain,
( X0 != sK49
| ~ element(X1,powerset(the_carrier(X0)))
| ~ empty(X1)
| ~ top_str(X0)
| open_subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_70,c_362]) ).
cnf(c_6157,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ empty(X0)
| ~ top_str(sK49)
| open_subset(X0,sK49) ),
inference(unflattening,[status(thm)],[c_6156]) ).
cnf(c_6159,plain,
( ~ empty(X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| open_subset(X0,sK49) ),
inference(global_subsumption_just,[status(thm)],[c_6157,c_361,c_6157]) ).
cnf(c_6160,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ empty(X0)
| open_subset(X0,sK49) ),
inference(renaming,[status(thm)],[c_6159]) ).
cnf(c_6324,plain,
( X0 != sK49
| one_sorted_str(X0) ),
inference(resolution_lifted,[status(thm)],[c_658,c_361]) ).
cnf(c_6325,plain,
one_sorted_str(sK49),
inference(unflattening,[status(thm)],[c_6324]) ).
cnf(c_6383,plain,
( X0 != sK49
| ~ element(X1,powerset(the_carrier(X0)))
| subset(interior(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_370,c_361]) ).
cnf(c_6384,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| subset(interior(sK49,X0),X0) ),
inference(unflattening,[status(thm)],[c_6383]) ).
cnf(c_6392,plain,
( X0 != sK49
| ~ element(X1,powerset(the_carrier(X0)))
| ~ boundary_set(X1,X0)
| empty(interior(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_129,c_361]) ).
cnf(c_6393,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ boundary_set(X0,sK49)
| empty(interior(sK49,X0)) ),
inference(unflattening,[status(thm)],[c_6392]) ).
cnf(c_6416,plain,
( X0 != sK49
| ~ element(X1,powerset(the_carrier(X0)))
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(resolution_lifted,[status(thm)],[c_109,c_361]) ).
cnf(c_6417,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| element(interior(sK49,X0),powerset(the_carrier(sK49))) ),
inference(unflattening,[status(thm)],[c_6416]) ).
cnf(c_7526,plain,
( X0 != sK50
| ~ in(X1,lim_points_of_net(sK49,X0))
| ~ point_neighbourhood(X2,sK49,X1)
| ~ element(X1,the_carrier(sK49))
| ~ net_str(X0,sK49)
| ~ transitive_relstr(X0)
| is_eventually_in(sK49,X0,X2)
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_5958,c_358]) ).
cnf(c_7527,plain,
( ~ in(X0,lim_points_of_net(sK49,sK50))
| ~ point_neighbourhood(X1,sK49,X0)
| ~ element(X0,the_carrier(sK49))
| ~ net_str(sK50,sK49)
| ~ transitive_relstr(sK50)
| is_eventually_in(sK49,sK50,X1)
| empty_carrier(sK50) ),
inference(unflattening,[status(thm)],[c_7526]) ).
cnf(c_7529,plain,
( is_eventually_in(sK49,sK50,X1)
| ~ element(X0,the_carrier(sK49))
| ~ point_neighbourhood(X1,sK49,X0)
| ~ in(X0,lim_points_of_net(sK49,sK50)) ),
inference(global_subsumption_just,[status(thm)],[c_7527,c_359,c_360,c_357,c_7527]) ).
cnf(c_7530,plain,
( ~ in(X0,lim_points_of_net(sK49,sK50))
| ~ point_neighbourhood(X1,sK49,X0)
| ~ element(X0,the_carrier(sK49))
| is_eventually_in(sK49,sK50,X1) ),
inference(renaming,[status(thm)],[c_7529]) ).
cnf(c_7544,plain,
( X0 != sK50
| ~ element(X1,the_carrier(sK49))
| ~ net_str(X0,sK49)
| ~ transitive_relstr(X0)
| point_neighbourhood(sK4(sK49,X0,X1),sK49,X1)
| in(X1,lim_points_of_net(sK49,X0))
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_5931,c_358]) ).
cnf(c_7545,plain,
( ~ element(X0,the_carrier(sK49))
| ~ net_str(sK50,sK49)
| ~ transitive_relstr(sK50)
| point_neighbourhood(sK4(sK49,sK50,X0),sK49,X0)
| in(X0,lim_points_of_net(sK49,sK50))
| empty_carrier(sK50) ),
inference(unflattening,[status(thm)],[c_7544]) ).
