SET007 Axioms: SET007+900.ax


%------------------------------------------------------------------------------
% File     : SET007+900 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Supercondensed Sets, Subcondensed Sets and Condensed Sets
% 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    : isomichi [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  104 (   1 unit)
%            Number of atoms       :  597 (  40 equality)
%            Maximal formula depth :   19 (   7 average)
%            Number of connectives :  546 (  53 ~  ;   5  |; 243  &)
%                                         (  25 <=>; 220 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   43 (   1 propositional; 0-2 arity)
%            Number of functors    :   25 (   3 constant; 0-3 arity)
%            Number of variables   :  210 (   0 singleton; 196 !;  14 ?)
%            Maximal term depth    :    6 (   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_isomichi,axiom,(
    ! [A] :
      ( ~ v1_realset1(A)
     => ( ~ v3_struct_0(k2_tex_1(A))
        & v1_pre_topc(k2_tex_1(A))
        & v2_pre_topc(k2_tex_1(A))
        & v2_tdlat_3(k2_tex_1(A))
        & v3_tdlat_3(k2_tex_1(A))
        & v4_tdlat_3(k2_tex_1(A))
        & v5_tdlat_3(k2_tex_1(A))
        & ~ v3_realset2(k2_tex_1(A)) ) ) )).

fof(rc1_isomichi,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v2_tdlat_3(A)
      & ~ v3_realset2(A) ) )).

fof(cc1_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
           => ( v1_isomichi(B,A)
              & v2_isomichi(B,A) ) ) ) ) )).

fof(cc2_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v1_isomichi(B,A)
              & v2_isomichi(B,A) )
           => v4_tops_1(B,A) ) ) ) )).

fof(rc2_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v4_tops_1(B,A)
          & v1_isomichi(B,A)
          & v2_isomichi(B,A) ) ) )).

fof(cc3_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_isomichi(B,A)
           => v1_decomp_1(B,A) ) ) ) )).

fof(cc4_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_decomp_1(B,A)
           => v2_isomichi(B,A) ) ) ) )).

fof(fc2_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_pre_topc(k2_pre_topc(A),A)
        & v4_pre_topc(k2_pre_topc(A),A)
        & v1_tops_1(k2_pre_topc(A),A)
        & v5_tops_1(k2_pre_topc(A),A)
        & v6_tops_1(k2_pre_topc(A),A) ) ) )).

fof(fc3_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_xboole_0(k1_pre_topc(A))
        & v3_pre_topc(k1_pre_topc(A),A)
        & v4_pre_topc(k1_pre_topc(A),A)
        & v2_tops_1(k1_pre_topc(A),A)
        & v3_tops_1(k1_pre_topc(A),A)
        & v5_tops_1(k1_pre_topc(A),A)
        & v6_tops_1(k1_pre_topc(A),A)
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A)) ) ) )).

fof(rc3_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v5_tops_1(B,A)
          & v6_tops_1(B,A) ) ) )).

fof(fc4_isomichi,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v6_tops_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) )).

fof(fc5_isomichi,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v5_tops_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v6_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) )).

fof(cc5_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
           => v3_pre_topc(B,A) ) ) ) )).

fof(cc6_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
           => v4_pre_topc(B,A) ) ) ) )).

fof(fc6_isomichi,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v3_pre_topc(k1_tops_1(A,k6_pre_topc(A,B)),A)
        & v6_tops_1(k1_tops_1(A,k6_pre_topc(A,B)),A) ) ) )).

fof(fc7_isomichi,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v4_pre_topc(k6_pre_topc(A,k1_tops_1(A,B)),A)
        & v5_tops_1(k6_pre_topc(A,k1_tops_1(A,B)),A) ) ) )).

fof(cc7_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
           => ( v3_pre_topc(B,A)
              & v4_tops_1(B,A)
              & v1_decomp_1(B,A)
              & v1_isomichi(B,A)
              & v2_isomichi(B,A) ) ) ) ) )).

