%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU388+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:20:23 PM UTC 2026
% Result : Theorem 0.55s 0.51s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 190
% Syntax : Number of formulae : 696 ( 76 unt; 147 def)
% Number of atoms : 2361 ( 37 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 2755 (1090 ~;1191 |; 264 &)
% ( 151 <=>; 58 =>; 0 <=; 1 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 191 ( 189 usr; 148 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-3 aty)
% Number of variables : 289 ( 265 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( rel_str(A)
=> ( ( complete_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( join_complete_relstr(A)
& up_complete_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( empty(B)
=> ( closed_subset(B,A)
& open_subset(B,A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( rel_str(A)
=> ( ( complete_relstr(A)
& ~ empty_carrier(A) )
=> ( with_infima_relstr(A)
& with_suprema_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( empty(B)
=> boundary_set(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( empty(B)
=> nowhere_dense(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( rel_str(A)
=> ( ( complete_relstr(A)
& ~ empty_carrier(A) )
=> ( bounded_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( nowhere_dense(B,A)
=> boundary_set(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
( rel_str(A)
=> ( bounded_relstr(A)
=> ( upper_bounded_relstr(A)
& lower_bounded_relstr(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( ( boundary_set(B,A)
& closed_subset(B,A) )
=> ( nowhere_dense(B,A)
& boundary_set(B,A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] :
( rel_str(A)
=> ( ( upper_bounded_relstr(A)
& lower_bounded_relstr(A) )
=> bounded_relstr(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( ( nowhere_dense(B,A)
& open_subset(B,A) )
=> ( nowhere_dense(B,A)
& boundary_set(B,A)
& v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B)
& closed_subset(B,A)
& open_subset(B,A)
& empty(B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> neighborhood_system(A,B) = a_2_0_yellow19(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B] :
( ( element(B,the_carrier(A))
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> element(neighborhood_system(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A] :
( top_str(A)
=> one_sorted_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B] :
( ( element(B,the_carrier(A))
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [C] :
( point_neighbourhood(C,A,B)
=> element(C,powerset(the_carrier(A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
? [A] : top_str(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A,B] :
( ( element(B,the_carrier(A))
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ? [C] : point_neighbourhood(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [A] :
( ( rel_str(A)
& ~ empty_carrier(A) )
=> ( upper_relstr_subset(cast_as_carrier_subset(A),A)
& lower_relstr_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& boolean_relstr(boole_POSet(A))
& complemented_relstr(boole_POSet(A))
& heyting_relstr(boole_POSet(A))
& distributive_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [A] :
( ( rel_str(A)
& with_suprema_relstr(A) )
=> ( directed_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [A] :
( ( rel_str(A)
& upper_bounded_relstr(A)
& ~ empty_carrier(A) )
=> ( directed_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [A] :
( ( rel_str(A)
& with_infima_relstr(A) )
=> ( filtered_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> closed_subset(cast_as_carrier_subset(A),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& ~ empty_carrier(A) )
=> ( filtered_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ( closed_subset(cast_as_carrier_subset(A),A)
& open_subset(cast_as_carrier_subset(A),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,axiom,
! [A,B,C] :
( ( element(C,the_carrier(B))
& top_str(B)
& topological_space(B)
& ~ empty_carrier(B) )
=> ( in(A,a_2_0_yellow19(B,C))
<=> ? [D] :
( A = D
& point_neighbourhood(D,B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [A] :
( ( rel_str(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ? [B] :
( upper_relstr_subset(B,A)
& filtered_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [A] :
( ( rel_str(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A) )
=> ? [B] :
( upper_relstr_subset(B,A)
& lower_relstr_subset(B,A)
& filtered_subset(B,A)
& directed_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
? [A] :
( connected_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f77,axiom,
? [A] :
( join_complete_relstr(A)
& up_complete_relstr(A)
& bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f79,axiom,
? [A] :
( complete_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ? [B] :
( open_subset(B,A)
& element(B,powerset(the_carrier(A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
? [A] :
( with_infima_relstr(A)
& with_suprema_relstr(A)
& boolean_relstr(A)
& complemented_relstr(A)
& heyting_relstr(A)
& distributive_relstr(A)
& ~ v1_yellow_3(A)
& bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ trivial_carrier(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f111,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,conjecture,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( in(C,neighborhood_system(A,B))
<=> point_neighbourhood(C,A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,negated_conjecture,
~ ! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( in(C,neighborhood_system(A,B))
<=> point_neighbourhood(C,A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f114]) ).
fof(f116,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f121,plain,
! [A] :
( A = rel_str_of(the_carrier(A),the_InternalRel(A))
| ~ strict_rel_str(A)
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f122,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
! [A] :
( ( join_complete_relstr(A)
& up_complete_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ complete_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f128,plain,
! [X0] :
( up_complete_relstr(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f129,plain,
! [X0] :
( join_complete_relstr(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f156,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f157,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f165,plain,
! [A] :
( ! [B] :
( ( closed_subset(B,A)
& open_subset(B,A) )
| ~ empty(B)
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f166,plain,
! [X0,X1] :
( open_subset(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f167,plain,
! [X0,X1] :
( closed_subset(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f168,plain,
! [A] :
( ( with_infima_relstr(A)
& with_suprema_relstr(A)
& ~ empty_carrier(A) )
| ~ complete_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f170,plain,
! [X0] :
( with_suprema_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f171,plain,
! [X0] :
( with_infima_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f172,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f173,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f176,plain,
! [A] :
( ! [B] :
( boundary_set(B,A)
| ~ empty(B)
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f177,plain,
! [X0,X1] :
( boundary_set(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f184,plain,
! [A] :
( ! [B] :
( nowhere_dense(B,A)
| ~ empty(B)
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f185,plain,
! [X0,X1] :
( nowhere_dense(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f184]) ).
fof(f186,plain,
! [A] :
( ( bounded_relstr(A)
& ~ empty_carrier(A) )
| ~ complete_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f188,plain,
! [X0] :
( bounded_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f189,plain,
! [A] :
( ! [B] :
( boundary_set(B,A)
| ~ nowhere_dense(B,A)
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f190,plain,
! [X0,X1] :
( boundary_set(X1,X0)
| ~ nowhere_dense(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f191,plain,
! [A] :
( ( upper_bounded_relstr(A)
& lower_bounded_relstr(A) )
| ~ bounded_relstr(A)
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f193,plain,
! [X0] :
( upper_bounded_relstr(X0)
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f194,plain,
! [A] :
( ! [B] :
( ( nowhere_dense(B,A)
& boundary_set(B,A) )
| ~ boundary_set(B,A)
| ~ closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f196,plain,
! [X0,X1] :
( nowhere_dense(X1,X0)
| ~ boundary_set(X1,X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f201,plain,
! [A] :
( bounded_relstr(A)
| ~ upper_bounded_relstr(A)
| ~ lower_bounded_relstr(A)
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f202,plain,
! [X0] :
( bounded_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f203,plain,
! [A] :
( ! [B] :
( ( nowhere_dense(B,A)
& boundary_set(B,A)
& v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B)
& closed_subset(B,A)
& open_subset(B,A)
& empty(B) )
| ~ nowhere_dense(B,A)
| ~ open_subset(B,A)
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f204,plain,
! [X0,X1] :
( empty(X1)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f206,plain,
! [X0,X1] :
( closed_subset(X1,X0)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f207,plain,
! [X0,X1] :
( v1_membered(X1)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f208,plain,
! [X0,X1] :
( v2_membered(X1)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f209,plain,
! [X0,X1] :
( v3_membered(X1)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f210,plain,
! [X0,X1] :
( v4_membered(X1)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f211,plain,
! [X0,X1] :
( v5_membered(X1)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f219,plain,
! [A] :
( ! [B] :
( neighborhood_system(A,B) = a_2_0_yellow19(A,B)
| ~ element(B,the_carrier(A)) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f220,plain,
! [X0,X1] :
( neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f224,plain,
! [A,B] :
( element(neighborhood_system(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
| ~ element(B,the_carrier(A))
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f225,plain,
! [X0,X1] :
( element(neighborhood_system(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f226,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f227,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f233,plain,
! [A] :
( one_sorted_str(A)
| ~ top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f234,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f235,plain,
! [A,B] :
( ! [C] :
( element(C,powerset(the_carrier(A)))
| ~ point_neighbourhood(C,A,B) )
| ~ element(B,the_carrier(A))
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f236,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(cnf_transformation,[status(thm)],[f235]) ).
fof(f243,plain,
top_str(sK1_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(A,sK1_skl)],[f45]) ).
fof(f244,plain,
top_str(sK1_skl),
inference(cnf_transformation,[status(thm)],[f243]) ).
fof(f247,plain,
! [A,B] :
( ? [C] : point_neighbourhood(C,A,B)
| ~ element(B,the_carrier(A))
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f248,plain,
! [A,B] :
( point_neighbourhood(sK3_skl(B,A),A,B)
| ~ element(B,the_carrier(A))
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(C,sK3_skl(B,A))],[f247]) ).
fof(f249,plain,
! [X0,X1] :
( point_neighbourhood(sK3_skl(X1,X0),X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f252,plain,
! [A] : element(sK5_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(B,sK5_skl(A))],[f49]) ).
fof(f253,plain,
! [X0] : element(sK5_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f261,plain,
! [A] :
( ( upper_relstr_subset(cast_as_carrier_subset(A),A)
& lower_relstr_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) )
| ~ rel_str(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f263,plain,
! [X0] :
( lower_relstr_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f264,plain,
! [X0] :
( upper_relstr_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f267,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f268,plain,
( ! [A] : complete_relstr(boole_POSet(A))
& ! [A] : with_infima_relstr(boole_POSet(A))
& ! [A] : with_suprema_relstr(boole_POSet(A))
& ! [A] : boolean_relstr(boole_POSet(A))
& ! [A] : complemented_relstr(boole_POSet(A))
& ! [A] : heyting_relstr(boole_POSet(A))
& ! [A] : distributive_relstr(boole_POSet(A))
& ! [A] : ~ v1_yellow_3(boole_POSet(A))
& ! [A] : join_complete_relstr(boole_POSet(A))
& ! [A] : up_complete_relstr(boole_POSet(A))
& ! [A] : bounded_relstr(boole_POSet(A))
& ! [A] : upper_bounded_relstr(boole_POSet(A))
& ! [A] : lower_bounded_relstr(boole_POSet(A))
& ! [A] : antisymmetric_relstr(boole_POSet(A))
& ! [A] : transitive_relstr(boole_POSet(A))
& ! [A] : reflexive_relstr(boole_POSet(A))
& ! [A] : strict_rel_str(boole_POSet(A))
& ! [A] : ~ empty_carrier(boole_POSet(A)) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f269,plain,
! [X0] : ~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[status(thm)],[f268]) ).
fof(f289,plain,
! [A] :
( ( directed_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) )
| ~ rel_str(A)
| ~ with_suprema_relstr(A) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f291,plain,
! [X0] :
( directed_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ with_suprema_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f289]) ).
fof(f314,plain,
! [A] :
( ( directed_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) )
| ~ rel_str(A)
| ~ upper_bounded_relstr(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f61]) ).
fof(f316,plain,
! [X0] :
( directed_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f321,plain,
! [A] :
( ( filtered_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) )
| ~ rel_str(A)
| ~ with_infima_relstr(A) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f323,plain,
! [X0] :
( filtered_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ with_infima_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f321]) ).
fof(f324,plain,
! [A] :
( closed_subset(cast_as_carrier_subset(A),A)
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f325,plain,
! [X0] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f324]) ).
fof(f326,plain,
! [A] :
( ( filtered_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) )
| ~ rel_str(A)
| ~ lower_bounded_relstr(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f66]) ).
fof(f328,plain,
! [X0] :
( filtered_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f326]) ).
fof(f335,plain,
! [A] :
( ( closed_subset(cast_as_carrier_subset(A),A)
& open_subset(cast_as_carrier_subset(A),A) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f336,plain,
! [X0] :
( open_subset(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f368,plain,
! [A,B,C] :
( ( in(A,a_2_0_yellow19(B,C))
<=> ? [D] :
( A = D
& point_neighbourhood(D,B,C) ) )
| ~ element(C,the_carrier(B))
| ~ top_str(B)
| ~ topological_space(B)
| empty_carrier(B) ),
inference(pre_NNF_transformation,[status(thm)],[f72]) ).
fof(f369,plain,
! [A,B,C] :
( ( ( ! [D] :
( A != D
| ~ point_neighbourhood(D,B,C) )
| in(A,a_2_0_yellow19(B,C)) )
& ( ? [D] :
( A = D
& point_neighbourhood(D,B,C) )
| ~ in(A,a_2_0_yellow19(B,C)) ) )
| ~ element(C,the_carrier(B))
| ~ top_str(B)
| ~ topological_space(B)
| empty_carrier(B) ),
inference(NNF_transformation,[status(thm)],[f368]) ).