cnf(c_7547,plain,
( in(X0,lim_points_of_net(sK49,sK50))
| point_neighbourhood(sK4(sK49,sK50,X0),sK49,X0)
| ~ element(X0,the_carrier(sK49)) ),
inference(global_subsumption_just,[status(thm)],[c_7545,c_359,c_360,c_357,c_7545]) ).
cnf(c_7548,plain,
( ~ element(X0,the_carrier(sK49))
| point_neighbourhood(sK4(sK49,sK50,X0),sK49,X0)
| in(X0,lim_points_of_net(sK49,sK50)) ),
inference(renaming,[status(thm)],[c_7547]) ).
cnf(c_7744,plain,
( X0 != sK50
| ~ is_eventually_in(sK49,X0,sK4(sK49,X0,X1))
| ~ element(X1,the_carrier(sK49))
| ~ net_str(X0,sK49)
| ~ transitive_relstr(X0)
| in(X1,lim_points_of_net(sK49,X0))
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_5675,c_358]) ).
cnf(c_7745,plain,
( ~ is_eventually_in(sK49,sK50,sK4(sK49,sK50,X0))
| ~ element(X0,the_carrier(sK49))
| ~ net_str(sK50,sK49)
| ~ transitive_relstr(sK50)
| in(X0,lim_points_of_net(sK49,sK50))
| empty_carrier(sK50) ),
inference(unflattening,[status(thm)],[c_7744]) ).
cnf(c_7747,plain,
( in(X0,lim_points_of_net(sK49,sK50))
| ~ element(X0,the_carrier(sK49))
| ~ is_eventually_in(sK49,sK50,sK4(sK49,sK50,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_7745,c_359,c_360,c_357,c_7745]) ).
cnf(c_7748,plain,
( ~ is_eventually_in(sK49,sK50,sK4(sK49,sK50,X0))
| ~ element(X0,the_carrier(sK49))
| in(X0,lim_points_of_net(sK49,sK50)) ),
inference(renaming,[status(thm)],[c_7747]) ).
cnf(c_8699,plain,
( X0 != sK49
| X1 != sK50
| ~ element(X2,powerset(the_carrier(X0)))
| ~ is_eventually_in(X0,X1,X2)
| ~ one_sorted_str(X0)
| in(X2,filter_of_net_str(X0,X1))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_351,c_357]) ).
cnf(c_8700,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ is_eventually_in(sK49,sK50,X0)
| ~ one_sorted_str(sK49)
| in(X0,filter_of_net_str(sK49,sK50))
| empty_carrier(sK49)
| empty_carrier(sK50) ),
inference(unflattening,[status(thm)],[c_8699]) ).
cnf(c_8702,plain,
( ~ is_eventually_in(sK49,sK50,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| in(X0,filter_of_net_str(sK49,sK50)) ),
inference(global_subsumption_just,[status(thm)],[c_8700,c_363,c_360,c_6325,c_8700]) ).
cnf(c_8703,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ is_eventually_in(sK49,sK50,X0)
| in(X0,filter_of_net_str(sK49,sK50)) ),
inference(renaming,[status(thm)],[c_8702]) ).
cnf(c_15543,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| subset(interior(sK49,X0),X0) ),
inference(prop_impl_just,[status(thm)],[c_6384]) ).
cnf(c_15545,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| element(interior(sK49,X0),powerset(the_carrier(sK49))) ),
inference(prop_impl_just,[status(thm)],[c_6417]) ).
cnf(c_15567,plain,
( element(sK5(sK49,X0,X1),powerset(the_carrier(sK49)))
| is_a_convergence_point_of_set(sK49,X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_361,c_5804]) ).
cnf(c_15577,plain,
( in(X0,sK5(sK49,X1,X0))
| is_a_convergence_point_of_set(sK49,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_361,c_5828]) ).
cnf(c_30475,plain,
( ~ boundary_set(sK43(sK49),sK49)
| empty(interior(sK49,sK43(sK49))) ),
inference(superposition,[status(thm)],[c_5721,c_6393]) ).
