SET007 Axioms: SET007+780.ax


%------------------------------------------------------------------------------
% File     : SET007+780 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Kuratowski Closure-Complement Problem
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : kurato_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  105 (  56 unit)
%            Number of atoms       :  310 (  53 equality)
%            Maximal formula depth :   11 (   4 average)
%            Number of connectives :  269 (  64 ~  ;   0  |; 136  &)
%                                         (   2 <=>;  67 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   24 (   1 propositional; 0-7 arity)
%            Number of functors    :   37 (  10 constant; 0-7 arity)
%            Number of variables   :   82 (   0 singleton;  79 !;   3 ?)
%            Maximal term depth    :   11 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_finset_1(k1_kurato_1(A,B)) ) )).

fof(fc2_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_finset_1(k2_kurato_1(A,B)) ) )).

fof(fc3_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_finset_1(k5_kurato_1(A,B)) ) )).

fof(fc4_kurato_1,axiom,
    ( ~ v3_pre_topc(k6_kurato_1,k3_topmetr)
    & ~ v4_pre_topc(k6_kurato_1,k3_topmetr) )).

fof(fc5_kurato_1,axiom,(
    v1_borsuk_5(k3_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr) )).

fof(fc6_kurato_1,axiom,(
    v1_borsuk_5(k4_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr) )).

fof(fc7_kurato_1,axiom,
    ( v1_finset_1(k2_kurato_1(k3_topmetr,k6_kurato_1))
    & v1_borsuk_5(k2_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr) )).

fof(fc8_kurato_1,axiom,
    ( v1_finset_1(k2_kurato_1(k3_topmetr,k6_kurato_1))
    & v1_borsuk_5(k2_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
    & v1_setfam_1(k2_kurato_1(k3_topmetr,k6_kurato_1)) )).

fof(fc9_kurato_1,axiom,
    ( v1_borsuk_5(k3_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
    & v1_setfam_1(k3_kurato_1(k3_topmetr,k6_kurato_1)) )).

fof(fc10_kurato_1,axiom,
    ( v1_borsuk_5(k4_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
    & v1_setfam_1(k4_kurato_1(k3_topmetr,k6_kurato_1)) )).

fof(rc1_kurato_1,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_topmetr))))
      & v1_borsuk_5(A,k3_topmetr)
      & v1_setfam_1(A) ) )).

fof(fc11_kurato_1,axiom,
    ( v1_borsuk_5(k3_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
    & v2_tops_2(k3_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
    & v1_setfam_1(k3_kurato_1(k3_topmetr,k6_kurato_1)) )).

fof(fc12_kurato_1,axiom,
    ( v1_borsuk_5(k4_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
    & v1_tops_2(k4_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
    & v1_setfam_1(k4_kurato_1(k3_topmetr,k6_kurato_1)) )).

fof(fc13_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_finset_1(k3_kurato_1(A,B)) ) )).

fof(fc14_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_finset_1(k4_kurato_1(A,B)) ) )).

fof(fc15_kurato_1,axiom,
    ( ~ v1_xboole_0(k6_kurato_1)
    & ~ v3_pre_topc(k6_kurato_1,k3_topmetr)
    & ~ v4_pre_topc(k6_kurato_1,k3_topmetr) )).

fof(fc16_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v1_xboole_0(k2_kurato_1(A,B))
        & v1_finset_1(k2_kurato_1(A,B)) ) ) )).

fof(fc17_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_finset_1(k2_kurato_1(A,B))
        & v1_kurato_1(k2_kurato_1(A,B),A) ) ) )).

fof(fc18_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_finset_1(k2_kurato_1(A,B))
        & v1_prob_1(k2_kurato_1(A,B),u1_struct_0(A)) ) ) )).

fof(fc19_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v1_xboole_0(k5_kurato_1(A,B))
        & v1_finset_1(k5_kurato_1(A,B)) ) ) )).

fof(fc20_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_finset_1(k5_kurato_1(A,B))
        & v2_kurato_1(k5_kurato_1(A,B),A) ) ) )).

fof(fc21_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_finset_1(k5_kurato_1(A,B))
        & v1_kurato_1(k5_kurato_1(A,B),A) ) ) )).