fof(f370,plain,
! [B,C] :
( ( ! [A] :
( ! [D] :
( A != D
| ~ point_neighbourhood(D,B,C) )
| in(A,a_2_0_yellow19(B,C)) )
& ! [A] :
( ? [D] :
( A = D
& point_neighbourhood(D,B,C) )
| ~ in(A,a_2_0_yellow19(B,C)) ) )
| ~ element(C,the_carrier(B))
| ~ top_str(B)
| ~ topological_space(B)
| empty_carrier(B) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
! [B,C] :
( ( ! [A] :
( ! [D] :
( A != D
| ~ point_neighbourhood(D,B,C) )
| in(A,a_2_0_yellow19(B,C)) )
& ! [A] :
( ( A = sK7_skl(A,C,B)
& point_neighbourhood(sK7_skl(A,C,B),B,C) )
| ~ in(A,a_2_0_yellow19(B,C)) ) )
| ~ element(C,the_carrier(B))
| ~ top_str(B)
| ~ topological_space(B)
| empty_carrier(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(D,sK7_skl(A,C,B))],[f370]) ).
fof(f372,plain,
! [X0,X1,X2] :
( point_neighbourhood(sK7_skl(X2,X1,X0),X0,X1)
| ~ in(X2,a_2_0_yellow19(X0,X1))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f373,plain,
! [X0,X1,X2] :
( X2 = sK7_skl(X2,X1,X0)
| ~ in(X2,a_2_0_yellow19(X0,X1))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f374,plain,
! [X0,X1,X2,X3] :
( X2 != X3
| ~ point_neighbourhood(X3,X0,X1)
| in(X2,a_2_0_yellow19(X0,X1))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f378,plain,
! [A] :
( ? [B] :
( upper_relstr_subset(B,A)
& filtered_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f74]) ).
fof(f379,plain,
! [A] :
( ( upper_relstr_subset(sK8_skl(A),A)
& filtered_subset(sK8_skl(A),A)
& ~ empty(sK8_skl(A))
& element(sK8_skl(A),powerset(the_carrier(A))) )
| ~ rel_str(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(B,sK8_skl(A))],[f378]) ).
fof(f380,plain,
! [X0] :
( element(sK8_skl(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f382,plain,
! [X0] :
( filtered_subset(sK8_skl(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f383,plain,
! [X0] :
( upper_relstr_subset(sK8_skl(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f384,plain,
! [A] :
( ? [B] :
( upper_relstr_subset(B,A)
& lower_relstr_subset(B,A)
& filtered_subset(B,A)
& directed_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A)
| ~ with_infima_relstr(A)
| ~ with_suprema_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f385,plain,
! [A] :
( ( upper_relstr_subset(sK9_skl(A),A)
& lower_relstr_subset(sK9_skl(A),A)
& filtered_subset(sK9_skl(A),A)
& directed_subset(sK9_skl(A),A)
& ~ empty(sK9_skl(A))
& element(sK9_skl(A),powerset(the_carrier(A))) )
| ~ rel_str(A)
| ~ with_infima_relstr(A)
| ~ with_suprema_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(B,sK9_skl(A))],[f384]) ).
fof(f386,plain,
! [X0] :
( element(sK9_skl(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f385]) ).
fof(f388,plain,
! [X0] :
( directed_subset(sK9_skl(X0),X0)
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f385]) ).
fof(f389,plain,
! [X0] :
( filtered_subset(sK9_skl(X0),X0)
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f385]) ).
fof(f390,plain,
! [X0] :
( lower_relstr_subset(sK9_skl(X0),X0)
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f385]) ).
fof(f391,plain,
! [X0] :
( upper_relstr_subset(sK9_skl(X0),X0)
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f385]) ).
fof(f392,plain,
( connected_relstr(sK10_skl)
& antisymmetric_relstr(sK10_skl)
& transitive_relstr(sK10_skl)
& reflexive_relstr(sK10_skl)
& ~ empty_carrier(sK10_skl)
& rel_str(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(A,sK10_skl)],[f76]) ).
fof(f393,plain,
rel_str(sK10_skl),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f394,plain,
~ empty_carrier(sK10_skl),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f395,plain,
reflexive_relstr(sK10_skl),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f396,plain,
transitive_relstr(sK10_skl),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f399,plain,
( join_complete_relstr(sK11_skl)
& up_complete_relstr(sK11_skl)
& bounded_relstr(sK11_skl)
& upper_bounded_relstr(sK11_skl)
& lower_bounded_relstr(sK11_skl)
& complete_relstr(sK11_skl)
& with_infima_relstr(sK11_skl)
& with_suprema_relstr(sK11_skl)
& antisymmetric_relstr(sK11_skl)
& transitive_relstr(sK11_skl)
& reflexive_relstr(sK11_skl)
& strict_rel_str(sK11_skl)
& ~ empty_carrier(sK11_skl)
& rel_str(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(A,sK11_skl)],[f77]) ).
fof(f400,plain,
rel_str(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f401,plain,
~ empty_carrier(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f402,plain,
strict_rel_str(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f403,plain,
reflexive_relstr(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f404,plain,
transitive_relstr(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f405,plain,
antisymmetric_relstr(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f406,plain,
with_suprema_relstr(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f407,plain,
with_infima_relstr(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f408,plain,
complete_relstr(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f409,plain,
lower_bounded_relstr(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f411,plain,
bounded_relstr(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f412,plain,
up_complete_relstr(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f413,plain,
join_complete_relstr(sK11_skl),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f417,plain,
( complete_relstr(sK13_skl)
& antisymmetric_relstr(sK13_skl)
& transitive_relstr(sK13_skl)
& reflexive_relstr(sK13_skl)
& strict_rel_str(sK13_skl)
& ~ empty_carrier(sK13_skl)
& rel_str(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f79]) ).
fof(f418,plain,
rel_str(sK13_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f419,plain,
~ empty_carrier(sK13_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f420,plain,
strict_rel_str(sK13_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f421,plain,
reflexive_relstr(sK13_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f422,plain,
transitive_relstr(sK13_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f424,plain,
complete_relstr(sK13_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f432,plain,
! [A] :
( ? [B] :
( open_subset(B,A)
& element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f433,plain,
! [A] :
( ( open_subset(sK16_skl(A),A)
& element(sK16_skl(A),powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(B,sK16_skl(A))],[f432]) ).
fof(f434,plain,
! [X0] :
( element(sK16_skl(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f441,plain,
( with_infima_relstr(sK18_skl)
& with_suprema_relstr(sK18_skl)
& boolean_relstr(sK18_skl)
& complemented_relstr(sK18_skl)
& heyting_relstr(sK18_skl)
& distributive_relstr(sK18_skl)
& ~ v1_yellow_3(sK18_skl)
& bounded_relstr(sK18_skl)
& upper_bounded_relstr(sK18_skl)
& lower_bounded_relstr(sK18_skl)
& antisymmetric_relstr(sK18_skl)
& transitive_relstr(sK18_skl)
& reflexive_relstr(sK18_skl)
& strict_rel_str(sK18_skl)
& ~ trivial_carrier(sK18_skl)
& ~ empty_carrier(sK18_skl)
& rel_str(sK18_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(A,sK18_skl)],[f84]) ).
fof(f442,plain,
rel_str(sK18_skl),
inference(cnf_transformation,[status(thm)],[f441]) ).
fof(f443,plain,
~ empty_carrier(sK18_skl),
inference(cnf_transformation,[status(thm)],[f441]) ).
fof(f445,plain,
strict_rel_str(sK18_skl),
inference(cnf_transformation,[status(thm)],[f441]) ).
fof(f446,plain,
reflexive_relstr(sK18_skl),
inference(cnf_transformation,[status(thm)],[f441]) ).
fof(f447,plain,
transitive_relstr(sK18_skl),
inference(cnf_transformation,[status(thm)],[f441]) ).
fof(f449,plain,
lower_bounded_relstr(sK18_skl),
inference(cnf_transformation,[status(thm)],[f441]) ).
fof(f450,plain,
upper_bounded_relstr(sK18_skl),
inference(cnf_transformation,[status(thm)],[f441]) ).
fof(f451,plain,
bounded_relstr(sK18_skl),
inference(cnf_transformation,[status(thm)],[f441]) ).
fof(f608,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f111]) ).
fof(f609,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f608]) ).
fof(f619,plain,
? [A] :
( ? [B] :
( ? [C] :
( in(C,neighborhood_system(A,B))
<~> point_neighbourhood(C,A,B) )
& element(B,the_carrier(A)) )
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f115]) ).
fof(f620,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( ~ point_neighbourhood(C,A,B)
| ~ in(C,neighborhood_system(A,B)) )
& ( point_neighbourhood(C,A,B)
| in(C,neighborhood_system(A,B)) ) )
& element(B,the_carrier(A)) )
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f619]) ).
fof(f621,plain,
( ( ~ point_neighbourhood(sK45_skl,sK43_skl,sK44_skl)
| ~ in(sK45_skl,neighborhood_system(sK43_skl,sK44_skl)) )
& ( point_neighbourhood(sK45_skl,sK43_skl,sK44_skl)
| in(sK45_skl,neighborhood_system(sK43_skl,sK44_skl)) )
& element(sK44_skl,the_carrier(sK43_skl))
& top_str(sK43_skl)
& topological_space(sK43_skl)
& ~ empty_carrier(sK43_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl,sK44_skl,sK45_skl]),skolemize(A,sK43_skl),skolemize(B,sK44_skl),skolemize(C,sK45_skl)],[f620]) ).
fof(f622,plain,
~ empty_carrier(sK43_skl),
inference(cnf_transformation,[status(thm)],[f621]) ).
fof(f623,plain,
topological_space(sK43_skl),
inference(cnf_transformation,[status(thm)],[f621]) ).
fof(f624,plain,
top_str(sK43_skl),
inference(cnf_transformation,[status(thm)],[f621]) ).
fof(f625,plain,
element(sK44_skl,the_carrier(sK43_skl)),
inference(cnf_transformation,[status(thm)],[f621]) ).
fof(f626,plain,
( point_neighbourhood(sK45_skl,sK43_skl,sK44_skl)
| in(sK45_skl,neighborhood_system(sK43_skl,sK44_skl)) ),
inference(cnf_transformation,[status(thm)],[f621]) ).
fof(f627,plain,
( ~ point_neighbourhood(sK45_skl,sK43_skl,sK44_skl)
| ~ in(sK45_skl,neighborhood_system(sK43_skl,sK44_skl)) ),
inference(cnf_transformation,[status(thm)],[f621]) ).
fof(f628,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f116]) ).
fof(f629,plain,
! [A,C] :
( element(A,C)
| ! [B] :
( ~ element(B,powerset(C))
| ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f628]) ).
fof(f630,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f629]) ).
fof(f631,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f117]) ).
fof(f632,plain,
! [C] :
( ~ empty(C)
| ! [B] :
( ~ element(B,powerset(C))
| ! [A] : ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f631]) ).
fof(f633,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f632]) ).
fof(f642,definition,
( sQ0_spl
<=> in(sK45_skl,neighborhood_system(sK43_skl,sK44_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f643,plain,
( ~ sQ0_spl
| in(sK45_skl,neighborhood_system(sK43_skl,sK44_skl)) ),
inference(component_clause,[status(thm)],[f642]) ).
fof(f644,plain,
( sQ0_spl
| ~ in(sK45_skl,neighborhood_system(sK43_skl,sK44_skl)) ),
inference(component_clause,[status(thm)],[f642]) ).
fof(f645,definition,
( sQ1_spl
<=> point_neighbourhood(sK45_skl,sK43_skl,sK44_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( ~ sQ1_spl
| point_neighbourhood(sK45_skl,sK43_skl,sK44_skl) ),
inference(component_clause,[status(thm)],[f645]) ).
fof(f648,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f626,f642,f645]) ).
fof(f649,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f627,f642,f645]) ).
fof(f654,plain,
! [X0,X1,X2] :
( ~ point_neighbourhood(X2,X0,X1)
| in(X2,a_2_0_yellow19(X0,X1))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f374]) ).
fof(f655,plain,
( element(neighborhood_system(sK43_skl,sK44_skl),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl)))))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f625,f225]) ).
fof(f656,plain,
( neighborhood_system(sK43_skl,sK44_skl) = a_2_0_yellow19(sK43_skl,sK44_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f625,f220]) ).