cnf(c_30486,plain,
empty(interior(sK49,sK43(sK49))),
inference(forward_subsumption_resolution,[status(thm)],[c_30475,c_5742]) ).
cnf(c_30556,plain,
( ~ in(X0,sK43(sK49))
| ~ open_subset(sK43(sK49),sK49)
| point_neighbourhood(sK43(sK49),sK49,X0) ),
inference(superposition,[status(thm)],[c_5721,c_5914]) ).
cnf(c_30574,plain,
( ~ in(X0,sK43(sK49))
| point_neighbourhood(sK43(sK49),sK49,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30556,c_5735]) ).
cnf(c_30804,plain,
( ~ in(X0,sK29(the_carrier(sK49)))
| ~ open_subset(sK29(the_carrier(sK49)),sK49)
| ~ is_a_convergence_point_of_set(sK49,X1,X0)
| in(sK29(the_carrier(sK49)),X1) ),
inference(superposition,[status(thm)],[c_284,c_6062]) ).
cnf(c_30809,plain,
( ~ empty(sK29(the_carrier(sK49)))
| open_subset(sK29(the_carrier(sK49)),sK49) ),
inference(superposition,[status(thm)],[c_284,c_6160]) ).
cnf(c_30811,plain,
open_subset(sK29(the_carrier(sK49)),sK49),
inference(forward_subsumption_resolution,[status(thm)],[c_30809,c_283]) ).
cnf(c_30821,plain,
( ~ in(X0,sK29(the_carrier(sK49)))
| ~ is_a_convergence_point_of_set(sK49,X1,X0)
| in(sK29(the_carrier(sK49)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30804,c_30811]) ).
cnf(c_31213,plain,
sK29(X0) = empty_set,
inference(superposition,[status(thm)],[c_283,c_374]) ).
cnf(c_31214,plain,
sK43(sK49) = empty_set,
inference(superposition,[status(thm)],[c_5728,c_374]) ).
cnf(c_31235,plain,
element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_284,c_31213]) ).
cnf(c_31237,plain,
( ~ is_a_convergence_point_of_set(sK49,X0,X1)
| ~ in(X1,empty_set)
| in(empty_set,X0) ),
inference(demodulation,[status(thm)],[c_30821,c_31213]) ).
cnf(c_31243,plain,
( ~ in(X0,empty_set)
| point_neighbourhood(empty_set,sK49,X0) ),
inference(demodulation,[status(thm)],[c_30574,c_31214]) ).
cnf(c_31245,plain,
empty(interior(sK49,empty_set)),
inference(demodulation,[status(thm)],[c_30486,c_31214]) ).
cnf(c_31393,plain,
( ~ is_a_convergence_point_of_set(sK49,X0,X1)
| ~ subset(X2,the_carrier(sK49))
| ~ in(X1,X2)
| ~ open_subset(X2,sK49)
| in(X2,X0) ),
inference(superposition,[status(thm)],[c_368,c_6062]) ).
cnf(c_32386,plain,
( ~ subset(X0,the_carrier(sK49))
| subset(interior(sK49,X0),X0) ),
inference(superposition,[status(thm)],[c_368,c_15543]) ).
cnf(c_32635,plain,
( subset(sK5(sK49,X0,X1),the_carrier(sK49))
| is_a_convergence_point_of_set(sK49,X0,X1) ),
inference(superposition,[status(thm)],[c_15567,c_369]) ).
cnf(c_32685,plain,
( ~ is_eventually_in(sK49,sK50,sK4(sK49,sK50,sK51))
| ~ element(sK51,the_carrier(sK49))
| in(sK51,lim_points_of_net(sK49,sK50)) ),
inference(instantiation,[status(thm)],[c_7748]) ).
cnf(c_32686,plain,
( ~ point_neighbourhood(X0,sK49,sK51)
| ~ element(sK51,the_carrier(sK49))
| element(X0,powerset(the_carrier(sK49))) ),
inference(instantiation,[status(thm)],[c_6027]) ).
cnf(c_32689,plain,
subset(empty_set,X0),
inference(superposition,[status(thm)],[c_31235,c_369]) ).
