%--------------------------------------------------------------------------
% File     : TOP004-1 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Topology
% Problem  : Topology generated by a basis forms a topological space, part 4
% Version  : [WM89] axioms : Incomplete.
% English  :

% Refs     : [WM89]  Wick & McCune (1989), Automated Reasoning about Elemen
% Source   : [WM89]
% Names    : Lemma 1d [WM89]

% Status   : Unsatisfiable
% Rating   : 0.00 v7.1.0, 0.17 v7.0.0, 0.12 v6.3.0, 0.14 v6.2.0, 0.00 v5.0.0, 0.07 v4.1.0, 0.00 v2.0.0
% Syntax   : Number of clauses     :  113 (   4 unt;  23 nHn; 106 RR)
%            Number of literals    :  340 (   0 equ; 206 neg)
%            Maximal clause size   :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   22 (  22 usr;   0 prp; 1-4 aty)
%            Number of functors    :   37 (  37 usr;   3 con; 0-5 aty)
%            Number of variables   :  361 (  60 sgn)
% SPC      : CNF_UNS_RFO_NEQ_NHN

% Comments : The axioms in this version are known to be incomplete. To
%            obtain a proof of this theorem it may be necessary to add
%            appropriate set theory axioms.
%--------------------------------------------------------------------------
%----Include Point-set topology axioms
include('Axioms/TOP001-0.ax').
%--------------------------------------------------------------------------
cnf(lemma_1d_1,negated_conjecture,
    basis(cx,f) ).

cnf(lemma_1d_2,negated_conjecture,
    element_of_collection(U,top_of_basis(f)) ).

cnf(lemma_1d_3,negated_conjecture,
    element_of_collection(V,top_of_basis(f)) ).

cnf(lemma_1d_4,negated_conjecture,
    ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)) ).

%--------------------------------------------------------------------------