fof(f657,definition,
( sQ2_spl
<=> empty_carrier(sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( ~ sQ2_spl
| empty_carrier(sK43_skl) ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f660,definition,
( sQ3_spl
<=> topological_space(sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f662,plain,
( sQ3_spl
| ~ topological_space(sK43_skl) ),
inference(component_clause,[status(thm)],[f660]) ).
fof(f663,definition,
( sQ4_spl
<=> top_str(sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f665,plain,
( sQ4_spl
| ~ top_str(sK43_skl) ),
inference(component_clause,[status(thm)],[f663]) ).
fof(f666,definition,
( sQ5_spl
<=> element(neighborhood_system(sK43_skl,sK44_skl),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f667,plain,
( ~ sQ5_spl
| element(neighborhood_system(sK43_skl,sK44_skl),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))))) ),
inference(component_clause,[status(thm)],[f666]) ).
fof(f669,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f655,f657,f660,f663,f666]) ).
fof(f670,definition,
( sQ6_spl
<=> neighborhood_system(sK43_skl,sK44_skl) = a_2_0_yellow19(sK43_skl,sK44_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f671,plain,
( ~ sQ6_spl
| neighborhood_system(sK43_skl,sK44_skl) = a_2_0_yellow19(sK43_skl,sK44_skl) ),
inference(component_clause,[status(thm)],[f670]) ).
fof(f673,plain,
( sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f656,f657,f660,f663,f670]) ).
fof(f674,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f665,f624]) ).
fof(f675,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f674]) ).
fof(f676,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f662,f623]) ).
fof(f677,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f676]) ).
fof(f678,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f658,f622]) ).
fof(f679,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f678]) ).
fof(f684,plain,
( in(sK44_skl,the_carrier(sK43_skl))
| empty(the_carrier(sK43_skl)) ),
inference(resolution,[status(thm)],[f609,f625]) ).
fof(f689,definition,
( sQ8_spl
<=> empty(the_carrier(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f690,plain,
( ~ sQ8_spl
| empty(the_carrier(sK43_skl)) ),
inference(component_clause,[status(thm)],[f689]) ).
fof(f692,definition,
( sQ9_spl
<=> in(sK44_skl,the_carrier(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f695,plain,
( sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f684,f689,f692]) ).
fof(f698,plain,
( ~ sQ5_spl
| in(neighborhood_system(sK43_skl,sK44_skl),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl)))))
| empty(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))))) ),
inference(resolution,[status(thm)],[f667,f609]) ).
fof(f699,definition,
( sQ10_spl
<=> empty(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f700,plain,
( ~ sQ10_spl
| empty(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))))) ),
inference(component_clause,[status(thm)],[f699]) ).
fof(f702,definition,
( sQ11_spl
<=> in(neighborhood_system(sK43_skl,sK44_skl),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f705,plain,
( ~ sQ5_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f698,f699,f702,f666]) ).
fof(f706,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f700,f267]) ).
fof(f707,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f706]) ).
fof(f727,plain,
( ~ sQ8_spl
| finite(the_carrier(sK43_skl)) ),
inference(resolution,[status(thm)],[f690,f157]) ).
fof(f738,definition,
( sQ16_spl
<=> empty_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f739,plain,
( ~ sQ16_spl
| empty_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))) ),
inference(component_clause,[status(thm)],[f738]) ).
fof(f771,plain,
( ~ sQ1_spl
| element(sK45_skl,powerset(the_carrier(sK43_skl)))
| ~ element(sK44_skl,the_carrier(sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f646,f236]) ).
fof(f772,definition,
( sQ24_spl
<=> element(sK44_skl,the_carrier(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f774,plain,
( sQ24_spl
| ~ element(sK44_skl,the_carrier(sK43_skl)) ),
inference(component_clause,[status(thm)],[f772]) ).
fof(f775,definition,
( sQ25_spl
<=> element(sK45_skl,powerset(the_carrier(sK43_skl))) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f776,plain,
( ~ sQ25_spl
| element(sK45_skl,powerset(the_carrier(sK43_skl))) ),
inference(component_clause,[status(thm)],[f775]) ).
fof(f778,plain,
( ~ sQ1_spl
| sQ25_spl
| ~ sQ24_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f771,f657,f660,f663,f772,f775,f645]) ).
fof(f779,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f774,f625]) ).
fof(f780,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f779]) ).
fof(f781,plain,
( ~ sQ25_spl
| boundary_set(sK45_skl,sK43_skl)
| ~ empty(sK45_skl)
| ~ top_str(sK43_skl) ),
inference(resolution,[status(thm)],[f776,f177]) ).
fof(f782,plain,
( ~ sQ25_spl
| closed_subset(sK45_skl,sK43_skl)
| ~ empty(sK45_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f776,f167]) ).
fof(f783,plain,
( ~ sQ25_spl
| open_subset(sK45_skl,sK43_skl)
| ~ empty(sK45_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f776,f166]) ).
fof(f784,plain,
( ~ sQ25_spl
| finite(sK45_skl)
| ~ finite(the_carrier(sK43_skl)) ),
inference(resolution,[status(thm)],[f776,f173]) ).
fof(f785,plain,
( ~ sQ25_spl
| in(sK45_skl,powerset(the_carrier(sK43_skl)))
| empty(powerset(the_carrier(sK43_skl))) ),
inference(resolution,[status(thm)],[f776,f609]) ).
fof(f786,definition,
( sQ26_spl
<=> empty(sK45_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f789,definition,
( sQ27_spl
<=> boundary_set(sK45_skl,sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f792,plain,
( ~ sQ25_spl
| sQ27_spl
| ~ sQ26_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f781,f663,f786,f789,f775]) ).
fof(f793,definition,
( sQ28_spl
<=> closed_subset(sK45_skl,sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f796,plain,
( ~ sQ25_spl
| sQ28_spl
| ~ sQ26_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f782,f660,f663,f786,f793,f775]) ).
fof(f797,definition,
( sQ29_spl
<=> open_subset(sK45_skl,sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f800,plain,
( ~ sQ25_spl
| sQ29_spl
| ~ sQ26_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f783,f660,f663,f786,f797,f775]) ).
fof(f801,definition,
( sQ30_spl
<=> finite(the_carrier(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f803,plain,
( sQ30_spl
| ~ finite(the_carrier(sK43_skl)) ),
inference(component_clause,[status(thm)],[f801]) ).
fof(f804,definition,
( sQ31_spl
<=> finite(sK45_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f807,plain,
( ~ sQ25_spl
| sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f784,f801,f804,f775]) ).
fof(f808,definition,
( sQ32_spl
<=> empty(powerset(the_carrier(sK43_skl))) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f809,plain,
( ~ sQ32_spl
| empty(powerset(the_carrier(sK43_skl))) ),
inference(component_clause,[status(thm)],[f808]) ).
fof(f811,definition,
( sQ33_spl
<=> in(sK45_skl,powerset(the_carrier(sK43_skl))) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f814,plain,
( ~ sQ25_spl
| sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f785,f808,f811,f775]) ).
fof(f815,plain,
( sQ30_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f803,f727]) ).
fof(f816,plain,
( sQ30_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f815]) ).
fof(f817,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f809,f267]) ).
fof(f818,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f817]) ).
fof(f825,definition,
( sQ34_spl
<=> rel_str(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f827,plain,
( sQ34_spl
| ~ rel_str(sK10_skl) ),
inference(component_clause,[status(thm)],[f825]) ).
fof(f828,definition,
( sQ35_spl
<=> empty_carrier(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f829,plain,
( ~ sQ35_spl
| empty_carrier(sK10_skl) ),
inference(component_clause,[status(thm)],[f828]) ).
fof(f831,definition,
( sQ36_spl
<=> reflexive_relstr(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f833,plain,
( sQ36_spl
| ~ reflexive_relstr(sK10_skl) ),
inference(component_clause,[status(thm)],[f831]) ).
fof(f841,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f739,f269]) ).
fof(f842,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f841]) ).
fof(f845,definition,
( sQ39_spl
<=> nowhere_dense(sK45_skl,sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f853,plain,
( ~ sQ25_spl
| boundary_set(sK45_skl,sK43_skl)
| ~ nowhere_dense(sK45_skl,sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f190,f776]) ).
fof(f855,plain,
( ~ sQ25_spl
| sQ27_spl
| ~ sQ39_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f853,f660,f663,f845,f789,f775]) ).
fof(f862,plain,
( sK11_skl = rel_str_of(the_carrier(sK11_skl),the_InternalRel(sK11_skl))
| ~ rel_str(sK11_skl) ),
inference(resolution,[status(thm)],[f402,f122]) ).
fof(f863,definition,
( sQ41_spl
<=> rel_str(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f865,plain,
( sQ41_spl
| ~ rel_str(sK11_skl) ),
inference(component_clause,[status(thm)],[f863]) ).
fof(f866,definition,
( sQ42_spl
<=> sK11_skl = rel_str_of(the_carrier(sK11_skl),the_InternalRel(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f869,plain,
( sQ42_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f862,f863,f866]) ).
fof(f870,plain,
( sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f865,f400]) ).
fof(f871,plain,
sQ41_spl,
inference(contradiction_clause,[status(thm)],[f870]) ).
fof(f872,plain,
( ~ sQ25_spl
| nowhere_dense(sK45_skl,sK43_skl)
| ~ boundary_set(sK45_skl,sK43_skl)
| ~ closed_subset(sK45_skl,sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f196,f776]) ).
fof(f874,plain,
( ~ sQ25_spl
| sQ39_spl
| ~ sQ27_spl
| ~ sQ28_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f872,f660,f663,f793,f789,f845,f775]) ).
fof(f876,plain,
( ~ sQ25_spl
| empty(sK45_skl)
| ~ nowhere_dense(sK45_skl,sK43_skl)
| ~ open_subset(sK45_skl,sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f204,f776]) ).
fof(f878,plain,
( ~ sQ25_spl
| sQ26_spl
| ~ sQ39_spl
| ~ sQ29_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f876,f660,f663,f797,f845,f786,f775]) ).
fof(f884,plain,
( ~ sQ25_spl
| v1_membered(sK45_skl)
| ~ nowhere_dense(sK45_skl,sK43_skl)
| ~ open_subset(sK45_skl,sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f207,f776]) ).
fof(f886,definition,
( sQ43_spl
<=> v1_membered(sK45_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f889,plain,
( ~ sQ25_spl
| sQ43_spl
| ~ sQ39_spl
| ~ sQ29_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f884,f660,f663,f797,f845,f886,f775]) ).
fof(f895,definition,
( sQ45_spl
<=> empty_carrier(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f896,plain,
( ~ sQ45_spl
| empty_carrier(sK11_skl) ),
inference(component_clause,[status(thm)],[f895]) ).
fof(f898,definition,
( sQ46_spl
<=> reflexive_relstr(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f900,plain,
( sQ46_spl
| ~ reflexive_relstr(sK11_skl) ),
inference(component_clause,[status(thm)],[f898]) ).
fof(f901,definition,
( sQ47_spl
<=> join_complete_relstr(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f903,plain,
( sQ47_spl
| ~ join_complete_relstr(sK11_skl) ),
inference(component_clause,[status(thm)],[f901]) ).
fof(f904,definition,
( sQ48_spl
<=> with_infima_relstr(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f908,plain,
( sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f903,f413]) ).
fof(f909,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f908]) ).
fof(f910,plain,
( sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f900,f403]) ).
fof(f911,plain,
sQ46_spl,
inference(contradiction_clause,[status(thm)],[f910]) ).
fof(f912,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f896,f401]) ).
fof(f913,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f912]) ).
fof(f914,plain,
( ~ sQ25_spl
| v2_membered(sK45_skl)
| ~ nowhere_dense(sK45_skl,sK43_skl)
| ~ open_subset(sK45_skl,sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f208,f776]) ).
fof(f916,definition,
( sQ49_spl
<=> v2_membered(sK45_skl) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f919,plain,
( ~ sQ25_spl
| sQ49_spl
| ~ sQ39_spl
| ~ sQ29_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f914,f660,f663,f797,f845,f916,f775]) ).
fof(f924,plain,
( ~ sQ25_spl
| v3_membered(sK45_skl)
| ~ nowhere_dense(sK45_skl,sK43_skl)
| ~ open_subset(sK45_skl,sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f209,f776]) ).
fof(f926,definition,
( sQ51_spl
<=> v3_membered(sK45_skl) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f929,plain,
( ~ sQ25_spl
| sQ51_spl
| ~ sQ39_spl
| ~ sQ29_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f924,f660,f663,f797,f845,f926,f775]) ).