cnf(c_32710,plain,
( ~ point_neighbourhood(X0,sK49,sK51)
| ~ element(sK51,the_carrier(sK49))
| in(sK51,interior(sK49,X0)) ),
inference(instantiation,[status(thm)],[c_5988]) ).
cnf(c_32712,plain,
( ~ in(sK51,lim_points_of_net(sK49,sK50))
| ~ point_neighbourhood(X0,sK49,sK51)
| ~ element(sK51,the_carrier(sK49))
| is_eventually_in(sK49,sK50,X0) ),
inference(instantiation,[status(thm)],[c_7530]) ).
cnf(c_32726,plain,
interior(sK49,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_31245,c_374]) ).
cnf(c_32815,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| subset(interior(sK49,X0),the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_15545,c_369]) ).
cnf(c_33239,plain,
( ~ one_sorted_str(sK49)
| filter_of_net_str(sK49,sK50) = a_2_1_yellow19(sK49,sK50)
| empty_carrier(sK49)
| empty_carrier(sK50) ),
inference(superposition,[status(thm)],[c_357,c_100]) ).
cnf(c_33240,plain,
filter_of_net_str(sK49,sK50) = a_2_1_yellow19(sK49,sK50),
inference(forward_subsumption_resolution,[status(thm)],[c_33239,c_360,c_363,c_6325]) ).
cnf(c_33573,plain,
( ~ in(X0,filter_of_net_str(sK49,sK50))
| ~ net_str(sK50,sK49)
| ~ one_sorted_str(sK49)
| sK14(X0,sK49,sK50) = X0
| empty_carrier(sK49)
| empty_carrier(sK50) ),
inference(superposition,[status(thm)],[c_33240,c_209]) ).
cnf(c_33574,plain,
( ~ in(X0,filter_of_net_str(sK49,sK50))
| sK14(X0,sK49,sK50) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[c_33573,c_360,c_363,c_6325,c_357]) ).
cnf(c_33829,plain,
( ~ in(X0,interior(sK49,sK14(X1,sK49,X2)))
| ~ in(X1,a_2_1_yellow19(sK49,X2))
| ~ element(X0,the_carrier(sK49))
| ~ net_str(X2,sK49)
| ~ one_sorted_str(sK49)
| point_neighbourhood(sK14(X1,sK49,X2),sK49,X0)
| empty_carrier(X2)
| empty_carrier(sK49) ),
inference(superposition,[status(thm)],[c_210,c_6082]) ).
cnf(c_33884,plain,
( ~ in(X0,interior(sK49,sK14(X1,sK49,X2)))
| ~ in(X1,a_2_1_yellow19(sK49,X2))
| ~ element(X0,the_carrier(sK49))
| ~ net_str(X2,sK49)
| point_neighbourhood(sK14(X1,sK49,X2),sK49,X0)
| empty_carrier(X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33829,c_363,c_6325]) ).
cnf(c_34849,plain,
( ~ subset(X0,the_carrier(sK49))
| element(X0,powerset(the_carrier(sK49))) ),
inference(instantiation,[status(thm)],[c_368]) ).
cnf(c_41235,plain,
( ~ subset(sK5(sK49,X0,X1),X2)
| is_a_convergence_point_of_set(sK49,X0,X1)
| element(X1,X2) ),
inference(superposition,[status(thm)],[c_15577,c_1090]) ).
cnf(c_41996,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| subset(X0,the_carrier(sK49)) ),
inference(instantiation,[status(thm)],[c_369]) ).
cnf(c_42410,plain,
( ~ subset(interior(sK49,X0),X1)
| ~ point_neighbourhood(X0,sK49,X2)
| ~ element(X2,the_carrier(sK49))
| ~ empty(X1) ),
inference(superposition,[status(thm)],[c_5988,c_1091]) ).
cnf(c_46925,plain,
( ~ element(X0,the_carrier(sK49))
| ~ point_neighbourhood(empty_set,sK49,X0)
| ~ subset(empty_set,X1)
| ~ empty(X1) ),
inference(superposition,[status(thm)],[c_32726,c_42410]) ).
cnf(c_46935,plain,
( ~ element(X0,the_carrier(sK49))
| ~ point_neighbourhood(empty_set,sK49,X0)
| ~ empty(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46925,c_32689]) ).
