SET007 Axioms: SET007+387.ax


%------------------------------------------------------------------------------
% File     : SET007+387 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Maximal Discrete Subspaces of Almost Discrete Topological Spaces
% 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    : tex_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  164 (   4 unit)
%            Number of atoms       : 1356 (  50 equality)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives : 1553 ( 361 ~  ;   4  |; 717  &)
%                                         (  23 <=>; 448 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   44 (   1 propositional; 0-3 arity)
%            Number of functors    :   18 (   2 constant; 0-4 arity)
%            Number of variables   :  386 (   0 singleton; 356 !;  30 ?)
%            Maximal term depth    :    4 (   1 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(rc1_tex_2,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) )).

fof(rc2_tex_2,axiom,(
    ! [A] :
    ? [B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) )).

fof(cc1_tex_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_tex_2(B,k1_zfmisc_1(A))
           => ~ v1_xboole_0(B) ) ) ) )).

fof(cc2_tex_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_xboole_0(B)
           => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) )).

fof(cc3_tex_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_tex_2(B,k1_zfmisc_1(A))
           => ( v1_xboole_0(B)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) )).

fof(cc4_tex_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_xboole_0(B)
           => ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) )).

fof(rc3_tex_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) )).

fof(rc4_tex_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) )).

fof(rc5_tex_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B) ) ) )).

fof(fc1_tex_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_realset1(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) )).

fof(cc5_tex_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & v1_realset1(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) )).

fof(cc6_tex_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & v1_realset1(B) )
           => ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) )).

fof(cc7_tex_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & ~ v1_realset1(B) ) ) ) ) )).

fof(rc6_tex_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) )).

fof(rc7_tex_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) )).

fof(cc8_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ~ v1_xboole_0(B)
           => ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(cc9_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_struct_0(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))) )
           => ( ~ v1_xboole_0(B)
              & v1_realset1(B) ) ) ) ) )).

fof(cc10_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ~ v1_xboole_0(B)
              & v1_realset1(B) )
           => ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(cc11_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(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))) )
           => ( ~ v1_xboole_0(B)
              & ~ v1_realset1(B) ) ) ) ) )).

fof(rc8_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(rc9_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(rc10_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(cc12_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v3_struct_0(B)
           => ( ~ v3_struct_0(B)
              & ~ v2_tex_2(B,A) ) ) ) ) )).

fof(cc13_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v2_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v3_realset2(B) ) ) ) ) )).

fof(cc14_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_tex_2(B,A) ) ) ) ) )).

fof(cc15_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v2_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & ~ v3_realset2(B) ) ) ) ) )).

fof(rc11_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & ~ v2_tex_2(B,A) ) ) )).

fof(cc16_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v1_tdlat_3(B)
           => v2_pre_topc(B) ) ) ) )).

fof(cc17_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v2_tdlat_3(B)
           => v2_pre_topc(B) ) ) ) )).

fof(cc18_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v2_pre_topc(B)
           => ~ v1_tdlat_3(B) ) ) ) )).

fof(cc19_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v2_pre_topc(B)
           => ~ v2_tdlat_3(B) ) ) ) )).

fof(cc20_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v1_tdlat_3(B)
           => v3_tdlat_3(B) ) ) ) )).

fof(cc21_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v3_tdlat_3(B)
           => ~ v1_tdlat_3(B) ) ) ) )).

fof(cc22_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v2_tdlat_3(B)
           => v3_tdlat_3(B) ) ) ) )).

fof(cc23_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v3_tdlat_3(B)
           => ~ v2_tdlat_3(B) ) ) ) )).

fof(cc24_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & v3_realset2(B) ) ) ) ) )).

fof(cc25_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_tdlat_3(B)
              & ~ v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & ~ v1_tdlat_3(B) ) ) ) ) )).

fof(cc26_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_tdlat_3(B)
              & ~ v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & ~ v2_tdlat_3(B) ) ) ) ) )).

fof(rc12_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v3_realset2(B) ) ) )).