fof(f934,plain,
( ~ sQ25_spl
| v4_membered(sK45_skl)
| ~ nowhere_dense(sK45_skl,sK43_skl)
| ~ open_subset(sK45_skl,sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f210,f776]) ).
fof(f936,definition,
( sQ53_spl
<=> v4_membered(sK45_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f939,plain,
( ~ sQ25_spl
| sQ53_spl
| ~ sQ39_spl
| ~ sQ29_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f934,f660,f663,f797,f845,f936,f775]) ).
fof(f944,plain,
( ~ sQ25_spl
| v5_membered(sK45_skl)
| ~ nowhere_dense(sK45_skl,sK43_skl)
| ~ open_subset(sK45_skl,sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f211,f776]) ).
fof(f946,definition,
( sQ55_spl
<=> v5_membered(sK45_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f949,plain,
( ~ sQ25_spl
| sQ55_spl
| ~ sQ39_spl
| ~ sQ29_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f944,f660,f663,f797,f845,f946,f775]) ).
fof(f956,definition,
( sQ57_spl
<=> up_complete_relstr(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f958,plain,
( sQ57_spl
| ~ up_complete_relstr(sK11_skl) ),
inference(component_clause,[status(thm)],[f956]) ).
fof(f959,definition,
( sQ58_spl
<=> upper_bounded_relstr(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f964,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f958,f412]) ).
fof(f965,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f964]) ).
fof(f968,plain,
( bounded_relstr(sK11_skl)
| empty_carrier(sK11_skl)
| ~ rel_str(sK11_skl) ),
inference(resolution,[status(thm)],[f408,f188]) ).
fof(f969,plain,
( with_infima_relstr(sK11_skl)
| empty_carrier(sK11_skl)
| ~ rel_str(sK11_skl) ),
inference(resolution,[status(thm)],[f408,f171]) ).
fof(f970,plain,
( with_suprema_relstr(sK11_skl)
| empty_carrier(sK11_skl)
| ~ rel_str(sK11_skl) ),
inference(resolution,[status(thm)],[f408,f170]) ).
fof(f973,definition,
( sQ59_spl
<=> bounded_relstr(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f976,plain,
( sQ59_spl
| sQ45_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f968,f863,f895,f973]) ).
fof(f977,plain,
( sQ48_spl
| sQ45_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f969,f863,f895,f904]) ).
fof(f978,definition,
( sQ60_spl
<=> with_suprema_relstr(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f981,plain,
( sQ60_spl
| sQ45_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f970,f863,f895,f978]) ).
fof(f992,plain,
one_sorted_str(sK43_skl),
inference(resolution,[status(thm)],[f234,f624]) ).
fof(f993,plain,
element(cast_as_carrier_subset(sK43_skl),powerset(the_carrier(sK43_skl))),
inference(resolution,[status(thm)],[f992,f227]) ).
fof(f994,plain,
( v5_membered(cast_as_carrier_subset(sK43_skl))
| ~ nowhere_dense(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ open_subset(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f993,f211]) ).
fof(f995,plain,
( v4_membered(cast_as_carrier_subset(sK43_skl))
| ~ nowhere_dense(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ open_subset(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f993,f210]) ).
fof(f996,plain,
( v3_membered(cast_as_carrier_subset(sK43_skl))
| ~ nowhere_dense(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ open_subset(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f993,f209]) ).
fof(f997,plain,
( v2_membered(cast_as_carrier_subset(sK43_skl))
| ~ nowhere_dense(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ open_subset(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f993,f208]) ).
fof(f998,plain,
( v1_membered(cast_as_carrier_subset(sK43_skl))
| ~ nowhere_dense(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ open_subset(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f993,f207]) ).
fof(f1002,plain,
( boundary_set(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ nowhere_dense(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f993,f190]) ).
fof(f1003,plain,
( nowhere_dense(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ empty(cast_as_carrier_subset(sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f993,f185]) ).
fof(f1007,plain,
( finite(cast_as_carrier_subset(sK43_skl))
| ~ finite(the_carrier(sK43_skl)) ),
inference(resolution,[status(thm)],[f993,f173]) ).
fof(f1008,plain,
( in(cast_as_carrier_subset(sK43_skl),powerset(the_carrier(sK43_skl)))
| empty(powerset(the_carrier(sK43_skl))) ),
inference(resolution,[status(thm)],[f993,f609]) ).
fof(f1009,definition,
( sQ61_spl
<=> open_subset(cast_as_carrier_subset(sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1012,definition,
( sQ62_spl
<=> nowhere_dense(cast_as_carrier_subset(sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1015,definition,
( sQ63_spl
<=> v5_membered(cast_as_carrier_subset(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1018,plain,
( sQ63_spl
| ~ sQ62_spl
| ~ sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f994,f660,f663,f1009,f1012,f1015]) ).
fof(f1019,definition,
( sQ64_spl
<=> v4_membered(cast_as_carrier_subset(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1022,plain,
( sQ64_spl
| ~ sQ62_spl
| ~ sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f995,f660,f663,f1009,f1012,f1019]) ).
fof(f1023,definition,
( sQ65_spl
<=> v3_membered(cast_as_carrier_subset(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1026,plain,
( sQ65_spl
| ~ sQ62_spl
| ~ sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f996,f660,f663,f1009,f1012,f1023]) ).
fof(f1027,definition,
( sQ66_spl
<=> v2_membered(cast_as_carrier_subset(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1030,plain,
( sQ66_spl
| ~ sQ62_spl
| ~ sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f997,f660,f663,f1009,f1012,f1027]) ).
fof(f1031,definition,
( sQ67_spl
<=> v1_membered(cast_as_carrier_subset(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1034,plain,
( sQ67_spl
| ~ sQ62_spl
| ~ sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f998,f660,f663,f1009,f1012,f1031]) ).
fof(f1035,definition,
( sQ68_spl
<=> closed_subset(cast_as_carrier_subset(sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1039,definition,
( sQ69_spl
<=> empty(cast_as_carrier_subset(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1043,definition,
( sQ70_spl
<=> boundary_set(cast_as_carrier_subset(sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1047,plain,
( sQ70_spl
| ~ sQ62_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1002,f660,f663,f1012,f1043]) ).
fof(f1048,plain,
( sQ62_spl
| ~ sQ69_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1003,f660,f663,f1039,f1012]) ).
fof(f1052,definition,
( sQ71_spl
<=> finite(cast_as_carrier_subset(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1055,plain,
( sQ71_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1007,f801,f1052]) ).
fof(f1056,definition,
( sQ72_spl
<=> in(cast_as_carrier_subset(sK43_skl),powerset(the_carrier(sK43_skl))) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1059,plain,
( sQ72_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1008,f808,f1056]) ).
fof(f1067,definition,
( sQ73_spl
<=> lower_bounded_relstr(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1069,plain,
( sQ73_spl
| ~ lower_bounded_relstr(sK11_skl) ),
inference(component_clause,[status(thm)],[f1067]) ).
fof(f1071,definition,
( sQ74_spl
<=> antisymmetric_relstr(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1073,plain,
( sQ74_spl
| ~ antisymmetric_relstr(sK11_skl) ),
inference(component_clause,[status(thm)],[f1071]) ).
fof(f1075,plain,
( sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1069,f409]) ).
fof(f1076,plain,
sQ73_spl,
inference(contradiction_clause,[status(thm)],[f1075]) ).
fof(f1077,plain,
( upper_bounded_relstr(sK11_skl)
| ~ rel_str(sK11_skl) ),
inference(resolution,[status(thm)],[f411,f193]) ).
fof(f1079,plain,
( sQ58_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f1077,f863,f959]) ).
fof(f1085,plain,
( point_neighbourhood(sK3_skl(sK44_skl,sK43_skl),sK43_skl,sK44_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f249,f625]) ).
fof(f1086,definition,
( sQ75_spl
<=> point_neighbourhood(sK3_skl(sK44_skl,sK43_skl),sK43_skl,sK44_skl) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1087,plain,
( ~ sQ75_spl
| point_neighbourhood(sK3_skl(sK44_skl,sK43_skl),sK43_skl,sK44_skl) ),
inference(component_clause,[status(thm)],[f1086]) ).
fof(f1089,plain,
( sQ75_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1085,f657,f660,f663,f1086]) ).
fof(f1108,plain,
! [X0] :
( element(neighborhood_system(X0,sK5_skl(the_carrier(X0))),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f253,f225]) ).
fof(f1109,plain,
! [X0] :
( neighborhood_system(X0,sK5_skl(the_carrier(X0))) = a_2_0_yellow19(X0,sK5_skl(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f253,f220]) ).
fof(f1110,plain,
! [X0] :
( in(sK5_skl(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f253,f609]) ).
fof(f1112,plain,
( ~ sQ75_spl
| element(sK3_skl(sK44_skl,sK43_skl),powerset(the_carrier(sK43_skl)))
| ~ element(sK44_skl,the_carrier(sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f1087,f236]) ).
fof(f1113,definition,
( sQ76_spl
<=> element(sK3_skl(sK44_skl,sK43_skl),powerset(the_carrier(sK43_skl))) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1114,plain,
( ~ sQ76_spl
| element(sK3_skl(sK44_skl,sK43_skl),powerset(the_carrier(sK43_skl))) ),
inference(component_clause,[status(thm)],[f1113]) ).
fof(f1116,plain,
( ~ sQ75_spl
| sQ76_spl
| ~ sQ24_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1112,f657,f660,f663,f772,f1113,f1086]) ).
fof(f1117,plain,
( ~ sQ76_spl
| v5_membered(sK3_skl(sK44_skl,sK43_skl))
| ~ nowhere_dense(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ open_subset(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1114,f211]) ).
fof(f1118,plain,
( ~ sQ76_spl
| v4_membered(sK3_skl(sK44_skl,sK43_skl))
| ~ nowhere_dense(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ open_subset(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1114,f210]) ).
fof(f1119,plain,
( ~ sQ76_spl
| v3_membered(sK3_skl(sK44_skl,sK43_skl))
| ~ nowhere_dense(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ open_subset(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1114,f209]) ).
fof(f1120,plain,
( ~ sQ76_spl
| v2_membered(sK3_skl(sK44_skl,sK43_skl))
| ~ nowhere_dense(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ open_subset(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1114,f208]) ).
fof(f1121,plain,
( ~ sQ76_spl
| v1_membered(sK3_skl(sK44_skl,sK43_skl))
| ~ nowhere_dense(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ open_subset(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1114,f207]) ).
fof(f1125,plain,
( ~ sQ76_spl
| boundary_set(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ nowhere_dense(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1114,f190]) ).
fof(f1126,plain,
( ~ sQ76_spl
| nowhere_dense(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ empty(sK3_skl(sK44_skl,sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1114,f185]) ).
fof(f1128,plain,
( ~ sQ76_spl
| closed_subset(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ empty(sK3_skl(sK44_skl,sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1114,f167]) ).
fof(f1129,plain,
( ~ sQ76_spl
| open_subset(sK3_skl(sK44_skl,sK43_skl),sK43_skl)
| ~ empty(sK3_skl(sK44_skl,sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1114,f166]) ).
fof(f1130,plain,
( ~ sQ76_spl
| finite(sK3_skl(sK44_skl,sK43_skl))
| ~ finite(the_carrier(sK43_skl)) ),
inference(resolution,[status(thm)],[f1114,f173]) ).
fof(f1131,plain,
( ~ sQ76_spl
| in(sK3_skl(sK44_skl,sK43_skl),powerset(the_carrier(sK43_skl)))
| empty(powerset(the_carrier(sK43_skl))) ),
inference(resolution,[status(thm)],[f1114,f609]) ).
fof(f1132,definition,
( sQ77_spl
<=> open_subset(sK3_skl(sK44_skl,sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1135,definition,
( sQ78_spl
<=> nowhere_dense(sK3_skl(sK44_skl,sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1138,definition,
( sQ79_spl
<=> v5_membered(sK3_skl(sK44_skl,sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1141,plain,
( ~ sQ76_spl
| sQ79_spl
| ~ sQ78_spl
| ~ sQ77_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1117,f660,f663,f1132,f1135,f1138,f1113]) ).
fof(f1142,definition,
( sQ80_spl
<=> v4_membered(sK3_skl(sK44_skl,sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1145,plain,
( ~ sQ76_spl
| sQ80_spl
| ~ sQ78_spl
| ~ sQ77_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1118,f660,f663,f1132,f1135,f1142,f1113]) ).
fof(f1146,definition,
( sQ81_spl
<=> v3_membered(sK3_skl(sK44_skl,sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1149,plain,
( ~ sQ76_spl
| sQ81_spl
| ~ sQ78_spl
| ~ sQ77_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1119,f660,f663,f1132,f1135,f1146,f1113]) ).