cnf(c_48994,plain,
( ~ subset(X0,the_carrier(sK49))
| ~ in(sK51,X0)
| ~ open_subset(X0,sK49)
| in(X0,filter_of_net_str(sK49,sK50))
| in(sK51,lim_points_of_net(sK49,sK50)) ),
inference(superposition,[status(thm)],[c_355,c_31393]) ).
cnf(c_49027,plain,
( ~ point_neighbourhood(X0,sK49,sK51)
| ~ subset(X1,the_carrier(sK49))
| ~ element(sK51,the_carrier(sK49))
| ~ in(sK51,X1)
| ~ open_subset(X1,sK49)
| in(X1,filter_of_net_str(sK49,sK50))
| is_eventually_in(sK49,sK50,X0) ),
inference(superposition,[status(thm)],[c_48994,c_7530]) ).
cnf(c_49100,plain,
( ~ point_neighbourhood(X0,sK49,sK51)
| ~ subset(X1,the_carrier(sK49))
| ~ in(sK51,X1)
| ~ open_subset(X1,sK49)
| in(X1,filter_of_net_str(sK49,sK50))
| is_eventually_in(sK49,sK50,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49027,c_356]) ).
cnf(c_55687,plain,
( ~ element(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| ~ in(X0,sK5(sK49,filter_of_net_str(sK49,sK50),sK51))
| ~ open_subset(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),sK49)
| point_neighbourhood(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),sK49,X0) ),
inference(instantiation,[status(thm)],[c_5914]) ).
cnf(c_59775,plain,
( is_a_convergence_point_of_set(sK49,X0,X1)
| element(X1,the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_32635,c_41235]) ).
cnf(c_60151,plain,
( ~ in(X0,empty_set)
| element(X0,the_carrier(sK49))
| in(empty_set,X1) ),
inference(superposition,[status(thm)],[c_59775,c_31237]) ).
cnf(c_60212,plain,
( ~ in(X0,empty_set)
| ~ empty(X1)
| element(X0,the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_60151,c_375]) ).
cnf(c_60682,plain,
( ~ empty(X1)
| ~ in(X0,empty_set) ),
inference(global_subsumption_just,[status(thm)],[c_60212,c_31243,c_46935,c_60212]) ).
cnf(c_60683,plain,
( ~ in(X0,empty_set)
| ~ empty(X1) ),
inference(renaming,[status(thm)],[c_60682]) ).
cnf(c_60693,plain,
( ~ empty(X0)
| X1 = empty_set
| in(sK52(empty_set,X1),X1) ),
inference(superposition,[status(thm)],[c_367,c_60683]) ).
cnf(c_62942,plain,
( X0 = empty_set
| in(sK52(empty_set,X0),X0) ),
inference(superposition,[status(thm)],[c_169,c_60693]) ).
cnf(c_62999,plain,
( sK14(sK52(empty_set,filter_of_net_str(sK49,sK50)),sK49,sK50) = sK52(empty_set,filter_of_net_str(sK49,sK50))
| filter_of_net_str(sK49,sK50) = empty_set ),
inference(superposition,[status(thm)],[c_62942,c_33574]) ).
cnf(c_67213,plain,
( ~ in(X0,interior(sK49,sK52(empty_set,filter_of_net_str(sK49,sK50))))
| ~ in(sK52(empty_set,filter_of_net_str(sK49,sK50)),a_2_1_yellow19(sK49,sK50))
| ~ element(X0,the_carrier(sK49))
| ~ net_str(sK50,sK49)
| filter_of_net_str(sK49,sK50) = empty_set
| point_neighbourhood(sK14(sK52(empty_set,filter_of_net_str(sK49,sK50)),sK49,sK50),sK49,X0)
| empty_carrier(sK50) ),
inference(superposition,[status(thm)],[c_62999,c_33884]) ).