fof(cc8_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_pre_topc(B,A)
              & v4_tops_1(B,A) )
           => ( v3_pre_topc(B,A)
              & v6_tops_1(B,A) ) ) ) ) )).

fof(cc9_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
           => ( v4_pre_topc(B,A)
              & v4_tops_1(B,A)
              & v1_decomp_1(B,A)
              & v1_isomichi(B,A)
              & v2_isomichi(B,A) ) ) ) ) )).

fof(cc10_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v4_pre_topc(B,A)
              & v4_tops_1(B,A) )
           => ( v4_pre_topc(B,A)
              & v5_tops_1(B,A) ) ) ) ) )).

fof(fc8_isomichi,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v4_pre_topc(k2_tops_1(A,B),A) ) )).

fof(fc9_isomichi,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v3_pre_topc(k1_isomichi(A,B),A)
        & v4_tops_1(k1_isomichi(A,B),A)
        & v6_tops_1(k1_isomichi(A,B),A)
        & v1_decomp_1(k1_isomichi(A,B),A)
        & v1_isomichi(k1_isomichi(A,B),A)
        & v2_isomichi(k1_isomichi(A,B),A) ) ) )).

fof(fc10_isomichi,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_xboole_0(k1_isomichi(A,k1_isomichi(A,B)))
        & v3_pre_topc(k1_isomichi(A,k1_isomichi(A,B)),A)
        & v4_pre_topc(k1_isomichi(A,k1_isomichi(A,B)),A)
        & v2_tops_1(k1_isomichi(A,k1_isomichi(A,B)),A)
        & v3_tops_1(k1_isomichi(A,k1_isomichi(A,B)),A)
        & v4_tops_1(k1_isomichi(A,k1_isomichi(A,B)),A)
        & v5_tops_1(k1_isomichi(A,k1_isomichi(A,B)),A)
        & v6_tops_1(k1_isomichi(A,k1_isomichi(A,B)),A)
        & v1_membered(k1_isomichi(A,k1_isomichi(A,B)))
        & v2_membered(k1_isomichi(A,k1_isomichi(A,B)))
        & v3_membered(k1_isomichi(A,k1_isomichi(A,B)))
        & v4_membered(k1_isomichi(A,k1_isomichi(A,B)))
        & v5_membered(k1_isomichi(A,k1_isomichi(A,B)))
        & v1_decomp_1(k1_isomichi(A,k1_isomichi(A,B)),A)
        & v1_isomichi(k1_isomichi(A,k1_isomichi(A,B)),A)
        & v2_isomichi(k1_isomichi(A,k1_isomichi(A,B)),A) ) ) )).

fof(cc11_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_isomichi(B,A)
           => ( ~ v4_isomichi(B,A)
              & ~ v5_isomichi(B,A) ) ) ) ) )).

fof(cc12_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_isomichi(B,A)
           => ( ~ v3_isomichi(B,A)
              & ~ v5_isomichi(B,A) ) ) ) ) )).

fof(cc13_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_isomichi(B,A)
           => ( ~ v3_isomichi(B,A)
              & ~ v4_isomichi(B,A) ) ) ) ) )).

fof(cc14_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_isomichi(B,A)
           => ( v3_isomichi(B,A)
              & ~ v4_isomichi(B,A)
              & ~ v5_isomichi(B,A) ) ) ) ) )).

fof(cc15_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_isomichi(B,A)
           => ( v3_isomichi(B,A)
              & ~ v4_isomichi(B,A)
              & ~ v5_isomichi(B,A) ) ) ) ) )).

fof(cc16_isomichi,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ( ~ v3_isomichi(B,A)
              & v4_isomichi(B,A)
              & ~ v5_isomichi(B,A) ) ) ) ) )).

fof(rc4_isomichi,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_pre_topc(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v3_isomichi(B,A)
          & v4_isomichi(B,A)
          & ~ v5_isomichi(B,A) ) ) )).