fof(f1150,definition,
( sQ82_spl
<=> v2_membered(sK3_skl(sK44_skl,sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1153,plain,
( ~ sQ76_spl
| sQ82_spl
| ~ sQ78_spl
| ~ sQ77_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1120,f660,f663,f1132,f1135,f1150,f1113]) ).
fof(f1154,definition,
( sQ83_spl
<=> v1_membered(sK3_skl(sK44_skl,sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1157,plain,
( ~ sQ76_spl
| sQ83_spl
| ~ sQ78_spl
| ~ sQ77_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1121,f660,f663,f1132,f1135,f1154,f1113]) ).
fof(f1158,definition,
( sQ84_spl
<=> closed_subset(sK3_skl(sK44_skl,sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1162,definition,
( sQ85_spl
<=> empty(sK3_skl(sK44_skl,sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1166,definition,
( sQ86_spl
<=> boundary_set(sK3_skl(sK44_skl,sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1170,plain,
( ~ sQ76_spl
| sQ86_spl
| ~ sQ78_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1125,f660,f663,f1135,f1166,f1113]) ).
fof(f1171,plain,
( ~ sQ76_spl
| sQ78_spl
| ~ sQ85_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1126,f660,f663,f1162,f1135,f1113]) ).
fof(f1173,plain,
( ~ sQ76_spl
| sQ84_spl
| ~ sQ85_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1128,f660,f663,f1162,f1158,f1113]) ).
fof(f1174,plain,
( ~ sQ76_spl
| sQ77_spl
| ~ sQ85_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1129,f660,f663,f1162,f1132,f1113]) ).
fof(f1175,definition,
( sQ87_spl
<=> finite(sK3_skl(sK44_skl,sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1178,plain,
( ~ sQ76_spl
| sQ87_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1130,f801,f1175,f1113]) ).
fof(f1179,definition,
( sQ88_spl
<=> in(sK3_skl(sK44_skl,sK43_skl),powerset(the_carrier(sK43_skl))) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1182,plain,
( ~ sQ76_spl
| sQ88_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1131,f808,f1179,f1113]) ).
fof(f1184,plain,
( element(neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl))),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl)))))
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f1108,f624]) ).
fof(f1195,definition,
( sQ92_spl
<=> element(neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl))),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1196,plain,
( ~ sQ92_spl
| element(neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl))),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))))) ),
inference(component_clause,[status(thm)],[f1195]) ).
fof(f1198,plain,
( sQ92_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1184,f657,f660,f1195]) ).
fof(f1200,plain,
( neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl))) = a_2_0_yellow19(sK43_skl,sK5_skl(the_carrier(sK43_skl)))
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f1109,f624]) ).
fof(f1205,definition,
( sQ94_spl
<=> neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl))) = a_2_0_yellow19(sK43_skl,sK5_skl(the_carrier(sK43_skl))) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1206,plain,
( ~ sQ94_spl
| neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl))) = a_2_0_yellow19(sK43_skl,sK5_skl(the_carrier(sK43_skl))) ),
inference(component_clause,[status(thm)],[f1205]) ).
fof(f1208,plain,
( sQ94_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1200,f657,f660,f1205]) ).
fof(f1209,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ element(X0,powerset(X1))
| empty(X0) ),
inference(resolution,[status(thm)],[f1110,f633]) ).
fof(f1210,plain,
! [X0,X1] :
( element(sK5_skl(X0),X1)
| ~ element(X0,powerset(X1))
| empty(X0) ),
inference(resolution,[status(thm)],[f1110,f630]) ).
fof(f1228,plain,
( ~ sQ92_spl
| in(neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl))),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl)))))
| empty(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))))) ),
inference(resolution,[status(thm)],[f1196,f609]) ).
fof(f1276,definition,
( sQ106_spl
<=> in(neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl))),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1279,plain,
( ~ sQ92_spl
| sQ106_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f1228,f699,f1276,f1195]) ).
fof(f1285,plain,
( lower_relstr_subset(cast_as_carrier_subset(sK11_skl),sK11_skl)
| empty_carrier(sK11_skl) ),
inference(resolution,[status(thm)],[f263,f400]) ).
fof(f1286,plain,
( lower_relstr_subset(cast_as_carrier_subset(sK10_skl),sK10_skl)
| empty_carrier(sK10_skl) ),
inference(resolution,[status(thm)],[f263,f393]) ).
fof(f1289,definition,
( sQ107_spl
<=> lower_relstr_subset(cast_as_carrier_subset(sK11_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1292,plain,
( sQ107_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1285,f895,f1289]) ).
fof(f1293,definition,
( sQ108_spl
<=> lower_relstr_subset(cast_as_carrier_subset(sK10_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1296,plain,
( sQ108_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f1286,f828,f1293]) ).
fof(f1304,plain,
( ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f829,f394]) ).
fof(f1305,plain,
~ sQ35_spl,
inference(contradiction_clause,[status(thm)],[f1304]) ).
fof(f1307,plain,
( upper_relstr_subset(cast_as_carrier_subset(sK11_skl),sK11_skl)
| empty_carrier(sK11_skl) ),
inference(resolution,[status(thm)],[f264,f400]) ).
fof(f1308,plain,
( upper_relstr_subset(cast_as_carrier_subset(sK10_skl),sK10_skl)
| empty_carrier(sK10_skl) ),
inference(resolution,[status(thm)],[f264,f393]) ).
fof(f1311,definition,
( sQ111_spl
<=> upper_relstr_subset(cast_as_carrier_subset(sK11_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1314,plain,
( sQ111_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1307,f895,f1311]) ).
fof(f1315,definition,
( sQ112_spl
<=> upper_relstr_subset(cast_as_carrier_subset(sK10_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1318,plain,
( sQ112_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f1308,f828,f1315]) ).
fof(f1324,plain,
( ~ sQ76_spl
| ~ empty(the_carrier(sK43_skl))
| empty(sK3_skl(sK44_skl,sK43_skl)) ),
inference(resolution,[status(thm)],[f1209,f1114]) ).
fof(f1326,plain,
( ~ empty(the_carrier(sK43_skl))
| empty(cast_as_carrier_subset(sK43_skl)) ),
inference(resolution,[status(thm)],[f1209,f993]) ).
fof(f1327,plain,
( ~ sQ25_spl
| ~ empty(the_carrier(sK43_skl))
| empty(sK45_skl) ),
inference(resolution,[status(thm)],[f1209,f776]) ).
fof(f1330,plain,
( ~ sQ76_spl
| ~ sQ8_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1324,f1162,f689,f1113]) ).
fof(f1331,plain,
( ~ sQ8_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1326,f1039,f689]) ).
fof(f1332,plain,
( ~ sQ25_spl
| ~ sQ8_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f1327,f786,f689,f775]) ).
fof(f1338,plain,
( ~ sQ25_spl
| element(sK5_skl(sK45_skl),the_carrier(sK43_skl))
| empty(sK45_skl) ),
inference(resolution,[status(thm)],[f1210,f776]) ).
fof(f1349,definition,
( sQ116_spl
<=> element(sK5_skl(sK45_skl),the_carrier(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1350,plain,
( ~ sQ116_spl
| element(sK5_skl(sK45_skl),the_carrier(sK43_skl)) ),
inference(component_clause,[status(thm)],[f1349]) ).
fof(f1352,plain,
( ~ sQ25_spl
| sQ116_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f1338,f786,f1349,f775]) ).
fof(f1362,plain,
( upper_relstr_subset(cast_as_carrier_subset(sK13_skl),sK13_skl)
| empty_carrier(sK13_skl) ),
inference(resolution,[status(thm)],[f418,f264]) ).
fof(f1363,plain,
( lower_relstr_subset(cast_as_carrier_subset(sK13_skl),sK13_skl)
| empty_carrier(sK13_skl) ),
inference(resolution,[status(thm)],[f418,f263]) ).
fof(f1366,definition,
( sQ119_spl
<=> empty_carrier(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1367,plain,
( ~ sQ119_spl
| empty_carrier(sK13_skl) ),
inference(component_clause,[status(thm)],[f1366]) ).
fof(f1369,definition,
( sQ120_spl
<=> upper_relstr_subset(cast_as_carrier_subset(sK13_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1372,plain,
( sQ120_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f1362,f1366,f1369]) ).
fof(f1373,definition,
( sQ121_spl
<=> lower_relstr_subset(cast_as_carrier_subset(sK13_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1376,plain,
( sQ121_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f1363,f1366,f1373]) ).
fof(f1377,plain,
( ~ sQ119_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1367,f419]) ).
fof(f1378,plain,
~ sQ119_spl,
inference(contradiction_clause,[status(thm)],[f1377]) ).
fof(f1463,definition,
( sQ138_spl
<=> empty(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK1_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1464,plain,
( ~ sQ138_spl
| empty(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK1_skl))))) ),
inference(component_clause,[status(thm)],[f1463]) ).
fof(f1470,plain,
( ~ sQ138_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1464,f267]) ).
fof(f1471,plain,
~ sQ138_spl,
inference(contradiction_clause,[status(thm)],[f1470]) ).
fof(f1472,plain,
( sK13_skl = rel_str_of(the_carrier(sK13_skl),the_InternalRel(sK13_skl))
| ~ rel_str(sK13_skl) ),
inference(resolution,[status(thm)],[f420,f122]) ).
fof(f1473,definition,
( sQ140_spl
<=> rel_str(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1475,plain,
( sQ140_spl
| ~ rel_str(sK13_skl) ),
inference(component_clause,[status(thm)],[f1473]) ).
fof(f1476,definition,
( sQ141_spl
<=> sK13_skl = rel_str_of(the_carrier(sK13_skl),the_InternalRel(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1479,plain,
( sQ141_spl
| ~ sQ140_spl ),
inference(split_clause,[status(thm)],[f1472,f1473,f1476]) ).
fof(f1480,plain,
( sQ140_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1475,f418]) ).
fof(f1481,plain,
sQ140_spl,
inference(contradiction_clause,[status(thm)],[f1480]) ).
fof(f1494,definition,
( sQ142_spl
<=> reflexive_relstr(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1496,plain,
( sQ142_spl
| ~ reflexive_relstr(sK13_skl) ),
inference(component_clause,[status(thm)],[f1494]) ).
fof(f1497,definition,
( sQ143_spl
<=> join_complete_relstr(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1500,definition,
( sQ144_spl
<=> with_infima_relstr(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1504,plain,
( sQ142_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1496,f421]) ).
fof(f1505,plain,
sQ142_spl,
inference(contradiction_clause,[status(thm)],[f1504]) ).
fof(f1506,plain,
( bounded_relstr(sK13_skl)
| empty_carrier(sK13_skl)
| ~ rel_str(sK13_skl) ),
inference(resolution,[status(thm)],[f424,f188]) ).
fof(f1507,plain,
( with_infima_relstr(sK13_skl)
| empty_carrier(sK13_skl)
| ~ rel_str(sK13_skl) ),
inference(resolution,[status(thm)],[f424,f171]) ).
fof(f1508,plain,
( with_suprema_relstr(sK13_skl)
| empty_carrier(sK13_skl)
| ~ rel_str(sK13_skl) ),
inference(resolution,[status(thm)],[f424,f170]) ).
fof(f1509,plain,
( join_complete_relstr(sK13_skl)
| ~ reflexive_relstr(sK13_skl)
| empty_carrier(sK13_skl)
| ~ rel_str(sK13_skl) ),
inference(resolution,[status(thm)],[f424,f129]) ).
fof(f1510,plain,
( up_complete_relstr(sK13_skl)
| ~ reflexive_relstr(sK13_skl)
| empty_carrier(sK13_skl)
| ~ rel_str(sK13_skl) ),
inference(resolution,[status(thm)],[f424,f128]) ).
fof(f1511,definition,
( sQ145_spl
<=> bounded_relstr(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1514,plain,
( sQ145_spl
| sQ119_spl
| ~ sQ140_spl ),
inference(split_clause,[status(thm)],[f1506,f1473,f1366,f1511]) ).
fof(f1515,plain,
( sQ144_spl
| sQ119_spl
| ~ sQ140_spl ),
inference(split_clause,[status(thm)],[f1507,f1473,f1366,f1500]) ).
fof(f1516,definition,
( sQ146_spl
<=> with_suprema_relstr(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1519,plain,
( sQ146_spl
| sQ119_spl
| ~ sQ140_spl ),
inference(split_clause,[status(thm)],[f1508,f1473,f1366,f1516]) ).