fof(fc2_tex_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k1_tex_2(A,B))
        & v1_pre_topc(k1_tex_2(A,B))
        & v3_realset2(k1_tex_2(A,B)) ) ) )).

fof(rc13_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v3_realset2(B)
          & v2_tex_2(B,A) ) ) )).

fof(cc27_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B) ) ) ) ) )).

fof(rc14_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_tdlat_3(B)
          & v2_tdlat_3(B)
          & v3_tdlat_3(B)
          & v4_tdlat_3(B)
          & v5_tdlat_3(B)
          & v3_realset2(B) ) ) )).

fof(fc3_tex_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k1_tex_2(A,B))
        & v1_pre_topc(k1_tex_2(A,B))
        & v2_pre_topc(k1_tex_2(A,B))
        & v1_tdlat_3(k1_tex_2(A,B))
        & v2_tdlat_3(k1_tex_2(A,B))
        & v3_tdlat_3(k1_tex_2(A,B))
        & v4_tdlat_3(k1_tex_2(A,B))
        & v5_tdlat_3(k1_tex_2(A,B))
        & v3_realset2(k1_tex_2(A,B)) ) ) )).

fof(rc15_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_tdlat_3(B)
          & v2_tdlat_3(B)
          & v3_tdlat_3(B)
          & v4_tdlat_3(B)
          & v5_tdlat_3(B)
          & v3_realset2(B) ) ) )).

fof(fc4_tex_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k1_tex_2(A,B))
        & v1_pre_topc(k1_tex_2(A,B))
        & v2_pre_topc(k1_tex_2(A,B))
        & v1_tdlat_3(k1_tex_2(A,B))
        & v2_tdlat_3(k1_tex_2(A,B))
        & v3_tdlat_3(k1_tex_2(A,B))
        & v4_tdlat_3(k1_tex_2(A,B))
        & v5_tdlat_3(k1_tex_2(A,B))
        & v3_realset2(k1_tex_2(A,B)) ) ) )).

fof(cc28_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v2_tex_2(B,A)
           => ( v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A) ) ) ) ) )).

fof(cc29_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v1_tsep_1(B,A)
           => ( v2_pre_topc(B)
              & v2_tex_2(B,A) ) ) ) ) )).

fof(cc30_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v1_borsuk_1(B,A)
           => ( v2_pre_topc(B)
              & v2_tex_2(B,A) ) ) ) ) )).

fof(rc16_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_tsep_1(B,A)
          & v1_borsuk_1(B,A) ) ) )).

fof(cc31_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B) ) ) ) ) )).

fof(cc32_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & ~ v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v3_realset2(B) ) ) ) ) )).

fof(rc17_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_tsep_1(B,A)
          & v1_borsuk_1(B,A)
          & v1_tdlat_3(B)
          & v3_tdlat_3(B)
          & v2_tex_2(B,A) ) ) )).

fof(cc33_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B) ) ) ) ) )).

fof(cc34_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & ~ v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v3_realset2(B) ) ) ) ) )).

fof(cc35_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & ~ v1_tsep_1(B,A)
              & ~ v1_borsuk_1(B,A)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v2_tex_2(B,A) ) ) ) ) )).

fof(cc36_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B)
              & v2_tex_2(B,A) ) ) ) ) )).

fof(rc18_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & ~ v1_tsep_1(B,A)
          & ~ v1_borsuk_1(B,A)
          & v2_tdlat_3(B)
          & v3_tdlat_3(B)
          & v2_tex_2(B,A) ) ) )).

fof(rc19_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v3_tdlat_3(B)
          & v4_tdlat_3(B)
          & v5_tdlat_3(B)
          & v2_tex_2(B,A) ) ) )).

fof(cc37_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v5_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B) ) ) ) ) )).

fof(cc38_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v1_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & ~ v5_tex_2(B,A) ) ) ) ) )).

fof(cc39_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v5_tex_2(B,A)
           => ( v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & v3_tdlat_3(B)
              & ~ v2_tex_2(B,A) ) ) ) ) )).