fof(rc5_isomichi,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & ~ v3_realset2(A)
      & v6_isomichi(A)
      & v7_isomichi(A) ) )).

fof(rc6_isomichi,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v8_isomichi(A) ) )).

fof(rc7_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_isomichi(B,A)
          & ~ v4_isomichi(B,A)
          & ~ v5_isomichi(B,A) ) ) )).

fof(rc8_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v7_isomichi(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v3_isomichi(B,A)
          & v4_isomichi(B,A)
          & ~ v5_isomichi(B,A) ) ) )).

fof(rc9_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v8_isomichi(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v3_isomichi(B,A)
          & ~ v4_isomichi(B,A)
          & v5_isomichi(B,A) ) ) )).

fof(fc11_isomichi,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v3_isomichi(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v3_isomichi(k3_subset_1(u1_struct_0(A),B),A)
        & ~ v4_isomichi(k3_subset_1(u1_struct_0(A),B),A)
        & ~ v5_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) )).

fof(fc12_isomichi,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & v7_isomichi(A)
        & l1_pre_topc(A)
        & v4_isomichi(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_isomichi(k3_subset_1(u1_struct_0(A),B),A)
        & v4_isomichi(k3_subset_1(u1_struct_0(A),B),A)
        & ~ v5_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) )).

fof(fc13_isomichi,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & v8_isomichi(A)
        & l1_pre_topc(A)
        & v5_isomichi(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_isomichi(k3_subset_1(u1_struct_0(A),B),A)
        & ~ v4_isomichi(k3_subset_1(u1_struct_0(A),B),A)
        & v5_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) )).

fof(t1_isomichi,axiom,(
    ! [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)))
             => k5_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B))),k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,C)))) = k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)))) ) ) ) )).

fof(t2_isomichi,axiom,(
    ! [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)))
             => k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C)))) = k4_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))),k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,C)))) ) ) ) )).

fof(d1_isomichi,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_isomichi(B,A)
          <=> k1_tops_1(A,k6_pre_topc(A,B)) = k1_tops_1(A,B) ) ) ) )).

fof(d2_isomichi,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_isomichi(B,A)
          <=> k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,B) ) ) ) )).

fof(t3_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
           => v1_isomichi(B,A) ) ) ) )).

fof(t4_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
           => v2_isomichi(B,A) ) ) ) )).

fof(d3_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
          <=> ( k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,B)
              & k1_tops_1(A,k6_pre_topc(A,B)) = k1_tops_1(A,B) ) ) ) ) )).

fof(t5_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
          <=> ( v2_isomichi(B,A)
              & v1_isomichi(B,A) ) ) ) ) )).

fof(t6_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_isomichi(B,A)
           => v2_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t7_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_isomichi(B,A)
           => v1_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t8_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_isomichi(B,A)
          <=> r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B) ) ) ) )).

fof(t9_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_isomichi(B,A)
          <=> r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) )).

fof(t10_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
          <=> ( r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B)
              & r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) ) )).

fof(t11_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v6_tops_1(k2_pre_topc(A),A)
        & v5_tops_1(k2_pre_topc(A),A) ) ) )).

fof(t12_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v6_tops_1(k1_pre_topc(A),A)
        & v5_tops_1(k1_pre_topc(A),A) ) ) )).

fof(t13_isomichi,axiom,(
    $true )).

fof(t14_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k1_tops_1(A,k6_pre_topc(A,k1_pre_topc(A))) = k1_pre_topc(A) ) )).

fof(t15_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
           => v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t16_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
           => v6_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t17_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(k1_tops_1(A,k6_pre_topc(A,B)),A)
            & v5_tops_1(k6_pre_topc(A,k1_tops_1(A,B)),A) ) ) ) )).

fof(t18_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
          <=> ( v1_isomichi(B,A)
              & v3_pre_topc(B,A) ) ) ) ) )).