fof(rc2_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & ~ v1_xboole_0(B)
          & v1_kurato_1(B,A)
          & v2_kurato_1(B,A) ) ) )).

fof(rc3_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & ~ v1_xboole_0(B)
          & v1_prob_1(B,u1_struct_0(A))
          & v1_kurato_1(B,A) ) ) )).

fof(t1_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))))) = k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))) ) ) )).

fof(d1_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_kurato_1(A,B) = k5_enumset1(B,k6_pre_topc(A,B),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))))) ) ) )).

fof(d2_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_kurato_1(A,B) = k2_xboole_0(k5_enumset1(B,k6_pre_topc(A,B),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))))),k5_enumset1(k3_subset_1(u1_struct_0(A),B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))))) ) ) )).

fof(t2_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_kurato_1(A,B) = k2_xboole_0(k1_kurato_1(A,B),k1_kurato_1(A,k3_subset_1(u1_struct_0(A),B))) ) ) )).

fof(t3_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_hidden(B,k2_kurato_1(A,B))
            & r2_hidden(k6_pre_topc(A,B),k2_kurato_1(A,B))
            & r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)),k2_kurato_1(A,B))
            & r2_hidden(k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))),k2_kurato_1(A,B))
            & r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))),k2_kurato_1(A,B))
            & r2_hidden(k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))),k2_kurato_1(A,B))
            & r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))))),k2_kurato_1(A,B)) ) ) ) )).

fof(t4_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_hidden(k3_subset_1(u1_struct_0(A),B),k2_kurato_1(A,B))
            & r2_hidden(k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),k2_kurato_1(A,B))
            & r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))),k2_kurato_1(A,B))
            & r2_hidden(k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))),k2_kurato_1(A,B))
            & r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))),k2_kurato_1(A,B))
            & r2_hidden(k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))))),k2_kurato_1(A,B))
            & r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))),k2_kurato_1(A,B)) ) ) ) )).

fof(d3_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_kurato_1(A,B) = k4_enumset1(k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))) ) ) )).

fof(d4_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_kurato_1(A,B) = k4_enumset1(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))))))) ) ) )).

fof(t5_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_kurato_1(A,B) = k2_xboole_0(k2_xboole_0(k2_tarski(B,k3_subset_1(u1_struct_0(A),B)),k3_kurato_1(A,B)),k4_kurato_1(A,B)) ) ) )).

fof(t6_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(C,k2_kurato_1(A,B))
               => ( r2_hidden(k3_subset_1(u1_struct_0(A),C),k2_kurato_1(A,B))
                  & r2_hidden(k6_pre_topc(A,C),k2_kurato_1(A,B)) ) ) ) ) ) )).

fof(t7_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_xreal_0(k4_card_1(k2_kurato_1(A,B)),np__14) ) ) )).

fof(d5_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_kurato_1(A,B) = k5_enumset1(B,k1_tops_1(A,B),k6_pre_topc(A,B),k1_tops_1(A,k6_pre_topc(A,B)),k6_pre_topc(A,k1_tops_1(A,B)),k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))),k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))) ) ) )).

fof(t8_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_hidden(B,k5_kurato_1(A,B))
            & r2_hidden(k1_tops_1(A,B),k5_kurato_1(A,B))
            & r2_hidden(k6_pre_topc(A,B),k5_kurato_1(A,B))
            & r2_hidden(k1_tops_1(A,k6_pre_topc(A,B)),k5_kurato_1(A,B))
            & r2_hidden(k6_pre_topc(A,k1_tops_1(A,B)),k5_kurato_1(A,B))
            & r2_hidden(k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))),k5_kurato_1(A,B))
            & r2_hidden(k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B))),k5_kurato_1(A,B)) ) ) ) )).

fof(t9_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_kurato_1(A,B) = k2_xboole_0(k2_xboole_0(k1_tarski(B),k1_enumset1(k1_tops_1(A,B),k1_tops_1(A,k6_pre_topc(A,B)),k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B))))),k1_enumset1(k6_pre_topc(A,B),k6_pre_topc(A,k1_tops_1(A,B)),k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))))) ) ) )).