cnf(c_67271,plain,
( ~ in(X0,interior(sK49,sK52(empty_set,filter_of_net_str(sK49,sK50))))
| ~ in(sK52(empty_set,filter_of_net_str(sK49,sK50)),filter_of_net_str(sK49,sK50))
| ~ element(X0,the_carrier(sK49))
| ~ net_str(sK50,sK49)
| filter_of_net_str(sK49,sK50) = empty_set
| point_neighbourhood(sK14(sK52(empty_set,filter_of_net_str(sK49,sK50)),sK49,sK50),sK49,X0)
| empty_carrier(sK50) ),
inference(light_normalisation,[status(thm)],[c_67213,c_33240]) ).
cnf(c_67272,plain,
( ~ in(X0,interior(sK49,sK52(empty_set,filter_of_net_str(sK49,sK50))))
| ~ in(sK52(empty_set,filter_of_net_str(sK49,sK50)),filter_of_net_str(sK49,sK50))
| ~ element(X0,the_carrier(sK49))
| filter_of_net_str(sK49,sK50) = empty_set
| point_neighbourhood(sK14(sK52(empty_set,filter_of_net_str(sK49,sK50)),sK49,sK50),sK49,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67271,c_360,c_357]) ).
cnf(c_67769,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ in(sK51,X0)
| ~ open_subset(X0,sK49)
| point_neighbourhood(X0,sK49,sK51) ),
inference(instantiation,[status(thm)],[c_5914]) ).
cnf(c_69173,plain,
( ~ in(X0,interior(sK49,sK52(empty_set,filter_of_net_str(sK49,sK50))))
| ~ element(X0,the_carrier(sK49))
| filter_of_net_str(sK49,sK50) = empty_set
| point_neighbourhood(sK14(sK52(empty_set,filter_of_net_str(sK49,sK50)),sK49,sK50),sK49,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67272,c_62942]) ).
cnf(c_69182,plain,
( ~ in(sK51,interior(sK49,sK52(empty_set,filter_of_net_str(sK49,sK50))))
| ~ subset(X0,the_carrier(sK49))
| ~ element(sK51,the_carrier(sK49))
| ~ in(sK51,X0)
| ~ open_subset(X0,sK49)
| filter_of_net_str(sK49,sK50) = empty_set
| is_eventually_in(sK49,sK50,sK14(sK52(empty_set,filter_of_net_str(sK49,sK50)),sK49,sK50))
| in(X0,filter_of_net_str(sK49,sK50)) ),
inference(superposition,[status(thm)],[c_69173,c_49100]) ).
cnf(c_69191,plain,
( ~ in(sK51,interior(sK49,sK52(empty_set,filter_of_net_str(sK49,sK50))))
| ~ subset(X0,the_carrier(sK49))
| ~ in(sK51,X0)
| ~ open_subset(X0,sK49)
| filter_of_net_str(sK49,sK50) = empty_set
| is_eventually_in(sK49,sK50,sK14(sK52(empty_set,filter_of_net_str(sK49,sK50)),sK49,sK50))
| in(X0,filter_of_net_str(sK49,sK50)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69182,c_356]) ).
cnf(c_69209,plain,
( ~ subset(X0,the_carrier(sK49))
| ~ in(sK51,X0)
| ~ open_subset(X0,sK49)
| in(X0,filter_of_net_str(sK49,sK50)) ),
inference(global_subsumption_just,[status(thm)],[c_69191,c_356,c_8703,c_32712,c_34849,c_48994,c_67769]) ).
cnf(c_69226,plain,
( ~ subset(X0,the_carrier(sK49))
| ~ in(sK51,X0)
| ~ open_subset(X0,sK49)
| ~ net_str(sK50,sK49)
| ~ one_sorted_str(sK49)
| is_eventually_in(sK49,sK50,X0)
| empty_carrier(sK49)
| empty_carrier(sK50) ),
inference(superposition,[status(thm)],[c_69209,c_353]) ).
cnf(c_69270,plain,
( ~ subset(X0,the_carrier(sK49))
| ~ in(sK51,X0)
| ~ open_subset(X0,sK49)
| is_eventually_in(sK49,sK50,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69226,c_360,c_363,c_6325,c_357]) ).
cnf(c_69342,plain,
( ~ in(sK51,interior(sK49,X0))
| ~ element(X0,powerset(the_carrier(sK49)))
| ~ open_subset(interior(sK49,X0),sK49)
| is_eventually_in(sK49,sK50,interior(sK49,X0)) ),
inference(superposition,[status(thm)],[c_32815,c_69270]) ).