fof(t19_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
          <=> ( v2_isomichi(B,A)
              & v4_pre_topc(B,A) ) ) ) ) )).

fof(t20_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                & v6_tops_1(C,A)
                & r1_tarski(C,B)
                & r1_tarski(B,k6_pre_topc(A,C)) ) ) ) ) )).

fof(t21_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                & v5_tops_1(C,A)
                & r1_tarski(k1_tops_1(A,C),B)
                & r1_tarski(B,C) ) ) ) ) )).

fof(d4_isomichi,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k1_tops_1(A,B)) ) ) )).

fof(t22_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => v4_pre_topc(k2_tops_1(A,B),A) ) ) )).

fof(t23_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
          <=> ( k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B)))
              & k2_tops_1(A,B) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,B)),k6_pre_topc(A,k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)))) ) ) ) ) )).

fof(d5_isomichi,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_isomichi(A,B) = k1_tops_1(A,k2_tops_1(A,B)) ) ) )).

fof(t24_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(k1_isomichi(A,B),A)
            & k1_isomichi(A,B) = k6_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,B)),k6_pre_topc(A,k1_tops_1(A,B)))
            & k1_isomichi(A,B) = k5_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,B)),k1_tops_1(A,k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))) ) ) ) )).

fof(t25_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_isomichi(B,A)
          <=> ( v6_tops_1(k1_tops_1(A,B),A)
              & v1_xboole_0(k1_isomichi(A,B)) ) ) ) ) )).

fof(t26_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_isomichi(B,A)
          <=> ( v5_tops_1(k6_pre_topc(A,B),A)
              & v1_xboole_0(k1_isomichi(A,B)) ) ) ) ) )).

fof(t27_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
          <=> ( v6_tops_1(k1_tops_1(A,B),A)
              & v5_tops_1(k6_pre_topc(A,B),A)
              & v1_xboole_0(k1_isomichi(A,B)) ) ) ) ) )).

fof(t28_isomichi,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k2_limfunc1(B)
           => k1_tops_1(k3_topmetr,A) = k12_prob_1(B) ) ) ) )).

fof(t29_isomichi,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k3_limfunc1(B)
           => k1_tops_1(k3_topmetr,A) = k4_limfunc1(B) ) ) ) )).

fof(t30_isomichi,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_limfunc1(B),k3_borsuk_5(B,C)),k3_limfunc1(C))
               => k6_pre_topc(k3_topmetr,A) = u1_struct_0(k3_topmetr) ) ) ) ) )).

fof(t31_isomichi,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k2_borsuk_5(B,C)
               => k1_tops_1(k3_topmetr,A) = k1_xboole_0 ) ) ) ) )).

fof(t32_isomichi,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k3_borsuk_5(B,C)
               => k1_tops_1(k3_topmetr,A) = k1_xboole_0 ) ) ) ) )).

fof(t33_isomichi,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k6_subset_1(k1_numbers,k2_limfunc1(A),k12_prob_1(B)) = k1_rcomp_1(B,A) ) ) )).

fof(t34_isomichi,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(B,A)
           => r1_xboole_0(k3_limfunc1(B),k12_prob_1(A)) ) ) ) )).

fof(t35_isomichi,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(B,A)
           => k3_borsuk_5(A,B) = k1_xboole_0 ) ) ) )).

fof(t36_isomichi,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => r1_tarski(k3_borsuk_5(A,B),k3_limfunc1(A)) ) ) )).

fof(t37_isomichi,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( A = k4_subset_1(k1_numbers,k12_prob_1(B),k2_borsuk_5(C,D))
                   => ( r1_xreal_0(C,B)
                      | r1_xreal_0(D,C)
                      | k1_tops_1(k3_topmetr,A) = k12_prob_1(B) ) ) ) ) ) ) )).

fof(t38_isomichi,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => r1_xboole_0(k1_rcomp_1(A,B),k4_limfunc1(B)) ) ) )).