fof(cc40_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v2_tex_2(B,A)
           => ( v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & v3_tdlat_3(B)
              & ~ v5_tex_2(B,A) ) ) ) ) )).

fof(cc41_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v2_tex_2(B,A)
           => ( v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & v3_tdlat_3(B)
              & v5_tex_2(B,A) ) ) ) ) )).

fof(cc42_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v5_tex_2(B,A)
           => ( v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & v3_tdlat_3(B)
              & v2_tex_2(B,A) ) ) ) ) )).

fof(cc43_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v5_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B) ) ) ) ) )).

fof(cc44_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v5_tex_2(B,A) ) ) ) ) )).

fof(cc45_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B)
              & v5_tex_2(B,A) ) ) ) ) )).

fof(cc46_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v5_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & ~ v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v3_realset2(B)
              & ~ v5_tex_2(B,A) ) ) ) ) )).

fof(cc47_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v1_tdlat_3(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v5_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v2_tex_2(B,A) ) ) ) ) )).

fof(cc48_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v1_tdlat_3(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v2_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v5_tex_2(B,A) ) ) ) ) )).

fof(cc49_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v2_tdlat_3(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v5_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v3_realset2(B) ) ) ) ) )).

fof(cc50_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v2_tdlat_3(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v5_tex_2(B,A) ) ) ) ) )).

fof(rc20_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_tdlat_3(B)
          & v3_tdlat_3(B)
          & v4_tdlat_3(B)
          & v5_tdlat_3(B)
          & v5_tex_2(B,A) ) ) )).

fof(d1_tex_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v1_realset1(A)
      <=> ? [B] :
            ( m1_subset_1(B,A)
            & A = k6_domain_1(A,B) ) ) ) )).

fof(t1_tex_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_realset1(B) )
         => ( r1_tarski(A,B)
           => A = B ) ) ) )).

fof(t2_tex_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] :
          ( ~ v1_xboole_0(k3_xboole_0(A,B))
         => r1_tarski(A,B) ) ) )).

fof(t3_tex_2,axiom,(
    $true )).

fof(t4_tex_2,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ( ( u1_struct_0(A) = u1_struct_0(B)
              & v3_realset2(A) )
           => v3_realset2(B) ) ) ) )).

fof(d2_tex_2,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,A)
     => ( v1_tex_2(B,A)
      <=> B != k3_tarski(A) ) ) )).

fof(t5_tex_2,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ( v1_tex_2(B,k1_zfmisc_1(A))
      <=> B != A ) ) )).

fof(t6_tex_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ~ ( v1_tex_2(k6_domain_1(A,B),k1_zfmisc_1(A))
              & v1_realset1(A) ) ) ) )).

fof(t7_tex_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] :
          ( m1_subset_1(B,A)
         => v1_tex_2(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ) )).

fof(t8_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ ( v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A)))
              & v3_realset2(A) ) ) ) )).

fof(t9_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(t10_tex_2,axiom,(
    $true )).

fof(t11_tex_2,axiom,(
    $true )).

fof(t12_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
              & v2_pre_topc(A) )
           => v2_pre_topc(B) ) ) ) )).

fof(d3_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v2_tex_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( C = u1_struct_0(B)
                 => v1_tex_2(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).

fof(t13_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = u1_struct_0(B)
               => ( v1_tex_2(C,k1_zfmisc_1(u1_struct_0(A)))
                <=> v2_tex_2(B,A) ) ) ) ) ) )).

fof(t14_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_pre_topc(C,A)
             => ( ( g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))
                  & v2_tex_2(B,A) )
               => v2_tex_2(C,A) ) ) ) ) )).

fof(t15_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ~ ( u1_struct_0(B) = u1_struct_0(A)
              & v2_tex_2(B,A) ) ) ) )).

fof(t16_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v2_tex_2(B,A)
            & m1_pre_topc(B,A) )
         => g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) )).

fof(t17_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
              & v1_tdlat_3(A) )
           => v1_tdlat_3(B) ) ) ) )).

fof(t18_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
              & v2_tdlat_3(A) )
           => v2_tdlat_3(B) ) ) ) )).