cnf(c_71350,plain,
( ~ element(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| ~ in(sK51,sK5(sK49,filter_of_net_str(sK49,sK50),sK51))
| ~ open_subset(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),sK49)
| point_neighbourhood(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),sK49,sK51) ),
inference(instantiation,[status(thm)],[c_55687]) ).
cnf(c_92850,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ in(sK51,interior(sK49,X0))
| is_eventually_in(sK49,sK50,interior(sK49,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_69342,c_361,c_6000,c_69342]) ).
cnf(c_92851,plain,
( ~ in(sK51,interior(sK49,X0))
| ~ element(X0,powerset(the_carrier(sK49)))
| is_eventually_in(sK49,sK50,interior(sK49,X0)) ),
inference(renaming,[status(thm)],[c_92850]) ).
cnf(c_92860,plain,
( ~ subset(interior(sK49,X0),X1)
| ~ in(sK51,interior(sK49,X0))
| ~ element(X0,powerset(the_carrier(sK49)))
| ~ net_str(sK50,sK49)
| ~ one_sorted_str(sK49)
| is_eventually_in(sK49,sK50,X1)
| empty_carrier(sK49)
| empty_carrier(sK50) ),
inference(superposition,[status(thm)],[c_92851,c_378]) ).
cnf(c_92875,plain,
( ~ subset(interior(sK49,X0),X1)
| ~ in(sK51,interior(sK49,X0))
| ~ element(X0,powerset(the_carrier(sK49)))
| is_eventually_in(sK49,sK50,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_92860,c_360,c_363,c_6325,c_357]) ).
cnf(c_92943,plain,
( ~ subset(interior(sK49,X0),X1)
| ~ in(sK51,interior(sK49,X0))
| ~ subset(X0,the_carrier(sK49))
| is_eventually_in(sK49,sK50,X1) ),
inference(superposition,[status(thm)],[c_368,c_92875]) ).
cnf(c_101779,plain,
( ~ subset(interior(sK49,X0),X1)
| ~ point_neighbourhood(X0,sK49,sK51)
| ~ subset(X0,the_carrier(sK49))
| ~ element(sK51,the_carrier(sK49))
| is_eventually_in(sK49,sK50,X1) ),
inference(superposition,[status(thm)],[c_5988,c_92943]) ).
cnf(c_101781,plain,
( ~ subset(interior(sK49,X0),X1)
| ~ point_neighbourhood(X0,sK49,sK51)
| ~ subset(X0,the_carrier(sK49))
| is_eventually_in(sK49,sK50,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101779,c_356]) ).
cnf(c_101787,plain,
( ~ point_neighbourhood(X0,sK49,sK51)
| ~ subset(interior(sK49,X0),X1)
| is_eventually_in(sK49,sK50,X1) ),
inference(global_subsumption_just,[status(thm)],[c_101781,c_356,c_32686,c_32710,c_92875]) ).
cnf(c_101788,plain,
( ~ subset(interior(sK49,X0),X1)
| ~ point_neighbourhood(X0,sK49,sK51)
| is_eventually_in(sK49,sK50,X1) ),
inference(renaming,[status(thm)],[c_101787]) ).
cnf(c_101798,plain,
( ~ point_neighbourhood(X0,sK49,sK51)
| ~ subset(X0,the_carrier(sK49))
| is_eventually_in(sK49,sK50,X0) ),
inference(superposition,[status(thm)],[c_32386,c_101788]) ).
cnf(c_102070,plain,
( ~ point_neighbourhood(X0,sK49,sK51)
| is_eventually_in(sK49,sK50,X0) ),
inference(global_subsumption_just,[status(thm)],[c_101798,c_356,c_32686,c_41996,c_101798]) ).
cnf(c_102084,plain,
( ~ element(sK51,the_carrier(sK49))
| is_eventually_in(sK49,sK50,sK4(sK49,sK50,sK51))
| in(sK51,lim_points_of_net(sK49,sK50)) ),
inference(superposition,[status(thm)],[c_7548,c_102070]) ).