fof(t39_isomichi,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k6_subset_1(k1_numbers,k3_limfunc1(A),k4_limfunc1(A)) = k1_seq_4(A) ) )).

fof(t40_isomichi,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(B,A)
           => k1_rcomp_1(A,B) = k6_subset_1(k1_numbers,k3_limfunc1(A),k4_limfunc1(B)) ) ) ) )).

fof(t41_isomichi,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(B,A)
           => k1_numbers = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k12_prob_1(A),k1_rcomp_1(A,B)),k4_limfunc1(B)) ) ) ) )).

fof(t42_isomichi,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k2_rcomp_1(A,B) = k6_subset_1(k1_numbers,k4_limfunc1(A),k3_limfunc1(B)) ) ) )).

fof(t43_isomichi,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(C,B)
                  & ~ r1_xreal_0(A,C)
                  & k6_subset_1(k1_numbers,k12_prob_1(A),k1_rcomp_1(B,C)) != k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_1(C,A)) ) ) ) ) )).

fof(t44_isomichi,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( A = k4_subset_1(k1_numbers,k2_limfunc1(B),k1_rcomp_1(C,D))
                   => ( r1_xreal_0(C,B)
                      | r1_xreal_0(D,C)
                      | k1_tops_1(k3_topmetr,A) = k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_1(C,D)) ) ) ) ) ) ) )).

fof(t45_isomichi,axiom,(
    ! [A,B] :
      ~ ( r3_xboole_0(A,B)
        & ~ r1_tarski(A,B)
        & ~ r2_xboole_0(B,A) ) )).

fof(d6_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_isomichi(B,A)
          <=> r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) )).

fof(d7_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_isomichi(B,A)
          <=> r2_xboole_0(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) ) ) ) )).

fof(d8_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_isomichi(B,A)
          <=> ~ r3_xboole_0(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) ) ) ) )).

fof(t46_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( ~ v3_isomichi(B,A)
              & ~ v4_isomichi(B,A)
              & ~ v5_isomichi(B,A) ) ) ) )).

fof(t47_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_isomichi(B,A)
          <=> v1_xboole_0(k1_isomichi(A,B)) ) ) ) )).

fof(d9_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v6_isomichi(A)
      <=> ? [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
            & v3_isomichi(B,A) ) ) ) )).

fof(d10_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v7_isomichi(A)
      <=> ? [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
            & v4_isomichi(B,A) ) ) ) )).

fof(d11_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v8_isomichi(A)
      <=> ? [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
            & v5_isomichi(B,A) ) ) ) )).

fof(t48_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_isomichi(B,A)
          <=> v3_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t49_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_isomichi(B,A)
          <=> v4_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t50_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_isomichi(B,A)
          <=> v5_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t51_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_isomichi(B,A)
           => ( k1_tops_1(A,k6_pre_topc(A,B)) = k1_tops_1(A,k6_pre_topc(A,k1_tops_1(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(t52_isomichi,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( k1_tops_1(A,k6_pre_topc(A,B)) = k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))
              | k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))) )
           => v3_isomichi(B,A) ) ) ) )).

fof(t53_isomichi,axiom,(
    ! [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)))
             => ( ( v3_isomichi(B,A)
                  & v3_isomichi(C,A) )
               => ( k5_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,B)),k1_tops_1(A,k6_pre_topc(A,C))) = k1_tops_1(A,k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)))
                  & k4_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,B)),k6_pre_topc(A,k1_tops_1(A,C))) = k6_pre_topc(A,k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C))) ) ) ) ) ) )).

fof(t54_isomichi,axiom,(
    ! [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)))
             => ( ( v3_isomichi(B,A)
                  & v3_isomichi(C,A) )
               => ( v3_isomichi(k4_subset_1(u1_struct_0(A),B,C),A)
                  & v3_isomichi(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) )).

fof(dt_k1_isomichi,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k1_isomichi(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
%------------------------------------------------------------------------------