fof(f1520,plain,
( sQ143_spl
| ~ sQ142_spl
| sQ119_spl
| ~ sQ140_spl ),
inference(split_clause,[status(thm)],[f1509,f1473,f1366,f1494,f1497]) ).
fof(f1521,definition,
( sQ147_spl
<=> up_complete_relstr(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1524,plain,
( sQ147_spl
| ~ sQ142_spl
| sQ119_spl
| ~ sQ140_spl ),
inference(split_clause,[status(thm)],[f1510,f1473,f1366,f1494,f1521]) ).
fof(f1541,plain,
( upper_relstr_subset(cast_as_carrier_subset(sK18_skl),sK18_skl)
| empty_carrier(sK18_skl) ),
inference(resolution,[status(thm)],[f442,f264]) ).
fof(f1542,plain,
( lower_relstr_subset(cast_as_carrier_subset(sK18_skl),sK18_skl)
| empty_carrier(sK18_skl) ),
inference(resolution,[status(thm)],[f442,f263]) ).
fof(f1545,definition,
( sQ148_spl
<=> empty_carrier(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1546,plain,
( ~ sQ148_spl
| empty_carrier(sK18_skl) ),
inference(component_clause,[status(thm)],[f1545]) ).
fof(f1548,definition,
( sQ149_spl
<=> upper_relstr_subset(cast_as_carrier_subset(sK18_skl),sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1551,plain,
( sQ149_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1541,f1545,f1548]) ).
fof(f1552,definition,
( sQ150_spl
<=> lower_relstr_subset(cast_as_carrier_subset(sK18_skl),sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1555,plain,
( sQ150_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1542,f1545,f1552]) ).
fof(f1556,plain,
( ~ sQ148_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1546,f443]) ).
fof(f1557,plain,
~ sQ148_spl,
inference(contradiction_clause,[status(thm)],[f1556]) ).
fof(f1559,plain,
( directed_subset(cast_as_carrier_subset(sK11_skl),sK11_skl)
| ~ rel_str(sK11_skl) ),
inference(resolution,[status(thm)],[f291,f406]) ).
fof(f1561,definition,
( sQ151_spl
<=> directed_subset(cast_as_carrier_subset(sK11_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1564,plain,
( sQ151_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f1559,f863,f1561]) ).
fof(f1569,plain,
( sK18_skl = rel_str_of(the_carrier(sK18_skl),the_InternalRel(sK18_skl))
| ~ rel_str(sK18_skl) ),
inference(resolution,[status(thm)],[f445,f122]) ).
fof(f1570,definition,
( sQ152_spl
<=> rel_str(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1572,plain,
( sQ152_spl
| ~ rel_str(sK18_skl) ),
inference(component_clause,[status(thm)],[f1570]) ).
fof(f1573,definition,
( sQ153_spl
<=> sK18_skl = rel_str_of(the_carrier(sK18_skl),the_InternalRel(sK18_skl)) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1576,plain,
( sQ153_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f1569,f1570,f1573]) ).
fof(f1577,plain,
( sQ152_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1572,f442]) ).
fof(f1578,plain,
sQ152_spl,
inference(contradiction_clause,[status(thm)],[f1577]) ).
fof(f1580,plain,
( filtered_subset(cast_as_carrier_subset(sK11_skl),sK11_skl)
| ~ rel_str(sK11_skl) ),
inference(resolution,[status(thm)],[f323,f407]) ).
fof(f1582,definition,
( sQ154_spl
<=> filtered_subset(cast_as_carrier_subset(sK11_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1585,plain,
( sQ154_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f1580,f863,f1582]) ).
fof(f1587,plain,
( closed_subset(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f325,f624]) ).
fof(f1592,plain,
( sQ68_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1587,f660,f1035]) ).
fof(f1597,plain,
( open_subset(cast_as_carrier_subset(sK43_skl),sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f336,f624]) ).
fof(f1602,plain,
( sQ61_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1597,f660,f1009]) ).
fof(f1638,plain,
( ~ sQ116_spl
| point_neighbourhood(sK3_skl(sK5_skl(sK45_skl),sK43_skl),sK43_skl,sK5_skl(sK45_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f1350,f249]) ).
fof(f1639,plain,
( ~ sQ116_spl
| element(neighborhood_system(sK43_skl,sK5_skl(sK45_skl)),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl)))))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f1350,f225]) ).
fof(f1640,plain,
( ~ sQ116_spl
| neighborhood_system(sK43_skl,sK5_skl(sK45_skl)) = a_2_0_yellow19(sK43_skl,sK5_skl(sK45_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f1350,f220]) ).
fof(f1641,plain,
( ~ sQ116_spl
| in(sK5_skl(sK45_skl),the_carrier(sK43_skl))
| empty(the_carrier(sK43_skl)) ),
inference(resolution,[status(thm)],[f1350,f609]) ).
fof(f1642,definition,
( sQ157_spl
<=> point_neighbourhood(sK3_skl(sK5_skl(sK45_skl),sK43_skl),sK43_skl,sK5_skl(sK45_skl)) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1645,plain,
( ~ sQ116_spl
| sQ157_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1638,f657,f660,f663,f1642,f1349]) ).
fof(f1646,definition,
( sQ158_spl
<=> element(neighborhood_system(sK43_skl,sK5_skl(sK45_skl)),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK43_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f1649,plain,
( ~ sQ116_spl
| sQ158_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1639,f657,f660,f663,f1646,f1349]) ).
fof(f1650,definition,
( sQ159_spl
<=> neighborhood_system(sK43_skl,sK5_skl(sK45_skl)) = a_2_0_yellow19(sK43_skl,sK5_skl(sK45_skl)) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1653,plain,
( ~ sQ116_spl
| sQ159_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1640,f657,f660,f663,f1650,f1349]) ).
fof(f1654,definition,
( sQ160_spl
<=> in(sK5_skl(sK45_skl),the_carrier(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f1657,plain,
( ~ sQ116_spl
| sQ160_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f1641,f689,f1654,f1349]) ).
fof(f1661,definition,
( sQ161_spl
<=> reflexive_relstr(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f1663,plain,
( sQ161_spl
| ~ reflexive_relstr(sK18_skl) ),
inference(component_clause,[status(thm)],[f1661]) ).
fof(f1671,plain,
( sQ161_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1663,f446]) ).
fof(f1672,plain,
sQ161_spl,
inference(contradiction_clause,[status(thm)],[f1671]) ).
fof(f1673,plain,
( filtered_subset(cast_as_carrier_subset(sK18_skl),sK18_skl)
| ~ rel_str(sK18_skl)
| empty_carrier(sK18_skl) ),
inference(resolution,[status(thm)],[f449,f328]) ).
fof(f1674,definition,
( sQ164_spl
<=> filtered_subset(cast_as_carrier_subset(sK18_skl),sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1677,plain,
( sQ164_spl
| ~ sQ152_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1673,f1545,f1570,f1674]) ).
fof(f1680,plain,
! [X0] :
( ~ sQ94_spl
| point_neighbourhood(sK7_skl(X0,sK5_skl(the_carrier(sK43_skl)),sK43_skl),sK43_skl,sK5_skl(the_carrier(sK43_skl)))
| ~ in(X0,neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl))))
| ~ element(sK5_skl(the_carrier(sK43_skl)),the_carrier(sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(paramodulation,[status(thm)],[f1206,f372]) ).
fof(f1681,plain,
! [X0] :
( ~ sQ6_spl
| point_neighbourhood(sK7_skl(X0,sK44_skl,sK43_skl),sK43_skl,sK44_skl)
| ~ in(X0,neighborhood_system(sK43_skl,sK44_skl))
| ~ element(sK44_skl,the_carrier(sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(paramodulation,[status(thm)],[f671,f372]) ).
fof(f1682,definition,
( sQ165_spl
<=> top_str(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1684,plain,
( sQ165_spl
| ~ top_str(sK1_skl) ),
inference(component_clause,[status(thm)],[f1682]) ).
fof(f1685,definition,
( sQ166_spl
<=> element(sK5_skl(the_carrier(sK1_skl)),the_carrier(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f1687,plain,
( sQ166_spl
| ~ element(sK5_skl(the_carrier(sK1_skl)),the_carrier(sK1_skl)) ),
inference(component_clause,[status(thm)],[f1685]) ).
fof(f1692,definition,
( sQ168_spl
<=> element(sK5_skl(the_carrier(sK43_skl)),the_carrier(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1694,plain,
( sQ168_spl
| ~ element(sK5_skl(the_carrier(sK43_skl)),the_carrier(sK43_skl)) ),
inference(component_clause,[status(thm)],[f1692]) ).
fof(f1695,definition,
! [X0] :
( sQ169_spl
<=> ( point_neighbourhood(sK7_skl(X0,sK5_skl(the_carrier(sK43_skl)),sK43_skl),sK43_skl,sK5_skl(the_carrier(sK43_skl)))
| ~ in(X0,neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f1698,plain,
( ~ sQ94_spl
| sQ169_spl
| ~ sQ168_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1680,f657,f660,f663,f1692,f1695,f1205]) ).
fof(f1699,definition,
! [X0] :
( sQ170_spl
<=> ( point_neighbourhood(sK7_skl(X0,sK44_skl,sK43_skl),sK43_skl,sK44_skl)
| ~ in(X0,neighborhood_system(sK43_skl,sK44_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1700,plain,
! [X0] :
( ~ sQ170_spl
| point_neighbourhood(sK7_skl(X0,sK44_skl,sK43_skl),sK43_skl,sK44_skl)
| ~ in(X0,neighborhood_system(sK43_skl,sK44_skl)) ),
inference(component_clause,[status(thm)],[f1699]) ).
fof(f1702,plain,
( ~ sQ6_spl
| sQ170_spl
| ~ sQ24_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1681,f657,f660,f663,f772,f1699,f670]) ).
fof(f1703,plain,
( sQ168_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1694,f253]) ).
fof(f1704,plain,
sQ168_spl,
inference(contradiction_clause,[status(thm)],[f1703]) ).
fof(f1705,plain,
( sQ166_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1687,f253]) ).
fof(f1706,plain,
sQ166_spl,
inference(contradiction_clause,[status(thm)],[f1705]) ).
fof(f1707,plain,
( sQ165_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1684,f244]) ).
fof(f1708,plain,
sQ165_spl,
inference(contradiction_clause,[status(thm)],[f1707]) ).
fof(f1710,plain,
! [X0] :
( ~ sQ94_spl
| X0 = sK7_skl(X0,sK5_skl(the_carrier(sK43_skl)),sK43_skl)
| ~ in(X0,neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl))))
| ~ element(sK5_skl(the_carrier(sK43_skl)),the_carrier(sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(paramodulation,[status(thm)],[f1206,f373]) ).
fof(f1711,plain,
! [X0] :
( ~ sQ6_spl
| X0 = sK7_skl(X0,sK44_skl,sK43_skl)
| ~ in(X0,neighborhood_system(sK43_skl,sK44_skl))
| ~ element(sK44_skl,the_carrier(sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(paramodulation,[status(thm)],[f671,f373]) ).
fof(f1712,definition,
! [X0] :
( sQ171_spl
<=> ( X0 = sK7_skl(X0,sK5_skl(the_carrier(sK43_skl)),sK43_skl)
| ~ in(X0,neighborhood_system(sK43_skl,sK5_skl(the_carrier(sK43_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1715,plain,
( ~ sQ94_spl
| sQ171_spl
| ~ sQ168_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1710,f657,f660,f663,f1692,f1712,f1205]) ).
fof(f1716,definition,
! [X0] :
( sQ172_spl
<=> ( X0 = sK7_skl(X0,sK44_skl,sK43_skl)
| ~ in(X0,neighborhood_system(sK43_skl,sK44_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1717,plain,
! [X0] :
( ~ sQ172_spl
| X0 = sK7_skl(X0,sK44_skl,sK43_skl)
| ~ in(X0,neighborhood_system(sK43_skl,sK44_skl)) ),
inference(component_clause,[status(thm)],[f1716]) ).
fof(f1719,plain,
( ~ sQ6_spl
| sQ172_spl
| ~ sQ24_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1711,f657,f660,f663,f772,f1716,f670]) ).
fof(f1720,plain,
( ~ sQ75_spl
| in(sK3_skl(sK44_skl,sK43_skl),a_2_0_yellow19(sK43_skl,sK44_skl))
| ~ element(sK44_skl,the_carrier(sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f654,f1087]) ).
fof(f1721,definition,
( sQ173_spl
<=> in(sK3_skl(sK44_skl,sK43_skl),a_2_0_yellow19(sK43_skl,sK44_skl)) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1724,plain,
( ~ sQ75_spl
| sQ173_spl
| ~ sQ24_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1720,f657,f660,f663,f772,f1721,f1086]) ).