fof(t10_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(C,k5_kurato_1(A,B))
               => ( r2_hidden(k1_tops_1(A,C),k5_kurato_1(A,B))
                  & r2_hidden(k6_pre_topc(A,C),k5_kurato_1(A,B)) ) ) ) ) ) )).

fof(t11_kurato_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_xreal_0(k4_card_1(k5_kurato_1(A,B)),np__7) ) ) )).

fof(d6_kurato_1,axiom,(
    k6_kurato_1 = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k1_seq_4(np__1),k2_borsuk_5(np__2,np__4)),k2_rcomp_1(np__4,np__5)),k4_limfunc1(np__5)) )).

fof(t12_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k6_kurato_1) = k4_subset_1(k1_numbers,k1_seq_4(np__1),k3_limfunc1(np__2)) )).

fof(t13_kurato_1,axiom,(
    k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k6_kurato_1)) = k4_subset_1(k1_numbers,k12_prob_1(np__1),k2_rcomp_1(np__1,np__2)) )).

fof(t14_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k6_kurato_1))) = k2_limfunc1(np__2) )).

fof(t15_kurato_1,axiom,(
    k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k6_kurato_1)))) = k4_limfunc1(np__2) )).

fof(t16_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k6_kurato_1))))) = k3_limfunc1(np__2) )).

fof(t17_kurato_1,axiom,(
    k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k6_kurato_1)))))) = k12_prob_1(np__2) )).

fof(t18_kurato_1,axiom,(
    k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1) = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k12_prob_1(np__1),k2_rcomp_2(np__1,np__2)),k3_borsuk_5(np__2,np__4)),k1_seq_4(np__4)),k1_seq_4(np__5)) )).

fof(t19_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1)) = k4_subset_1(k1_numbers,k2_limfunc1(np__4),k1_seq_4(np__5)) )).

fof(t20_kurato_1,axiom,(
    k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1))) = k4_subset_1(k1_numbers,k2_rcomp_1(np__4,np__5),k4_limfunc1(np__5)) )).

fof(t21_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1)))) = k3_limfunc1(np__4) )).

fof(t22_kurato_1,axiom,(
    k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1))))) = k12_prob_1(np__4) )).

fof(t23_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1)))))) = k2_limfunc1(np__4) )).

fof(t24_kurato_1,axiom,(
    k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1))))))) = k4_limfunc1(np__4) )).

fof(t25_kurato_1,axiom,(
    k1_tops_1(k3_topmetr,k6_kurato_1) = k4_subset_1(k1_numbers,k2_rcomp_1(np__4,np__5),k4_limfunc1(np__5)) )).

fof(t26_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) = k3_limfunc1(np__4) )).

fof(t27_kurato_1,axiom,(
    k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) = k4_limfunc1(np__4) )).

fof(t28_kurato_1,axiom,(
    k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) = k4_limfunc1(np__2) )).

fof(t29_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) = k3_limfunc1(np__2) )).

fof(t30_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) != k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) )).

fof(t31_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) != k6_pre_topc(k3_topmetr,k6_kurato_1) )).

fof(t32_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) != k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) )).

fof(t33_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) != k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) )).

fof(t34_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) != k1_tops_1(k3_topmetr,k6_kurato_1) )).

fof(t35_kurato_1,axiom,(
    k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) != k6_pre_topc(k3_topmetr,k6_kurato_1) )).

fof(t36_kurato_1,axiom,(
    k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) != k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) )).

fof(t37_kurato_1,axiom,(
    k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) != k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) )).

fof(t38_kurato_1,axiom,(
    k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) != k1_tops_1(k3_topmetr,k6_kurato_1) )).

fof(t39_kurato_1,axiom,(
    k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) != k6_pre_topc(k3_topmetr,k6_kurato_1) )).

fof(t40_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) != k6_pre_topc(k3_topmetr,k6_kurato_1) )).

fof(t41_kurato_1,axiom,(
    k1_tops_1(k3_topmetr,k6_kurato_1) != k6_pre_topc(k3_topmetr,k6_kurato_1) )).

fof(t42_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k6_kurato_1) != k6_kurato_1 )).

fof(t43_kurato_1,axiom,(
    k6_kurato_1 != k1_tops_1(k3_topmetr,k6_kurato_1) )).

fof(t44_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) != k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) )).