fof(t19_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
              & v3_tdlat_3(A) )
           => v3_tdlat_3(B) ) ) ) )).

fof(d4_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v1_pre_topc(C)
                & m1_pre_topc(C,A) )
             => ( C = k1_tex_2(A,B)
              <=> u1_struct_0(C) = k1_struct_0(A,B) ) ) ) ) )).

fof(t20_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v2_tex_2(k1_tex_2(A,B),A)
          <=> v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t21_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ ( v2_tex_2(k1_tex_2(A,B),A)
              & v3_realset2(A) ) ) ) )).

fof(t22_tex_2,axiom,(
    $true )).

fof(t23_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_realset2(B)
            & m1_pre_topc(B,A) )
         => ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(k1_tex_2(A,C)),u1_pre_topc(k1_tex_2(A,C))) ) ) ) )).

fof(t24_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v2_pre_topc(k1_tex_2(A,B))
           => ( v1_tdlat_3(k1_tex_2(A,B))
              & v2_tdlat_3(k1_tex_2(A,B)) ) ) ) ) )).

fof(d5_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tex_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( r1_tarski(C,B)
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( v3_pre_topc(D,A)
                            & k5_subset_1(u1_struct_0(A),B,D) = C ) ) ) ) ) ) ) )).

fof(d6_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tex_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( r1_tarski(C,B)
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( v4_pre_topc(D,A)
                            & k5_subset_1(u1_struct_0(A),B,D) = C ) ) ) ) ) ) ) )).

fof(t25_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & C = D
                      & v3_tex_2(C,A) )
                   => v3_tex_2(D,B) ) ) ) ) ) )).

fof(t26_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = u1_struct_0(B)
               => ( v3_tex_2(C,A)
                <=> v1_tdlat_3(B) ) ) ) ) ) )).

fof(t27_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( B = u1_struct_0(A)
           => ( v3_tex_2(B,A)
            <=> v1_tdlat_3(A) ) ) ) ) )).

fof(t28_tex_2,axiom,(
    ! [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)))
             => ( ( r1_tarski(C,B)
                  & v3_tex_2(B,A) )
               => v3_tex_2(C,A) ) ) ) ) )).

fof(t29_tex_2,axiom,(
    ! [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_tex_2(B,A)
                  | v3_tex_2(C,A) )
               => v3_tex_2(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t30_tex_2,axiom,(
    ! [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_pre_topc(B,A)
                    & v3_pre_topc(C,A) )
                 => ( v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)
                    & v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),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_pre_topc(B,A)
                    & v3_pre_topc(C,A)
                    & v3_tex_2(B,A)
                    & v3_tex_2(C,A) )
                 => v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) )).

fof(t31_tex_2,axiom,(
    ! [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)))
               => ( ( v4_pre_topc(B,A)
                    & v4_pre_topc(C,A) )
                 => ( v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)
                    & v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),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)))
               => ( ( v4_pre_topc(B,A)
                    & v4_pre_topc(C,A)
                    & v3_tex_2(B,A)
                    & v3_tex_2(C,A) )
                 => v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) )).

fof(t32_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tex_2(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( r2_hidden(C,B)
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( v3_pre_topc(D,A)
                            & k5_subset_1(u1_struct_0(A),B,D) = k1_tarski(C) ) ) ) ) ) ) ) )).

fof(t33_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tex_2(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( r2_hidden(C,B)
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( v4_pre_topc(D,A)
                            & k5_subset_1(u1_struct_0(A),B,D) = k1_tarski(C) ) ) ) ) ) ) ) )).

fof(t34_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ~ ( v3_tex_2(B,A)
              & ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v1_pre_topc(C)
                    & v1_tdlat_3(C)
                    & m1_pre_topc(C,A) )
                 => B != u1_struct_0(C) ) ) ) ) )).

fof(t35_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v3_tex_2(B,A) ) ) )).

fof(t36_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v3_tex_2(k1_struct_0(A,B),A) ) ) )).