fof(f1728,plain,
( element(sK8_skl(sK18_skl),powerset(the_carrier(sK18_skl)))
| ~ rel_str(sK18_skl)
| ~ reflexive_relstr(sK18_skl)
| empty_carrier(sK18_skl) ),
inference(resolution,[status(thm)],[f380,f447]) ).
fof(f1729,plain,
( element(sK8_skl(sK13_skl),powerset(the_carrier(sK13_skl)))
| ~ rel_str(sK13_skl)
| ~ reflexive_relstr(sK13_skl)
| empty_carrier(sK13_skl) ),
inference(resolution,[status(thm)],[f380,f422]) ).
fof(f1731,plain,
( element(sK8_skl(sK11_skl),powerset(the_carrier(sK11_skl)))
| ~ rel_str(sK11_skl)
| ~ reflexive_relstr(sK11_skl)
| empty_carrier(sK11_skl) ),
inference(resolution,[status(thm)],[f380,f404]) ).
fof(f1732,plain,
( element(sK8_skl(sK10_skl),powerset(the_carrier(sK10_skl)))
| ~ rel_str(sK10_skl)
| ~ reflexive_relstr(sK10_skl)
| empty_carrier(sK10_skl) ),
inference(resolution,[status(thm)],[f380,f396]) ).
fof(f1733,definition,
( sQ174_spl
<=> element(sK8_skl(sK18_skl),powerset(the_carrier(sK18_skl))) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f1736,plain,
( sQ174_spl
| ~ sQ152_spl
| ~ sQ161_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1728,f1545,f1661,f1570,f1733]) ).
fof(f1737,definition,
( sQ175_spl
<=> element(sK8_skl(sK13_skl),powerset(the_carrier(sK13_skl))) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f1740,plain,
( sQ175_spl
| ~ sQ140_spl
| ~ sQ142_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f1729,f1366,f1494,f1473,f1737]) ).
fof(f1742,definition,
( sQ176_spl
<=> element(sK8_skl(sK11_skl),powerset(the_carrier(sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f1745,plain,
( sQ176_spl
| ~ sQ41_spl
| ~ sQ46_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1731,f895,f898,f863,f1742]) ).
fof(f1746,definition,
( sQ177_spl
<=> element(sK8_skl(sK10_skl),powerset(the_carrier(sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1749,plain,
( sQ177_spl
| ~ sQ34_spl
| ~ sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f1732,f828,f831,f825,f1746]) ).
fof(f1750,plain,
( sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f827,f393]) ).
fof(f1751,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f1750]) ).
fof(f1752,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f833,f395]) ).
fof(f1753,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f1752]) ).
fof(f1762,plain,
( directed_subset(cast_as_carrier_subset(sK18_skl),sK18_skl)
| ~ rel_str(sK18_skl)
| empty_carrier(sK18_skl) ),
inference(resolution,[status(thm)],[f450,f316]) ).
fof(f1763,plain,
( bounded_relstr(sK18_skl)
| ~ lower_bounded_relstr(sK18_skl)
| ~ rel_str(sK18_skl) ),
inference(resolution,[status(thm)],[f450,f202]) ).
fof(f1765,definition,
( sQ178_spl
<=> directed_subset(cast_as_carrier_subset(sK18_skl),sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1768,plain,
( sQ178_spl
| ~ sQ152_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1762,f1545,f1570,f1765]) ).
fof(f1769,definition,
( sQ179_spl
<=> lower_bounded_relstr(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f1771,plain,
( sQ179_spl
| ~ lower_bounded_relstr(sK18_skl) ),
inference(component_clause,[status(thm)],[f1769]) ).
fof(f1772,definition,
( sQ180_spl
<=> bounded_relstr(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f1775,plain,
( sQ180_spl
| ~ sQ179_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f1763,f1570,f1769,f1772]) ).
fof(f1783,plain,
( sQ179_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1771,f449]) ).
fof(f1784,plain,
sQ179_spl,
inference(contradiction_clause,[status(thm)],[f1783]) ).
fof(f1785,plain,
( upper_bounded_relstr(sK18_skl)
| ~ rel_str(sK18_skl) ),
inference(resolution,[status(thm)],[f451,f193]) ).
fof(f1787,definition,
( sQ183_spl
<=> upper_bounded_relstr(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f1790,plain,
( sQ183_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f1785,f1570,f1787]) ).
fof(f1792,plain,
( filtered_subset(sK8_skl(sK18_skl),sK18_skl)
| ~ rel_str(sK18_skl)
| ~ reflexive_relstr(sK18_skl)
| empty_carrier(sK18_skl) ),
inference(resolution,[status(thm)],[f382,f447]) ).
fof(f1793,plain,
( filtered_subset(sK8_skl(sK13_skl),sK13_skl)
| ~ rel_str(sK13_skl)
| ~ reflexive_relstr(sK13_skl)
| empty_carrier(sK13_skl) ),
inference(resolution,[status(thm)],[f382,f422]) ).
fof(f1795,plain,
( filtered_subset(sK8_skl(sK11_skl),sK11_skl)
| ~ rel_str(sK11_skl)
| ~ reflexive_relstr(sK11_skl)
| empty_carrier(sK11_skl) ),
inference(resolution,[status(thm)],[f382,f404]) ).
fof(f1796,plain,
( filtered_subset(sK8_skl(sK10_skl),sK10_skl)
| ~ rel_str(sK10_skl)
| ~ reflexive_relstr(sK10_skl)
| empty_carrier(sK10_skl) ),
inference(resolution,[status(thm)],[f382,f396]) ).
fof(f1797,definition,
( sQ184_spl
<=> filtered_subset(sK8_skl(sK18_skl),sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f1800,plain,
( sQ184_spl
| ~ sQ152_spl
| ~ sQ161_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1792,f1545,f1661,f1570,f1797]) ).
fof(f1801,definition,
( sQ185_spl
<=> filtered_subset(sK8_skl(sK13_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f1804,plain,
( sQ185_spl
| ~ sQ140_spl
| ~ sQ142_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f1793,f1366,f1494,f1473,f1801]) ).
fof(f1806,definition,
( sQ186_spl
<=> filtered_subset(sK8_skl(sK11_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f1809,plain,
( sQ186_spl
| ~ sQ41_spl
| ~ sQ46_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1795,f895,f898,f863,f1806]) ).
fof(f1810,definition,
( sQ187_spl
<=> filtered_subset(sK8_skl(sK10_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1813,plain,
( sQ187_spl
| ~ sQ34_spl
| ~ sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f1796,f828,f831,f825,f1810]) ).
fof(f1814,plain,
( upper_relstr_subset(sK8_skl(sK18_skl),sK18_skl)
| ~ rel_str(sK18_skl)
| ~ reflexive_relstr(sK18_skl)
| empty_carrier(sK18_skl) ),
inference(resolution,[status(thm)],[f383,f447]) ).
fof(f1815,plain,
( upper_relstr_subset(sK8_skl(sK13_skl),sK13_skl)
| ~ rel_str(sK13_skl)
| ~ reflexive_relstr(sK13_skl)
| empty_carrier(sK13_skl) ),
inference(resolution,[status(thm)],[f383,f422]) ).
fof(f1817,plain,
( upper_relstr_subset(sK8_skl(sK11_skl),sK11_skl)
| ~ rel_str(sK11_skl)
| ~ reflexive_relstr(sK11_skl)
| empty_carrier(sK11_skl) ),
inference(resolution,[status(thm)],[f383,f404]) ).
fof(f1818,plain,
( upper_relstr_subset(sK8_skl(sK10_skl),sK10_skl)
| ~ rel_str(sK10_skl)
| ~ reflexive_relstr(sK10_skl)
| empty_carrier(sK10_skl) ),
inference(resolution,[status(thm)],[f383,f396]) ).
fof(f1819,definition,
( sQ188_spl
<=> upper_relstr_subset(sK8_skl(sK18_skl),sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f1822,plain,
( sQ188_spl
| ~ sQ152_spl
| ~ sQ161_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1814,f1545,f1661,f1570,f1819]) ).
fof(f1823,definition,
( sQ189_spl
<=> upper_relstr_subset(sK8_skl(sK13_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f1826,plain,
( sQ189_spl
| ~ sQ140_spl
| ~ sQ142_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f1815,f1366,f1494,f1473,f1823]) ).
fof(f1828,definition,
( sQ190_spl
<=> upper_relstr_subset(sK8_skl(sK11_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f1831,plain,
( sQ190_spl
| ~ sQ41_spl
| ~ sQ46_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1817,f895,f898,f863,f1828]) ).
fof(f1832,definition,
( sQ191_spl
<=> upper_relstr_subset(sK8_skl(sK10_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f1835,plain,
( sQ191_spl
| ~ sQ34_spl
| ~ sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f1818,f828,f831,f825,f1832]) ).
fof(f1837,plain,
( element(sK9_skl(sK11_skl),powerset(the_carrier(sK11_skl)))
| ~ rel_str(sK11_skl)
| ~ with_suprema_relstr(sK11_skl)
| ~ antisymmetric_relstr(sK11_skl)
| ~ transitive_relstr(sK11_skl)
| ~ reflexive_relstr(sK11_skl) ),
inference(resolution,[status(thm)],[f386,f407]) ).
fof(f1839,definition,
( sQ192_spl
<=> transitive_relstr(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f1841,plain,
( sQ192_spl
| ~ transitive_relstr(sK11_skl) ),
inference(component_clause,[status(thm)],[f1839]) ).
fof(f1842,definition,
( sQ193_spl
<=> element(sK9_skl(sK11_skl),powerset(the_carrier(sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f1845,plain,
( sQ193_spl
| ~ sQ41_spl
| ~ sQ60_spl
| ~ sQ74_spl
| ~ sQ192_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f1837,f898,f1839,f1071,f978,f863,f1842]) ).
fof(f1847,plain,
( directed_subset(sK9_skl(sK11_skl),sK11_skl)
| ~ rel_str(sK11_skl)
| ~ with_suprema_relstr(sK11_skl)
| ~ antisymmetric_relstr(sK11_skl)
| ~ transitive_relstr(sK11_skl)
| ~ reflexive_relstr(sK11_skl) ),
inference(resolution,[status(thm)],[f388,f407]) ).
fof(f1849,definition,
( sQ194_spl
<=> directed_subset(sK9_skl(sK11_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f1852,plain,
( sQ194_spl
| ~ sQ41_spl
| ~ sQ60_spl
| ~ sQ74_spl
| ~ sQ192_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f1847,f898,f1839,f1071,f978,f863,f1849]) ).
fof(f1853,plain,
( sQ74_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1073,f405]) ).
fof(f1854,plain,
sQ74_spl,
inference(contradiction_clause,[status(thm)],[f1853]) ).
fof(f1855,plain,
( sQ192_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1841,f404]) ).
fof(f1856,plain,
sQ192_spl,
inference(contradiction_clause,[status(thm)],[f1855]) ).
fof(f1894,plain,
( ~ sQ0_spl
| ~ sQ170_spl
| point_neighbourhood(sK7_skl(sK45_skl,sK44_skl,sK43_skl),sK43_skl,sK44_skl) ),
inference(resolution,[status(thm)],[f1700,f643]) ).
fof(f1901,plain,
( filtered_subset(sK9_skl(sK11_skl),sK11_skl)
| ~ rel_str(sK11_skl)
| ~ with_suprema_relstr(sK11_skl)
| ~ antisymmetric_relstr(sK11_skl)
| ~ transitive_relstr(sK11_skl)
| ~ reflexive_relstr(sK11_skl) ),
inference(resolution,[status(thm)],[f389,f407]) ).
fof(f1903,definition,
( sQ201_spl
<=> filtered_subset(sK9_skl(sK11_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f1906,plain,
( sQ201_spl
| ~ sQ41_spl
| ~ sQ60_spl
| ~ sQ74_spl
| ~ sQ192_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f1901,f898,f1839,f1071,f978,f863,f1903]) ).
fof(f1908,plain,
( lower_relstr_subset(sK9_skl(sK11_skl),sK11_skl)
| ~ rel_str(sK11_skl)
| ~ with_suprema_relstr(sK11_skl)
| ~ antisymmetric_relstr(sK11_skl)
| ~ transitive_relstr(sK11_skl)
| ~ reflexive_relstr(sK11_skl) ),
inference(resolution,[status(thm)],[f390,f407]) ).
fof(f1910,definition,
( sQ202_spl
<=> lower_relstr_subset(sK9_skl(sK11_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f1913,plain,
( sQ202_spl
| ~ sQ41_spl
| ~ sQ60_spl
| ~ sQ74_spl
| ~ sQ192_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f1908,f898,f1839,f1071,f978,f863,f1910]) ).