cnf(c_102104,plain,
( is_eventually_in(sK49,sK50,sK4(sK49,sK50,sK51))
| in(sK51,lim_points_of_net(sK49,sK50)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102084,c_356]) ).
cnf(c_102383,plain,
in(sK51,lim_points_of_net(sK49,sK50)),
inference(global_subsumption_just,[status(thm)],[c_102104,c_356,c_32685,c_102104]) ).
cnf(c_106908,plain,
( ~ point_neighbourhood(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),sK49,sK51)
| ~ in(sK51,lim_points_of_net(sK49,sK50))
| ~ element(sK51,the_carrier(sK49))
| is_eventually_in(sK49,sK50,sK5(sK49,filter_of_net_str(sK49,sK50),sK51)) ),
inference(instantiation,[status(thm)],[c_32712]) ).
cnf(c_124061,plain,
( ~ element(X0,powerset(the_carrier(sK49)))
| ~ is_eventually_in(sK49,sK50,X0)
| ~ net_str(sK50,sK49)
| ~ one_sorted_str(sK49)
| in(X0,filter_of_net_str(sK49,sK50))
| empty_carrier(sK49)
| empty_carrier(sK50) ),
inference(instantiation,[status(thm)],[c_351]) ).
cnf(c_129674,plain,
( ~ element(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| ~ is_eventually_in(sK49,sK50,sK5(sK49,filter_of_net_str(sK49,sK50),sK51))
| ~ net_str(sK50,sK49)
| ~ one_sorted_str(sK49)
| in(sK5(sK49,filter_of_net_str(sK49,sK50),sK51),filter_of_net_str(sK49,sK50))
| empty_carrier(sK49)
| empty_carrier(sK50) ),
inference(instantiation,[status(thm)],[c_124061]) ).
cnf(c_129676,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_129674,c_106908,c_102383,c_71350,c_6325,c_4671,c_4638,c_4628,c_4618,c_356,c_357,c_360,c_363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU392+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 21:37:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.21/4.23 % SZS status Started for theBenchmark.p
% 25.21/4.23 % SZS status Theorem for theBenchmark.p
% 25.21/4.23
% 25.21/4.23 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 25.21/4.23
% 25.21/4.23 ------ iProver source info
% 25.21/4.23
% 25.21/4.23 git: date: 2023-05-31 18:12:56 +0000
% 25.21/4.23 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 25.21/4.23 git: non_committed_changes: false
% 25.21/4.23 git: last_make_outside_of_git: false
% 25.21/4.23
% 25.21/4.23 ------ Parsing...
% 25.21/4.23 ------ Clausification by vclausify_rel & Parsing by iProver...
% 25.21/4.23
% 25.21/4.23 ------ Preprocessing... sup_sim: 0 sf_s rm: 12 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe_e
% 25.21/4.23
% 25.21/4.23 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 25.21/4.23
% 25.21/4.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 25.21/4.23 ------ Proving...
% 25.21/4.23 ------ Problem Properties
% 25.21/4.23
% 25.21/4.23
% 25.21/4.23 clauses 325
% 25.21/4.23 conjectures 6
% 25.21/4.23 EPR 49
% 25.21/4.23 Horn 285
% 25.21/4.23 unary 145
% 25.21/4.23 binary 117
% 25.21/4.23 lits 634
% 25.21/4.23 lits eq 87
% 25.21/4.23 fd_pure 0
% 25.21/4.23 fd_pseudo 0
% 25.21/4.23 fd_cond 9
% 25.21/4.23 fd_pseudo_cond 9
% 25.21/4.23 AC symbols 0
% 25.21/4.23
% 25.21/4.23 ------ Schedule dynamic 5 is on
% 25.21/4.23
% 25.21/4.23 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 25.21/4.23
% 25.21/4.23
% 25.21/4.23 ------
% 25.21/4.23 Current options:
% 25.21/4.23 ------
% 25.21/4.23
% 25.21/4.23
% 25.21/4.23
% 25.21/4.23
% 25.21/4.23 ------ Proving...
% 25.21/4.23
% 25.21/4.23
% 25.21/4.23 % SZS status Theorem for theBenchmark.p
% 25.21/4.23
% 25.21/4.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.21/4.23
% 25.21/4.24
%------------------------------------------------------------------------------