fof(t45_kurato_1,axiom,(
    k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) != k1_tops_1(k3_topmetr,k6_kurato_1) )).

fof(t46_kurato_1,axiom,(
    k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) != k1_tops_1(k3_topmetr,k6_kurato_1) )).

fof(t47_kurato_1,axiom,(
    k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) != k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) )).

fof(t48_kurato_1,axiom,(
    r1_incproj(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)))) )).

fof(t49_kurato_1,axiom,(
    r1_incproj(k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)))) )).

fof(t50_kurato_1,axiom,(
    ! [A] :
      ( r2_hidden(A,k1_enumset1(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)))))
     => ( ~ v1_xboole_0(A)
        & v3_pre_topc(A,k3_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) ) )).

fof(t51_kurato_1,axiom,(
    $true )).

fof(t52_kurato_1,axiom,(
    ! [A] :
      ~ ( r2_hidden(A,k1_enumset1(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)))))
        & A = k1_numbers ) )).

fof(t53_kurato_1,axiom,(
    ! [A] :
      ~ ( r2_hidden(A,k1_enumset1(k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)))))
        & A = k1_numbers ) )).

fof(t54_kurato_1,axiom,(
    r1_xboole_0(k1_enumset1(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)))),k1_enumset1(k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))))) )).

fof(t55_kurato_1,axiom,(
    r1_borsuk_5(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))),k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)))) )).

fof(t56_kurato_1,axiom,(
    r1_xboole_0(k4_enumset1(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))),k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)))),k1_tarski(k6_kurato_1)) )).

fof(t57_kurato_1,axiom,(
    r2_borsuk_5(k6_kurato_1,k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))),k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)))) )).

fof(t58_kurato_1,axiom,(
    k4_card_1(k5_kurato_1(k3_topmetr,k6_kurato_1)) = np__7 )).

fof(t59_kurato_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( r1_tarski(B,A)
         => v1_setfam_1(B) ) ) )).

fof(t60_kurato_1,axiom,(
    ! [A] :
      ( ( v1_borsuk_5(A,k3_topmetr)
        & v1_setfam_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_topmetr)))) )
     => ! [B] :
          ( ( v1_borsuk_5(B,k3_topmetr)
            & v1_setfam_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_topmetr)))) )
         => ( ( v1_tops_2(A,k3_topmetr)
              & v2_tops_2(B,k3_topmetr) )
           => r1_xboole_0(A,B) ) ) ) )).

fof(t61_kurato_1,axiom,(
    r1_xboole_0(k3_kurato_1(k3_topmetr,k6_kurato_1),k4_kurato_1(k3_topmetr,k6_kurato_1)) )).

fof(t62_kurato_1,axiom,(
    k4_card_1(k3_kurato_1(k3_topmetr,k6_kurato_1)) = np__6 )).

fof(t63_kurato_1,axiom,(
    k4_card_1(k4_kurato_1(k3_topmetr,k6_kurato_1)) = np__6 )).

fof(t64_kurato_1,axiom,(
    r1_xboole_0(k2_tarski(k6_kurato_1,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1)),k3_kurato_1(k3_topmetr,k6_kurato_1)) )).

fof(t65_kurato_1,axiom,(
    k6_kurato_1 != k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1) )).

fof(t66_kurato_1,axiom,(
    r1_xboole_0(k2_tarski(k6_kurato_1,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1)),k4_kurato_1(k3_topmetr,k6_kurato_1)) )).

fof(t67_kurato_1,axiom,(
    k4_card_1(k2_kurato_1(k3_topmetr,k6_kurato_1)) = np__14 )).

fof(d7_kurato_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_kurato_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => r2_hidden(k6_pre_topc(A,C),B) ) ) ) ) ) )).

fof(d8_kurato_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v2_kurato_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => r2_hidden(k1_tops_1(A,C),B) ) ) ) ) ) )).

fof(dt_k1_kurato_1,axiom,(
    $true )).

fof(dt_k2_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k2_kurato_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k3_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k3_kurato_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k4_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_kurato_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k5_kurato_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k5_kurato_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k6_kurato_1,axiom,(
    m1_subset_1(k6_kurato_1,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )).
%------------------------------------------------------------------------------