fof(f1915,plain,
( upper_relstr_subset(sK9_skl(sK11_skl),sK11_skl)
| ~ rel_str(sK11_skl)
| ~ with_suprema_relstr(sK11_skl)
| ~ antisymmetric_relstr(sK11_skl)
| ~ transitive_relstr(sK11_skl)
| ~ reflexive_relstr(sK11_skl) ),
inference(resolution,[status(thm)],[f391,f407]) ).
fof(f1917,definition,
( sQ203_spl
<=> upper_relstr_subset(sK9_skl(sK11_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f1920,plain,
( sQ203_spl
| ~ sQ41_spl
| ~ sQ60_spl
| ~ sQ74_spl
| ~ sQ192_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f1915,f898,f1839,f1071,f978,f863,f1917]) ).
fof(f1943,plain,
( element(sK16_skl(sK43_skl),powerset(the_carrier(sK43_skl)))
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f434,f624]) ).
fof(f1948,definition,
( sQ205_spl
<=> element(sK16_skl(sK43_skl),powerset(the_carrier(sK43_skl))) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f1949,plain,
( ~ sQ205_spl
| element(sK16_skl(sK43_skl),powerset(the_carrier(sK43_skl))) ),
inference(component_clause,[status(thm)],[f1948]) ).
fof(f1951,plain,
( sQ205_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1943,f660,f1948]) ).
fof(f1952,plain,
( ~ sQ205_spl
| v5_membered(sK16_skl(sK43_skl))
| ~ nowhere_dense(sK16_skl(sK43_skl),sK43_skl)
| ~ open_subset(sK16_skl(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1949,f211]) ).
fof(f1953,plain,
( ~ sQ205_spl
| v4_membered(sK16_skl(sK43_skl))
| ~ nowhere_dense(sK16_skl(sK43_skl),sK43_skl)
| ~ open_subset(sK16_skl(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1949,f210]) ).
fof(f1954,plain,
( ~ sQ205_spl
| v3_membered(sK16_skl(sK43_skl))
| ~ nowhere_dense(sK16_skl(sK43_skl),sK43_skl)
| ~ open_subset(sK16_skl(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1949,f209]) ).
fof(f1955,plain,
( ~ sQ205_spl
| v2_membered(sK16_skl(sK43_skl))
| ~ nowhere_dense(sK16_skl(sK43_skl),sK43_skl)
| ~ open_subset(sK16_skl(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1949,f208]) ).
fof(f1956,plain,
( ~ sQ205_spl
| v1_membered(sK16_skl(sK43_skl))
| ~ nowhere_dense(sK16_skl(sK43_skl),sK43_skl)
| ~ open_subset(sK16_skl(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1949,f207]) ).
fof(f1957,plain,
( ~ sQ205_spl
| closed_subset(sK16_skl(sK43_skl),sK43_skl)
| ~ nowhere_dense(sK16_skl(sK43_skl),sK43_skl)
| ~ open_subset(sK16_skl(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1949,f206]) ).
fof(f1958,plain,
( ~ sQ205_spl
| empty(sK16_skl(sK43_skl))
| ~ nowhere_dense(sK16_skl(sK43_skl),sK43_skl)
| ~ open_subset(sK16_skl(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1949,f204]) ).
fof(f1960,plain,
( ~ sQ205_spl
| boundary_set(sK16_skl(sK43_skl),sK43_skl)
| ~ nowhere_dense(sK16_skl(sK43_skl),sK43_skl)
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1949,f190]) ).
fof(f1961,plain,
( ~ sQ205_spl
| nowhere_dense(sK16_skl(sK43_skl),sK43_skl)
| ~ empty(sK16_skl(sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1949,f185]) ).
fof(f1964,plain,
( ~ sQ205_spl
| open_subset(sK16_skl(sK43_skl),sK43_skl)
| ~ empty(sK16_skl(sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl) ),
inference(resolution,[status(thm)],[f1949,f166]) ).
fof(f1965,plain,
( ~ sQ205_spl
| element(sK5_skl(sK16_skl(sK43_skl)),the_carrier(sK43_skl))
| empty(sK16_skl(sK43_skl)) ),
inference(resolution,[status(thm)],[f1949,f1210]) ).
fof(f1966,plain,
( ~ sQ205_spl
| ~ empty(the_carrier(sK43_skl))
| empty(sK16_skl(sK43_skl)) ),
inference(resolution,[status(thm)],[f1949,f1209]) ).
fof(f1967,plain,
( ~ sQ205_spl
| finite(sK16_skl(sK43_skl))
| ~ finite(the_carrier(sK43_skl)) ),
inference(resolution,[status(thm)],[f1949,f173]) ).
fof(f1968,plain,
( ~ sQ205_spl
| in(sK16_skl(sK43_skl),powerset(the_carrier(sK43_skl)))
| empty(powerset(the_carrier(sK43_skl))) ),
inference(resolution,[status(thm)],[f1949,f609]) ).
fof(f1969,definition,
( sQ206_spl
<=> open_subset(sK16_skl(sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f1972,definition,
( sQ207_spl
<=> nowhere_dense(sK16_skl(sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f1975,definition,
( sQ208_spl
<=> v5_membered(sK16_skl(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f1978,plain,
( ~ sQ205_spl
| sQ208_spl
| ~ sQ207_spl
| ~ sQ206_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1952,f660,f663,f1969,f1972,f1975,f1948]) ).
fof(f1979,definition,
( sQ209_spl
<=> v4_membered(sK16_skl(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f1982,plain,
( ~ sQ205_spl
| sQ209_spl
| ~ sQ207_spl
| ~ sQ206_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1953,f660,f663,f1969,f1972,f1979,f1948]) ).
fof(f1983,definition,
( sQ210_spl
<=> v3_membered(sK16_skl(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f1986,plain,
( ~ sQ205_spl
| sQ210_spl
| ~ sQ207_spl
| ~ sQ206_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1954,f660,f663,f1969,f1972,f1983,f1948]) ).
fof(f1987,definition,
( sQ211_spl
<=> v2_membered(sK16_skl(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f1990,plain,
( ~ sQ205_spl
| sQ211_spl
| ~ sQ207_spl
| ~ sQ206_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1955,f660,f663,f1969,f1972,f1987,f1948]) ).
fof(f1991,definition,
( sQ212_spl
<=> v1_membered(sK16_skl(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f1994,plain,
( ~ sQ205_spl
| sQ212_spl
| ~ sQ207_spl
| ~ sQ206_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1956,f660,f663,f1969,f1972,f1991,f1948]) ).
fof(f1995,definition,
( sQ213_spl
<=> closed_subset(sK16_skl(sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f1998,plain,
( ~ sQ205_spl
| sQ213_spl
| ~ sQ207_spl
| ~ sQ206_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1957,f660,f663,f1969,f1972,f1995,f1948]) ).
fof(f1999,definition,
( sQ214_spl
<=> empty(sK16_skl(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f2002,plain,
( ~ sQ205_spl
| sQ214_spl
| ~ sQ207_spl
| ~ sQ206_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1958,f660,f663,f1969,f1972,f1999,f1948]) ).
fof(f2003,definition,
( sQ215_spl
<=> boundary_set(sK16_skl(sK43_skl),sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2007,plain,
( ~ sQ205_spl
| sQ215_spl
| ~ sQ207_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1960,f660,f663,f1972,f2003,f1948]) ).
fof(f2008,plain,
( ~ sQ205_spl
| sQ207_spl
| ~ sQ214_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1961,f660,f663,f1999,f1972,f1948]) ).
fof(f2011,plain,
( ~ sQ205_spl
| sQ206_spl
| ~ sQ214_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1964,f660,f663,f1999,f1969,f1948]) ).
fof(f2012,definition,
( sQ216_spl
<=> element(sK5_skl(sK16_skl(sK43_skl)),the_carrier(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2015,plain,
( ~ sQ205_spl
| sQ216_spl
| sQ214_spl ),
inference(split_clause,[status(thm)],[f1965,f1999,f2012,f1948]) ).
fof(f2016,plain,
( ~ sQ205_spl
| ~ sQ8_spl
| sQ214_spl ),
inference(split_clause,[status(thm)],[f1966,f1999,f689,f1948]) ).
fof(f2017,definition,
( sQ217_spl
<=> finite(sK16_skl(sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2020,plain,
( ~ sQ205_spl
| sQ217_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1967,f801,f2017,f1948]) ).
fof(f2021,definition,
( sQ218_spl
<=> in(sK16_skl(sK43_skl),powerset(the_carrier(sK43_skl))) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2024,plain,
( ~ sQ205_spl
| sQ218_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1968,f808,f2021,f1948]) ).
fof(f2025,plain,
( ~ sQ0_spl
| ~ sQ172_spl
| sK45_skl = sK7_skl(sK45_skl,sK44_skl,sK43_skl) ),
inference(resolution,[status(thm)],[f1717,f643]) ).
fof(f2027,plain,
( ~ sQ0_spl
| ~ sQ170_spl
| ~ sQ172_spl
| point_neighbourhood(sK45_skl,sK43_skl,sK44_skl) ),
inference(backward_demodulation,[status(thm)],[f2025,f1894]) ).
fof(f2032,plain,
( ~ sQ0_spl
| ~ sQ170_spl
| ~ sQ172_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f2027,f645,f1716,f1699,f642]) ).
fof(f2034,plain,
( ~ sQ1_spl
| in(sK45_skl,a_2_0_yellow19(sK43_skl,sK44_skl))
| ~ element(sK44_skl,the_carrier(sK43_skl))
| ~ top_str(sK43_skl)
| ~ topological_space(sK43_skl)
| empty_carrier(sK43_skl) ),
inference(resolution,[status(thm)],[f646,f654]) ).
fof(f2036,definition,
( sQ220_spl
<=> in(sK45_skl,a_2_0_yellow19(sK43_skl,sK44_skl)) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2037,plain,
( ~ sQ220_spl
| in(sK45_skl,a_2_0_yellow19(sK43_skl,sK44_skl)) ),
inference(component_clause,[status(thm)],[f2036]) ).
fof(f2039,plain,
( ~ sQ1_spl
| sQ220_spl
| ~ sQ24_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f2034,f657,f660,f663,f772,f2036,f645]) ).
fof(f2041,plain,
( ~ sQ220_spl
| ~ sQ6_spl
| in(sK45_skl,neighborhood_system(sK43_skl,sK44_skl)) ),
inference(forward_demodulation,[status(thm)],[f671,f2037]) ).
fof(f2042,plain,
( ~ sQ220_spl
| ~ sQ6_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2041,f644]) ).
fof(f2043,plain,
( ~ sQ220_spl
| ~ sQ6_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f2042]) ).
fof(f2044,plain,
$false,
inference(sat_refutation,[status(thm)],[f648,f649,f669,f673,f675,f677,f679,f695,f705,f707,f778,f780,f792,f796,f800,f807,f814,f816,f818,f842,f855,f869,f871,f874,f878,f889,f909,f911,f913,f919,f929,f939,f949,f965,f976,f977,f981,f1018,f1022,f1026,f1030,f1034,f1047,f1048,f1055,f1059,f1076,f1079,f1089,f1116,f1141,f1145,f1149,f1153,f1157,f1170,f1171,f1173,f1174,f1178,f1182,f1198,f1208,f1279,f1292,f1296,f1305,f1314,f1318,f1330,f1331,f1332,f1352,f1372,f1376,f1378,f1471,f1479,f1481,f1505,f1514,f1515,f1519,f1520,f1524,f1551,f1555,f1557,f1564,f1576,f1578,f1585,f1592,f1602,f1645,f1649,f1653,f1657,f1672,f1677,f1698,f1702,f1704,f1706,f1708,f1715,f1719,f1724,f1736,f1740,f1745,f1749,f1751,f1753,f1768,f1775,f1784,f1790,f1800,f1804,f1809,f1813,f1822,f1826,f1831,f1835,f1845,f1852,f1854,f1856,f1906,f1913,f1920,f1951,f1978,f1982,f1986,f1990,f1994,f1998,f2002,f2007,f2008,f2011,f2015,f2016,f2020,f2024,f2032,f2039,f2043]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU388+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 06:18:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 0.55/0.51 % Refutation found
% 0.55/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.55/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.55/0.53 % Elapsed time: 0.165355 seconds
% 0.55/0.53 % CPU time: 0.939215 seconds
% 0.55/0.53 % Total memory used: 111.512 MB
% 0.55/0.53 % Net memory used: 110.507 MB
%------------------------------------------------------------------------------