fof(t37_tex_2,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,u1_struct_0(A))
               => ~ ( r2_hidden(C,B)
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( v3_pre_topc(D,A)
                            & k5_subset_1(u1_struct_0(A),B,D) = k1_struct_0(A,C) ) ) ) )
           => v3_tex_2(B,A) ) ) ) )).

fof(t38_tex_2,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)))
             => ( ( v3_pre_topc(B,A)
                  & v3_pre_topc(C,A)
                  & v3_tex_2(B,A)
                  & v3_tex_2(C,A) )
               => v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t39_tex_2,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)))
             => ( ( v4_pre_topc(B,A)
                  & v4_pre_topc(C,A)
                  & v3_tex_2(B,A)
                  & v3_tex_2(C,A) )
               => v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t40_tex_2,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)))
         => ( ( v1_tops_3(B,A)
              & v3_tex_2(B,A) )
           => v3_pre_topc(B,A) ) ) ) )).

fof(t41_tex_2,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)))
         => ( v3_tex_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r1_tarski(C,B)
                 => k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)) = C ) ) ) ) ) )).

fof(t42_tex_2,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)))
         => ( v3_tex_2(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,C) ) ) ) ) ) )).

fof(t43_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => v3_tex_2(B,A) ) ) )).

fof(t44_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v3_tex_2(B,A)
          <=> v1_realset1(B) ) ) ) )).

fof(d7_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tex_2(B,A)
          <=> ( v3_tex_2(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v3_tex_2(C,A)
                      & r1_tarski(B,C) )
                   => B = C ) ) ) ) ) ) )).

fof(t45_tex_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & C = D
                      & v4_tex_2(C,A) )
                   => v4_tex_2(D,B) ) ) ) ) ) )).

fof(t46_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ~ v4_tex_2(B,A) ) ) )).

fof(t47_tex_2,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)))
         => ( ( v3_pre_topc(B,A)
              & v4_tex_2(B,A) )
           => v1_tops_1(B,A) ) ) ) )).

fof(t48_tex_2,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)))
         => ( ( v1_tops_1(B,A)
              & v3_tex_2(B,A) )
           => v4_tex_2(B,A) ) ) ) )).

fof(t49_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tex_2(B,A)
          <=> ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t50_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v4_tex_2(B,A)
          <=> v1_realset1(B) ) ) ) )).

fof(d8_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v5_tex_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( C = u1_struct_0(B)
                 => v4_tex_2(C,A) ) ) ) ) ) )).

fof(t51_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = u1_struct_0(B)
               => ( v4_tex_2(C,A)
                <=> v5_tex_2(B,A) ) ) ) ) ) )).

fof(t52_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ( v5_tex_2(B,A)
          <=> ( v1_tdlat_3(B)
              & ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v1_tdlat_3(C)
                    & m1_pre_topc(C,A) )
                 => ( m1_pre_topc(B,C)
                   => g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) ) ) ) ) ) ) )).

fof(t53_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ~ ( v4_tex_2(B,A)
              & ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v1_pre_topc(C)
                    & m1_pre_topc(C,A) )
                 => ~ ( v5_tex_2(C,A)
                      & B = u1_struct_0(C) ) ) ) ) ) )).

fof(t55_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C)))
               => k6_pre_topc(A,k1_struct_0(A,B)) = k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) )).

fof(t56_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_xboole_0(k6_pre_topc(A,k1_struct_0(A,B)),k6_pre_topc(A,k1_struct_0(A,C)))
                | k6_pre_topc(A,k1_struct_0(A,B)) = k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) )).

fof(t57_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( r2_hidden(C,B)
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( v4_pre_topc(D,A)
                            & k5_subset_1(u1_struct_0(A),B,D) = k1_struct_0(A,C) ) ) ) )
           => v3_tex_2(B,A) ) ) ) )).

fof(t58_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,C) ) )
           => v3_tex_2(B,A) ) ) ) )).

fof(t59_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tex_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => ( C = D
                        | r1_xboole_0(k6_pre_topc(A,k1_struct_0(A,C)),k6_pre_topc(A,k1_struct_0(A,D))) ) ) ) ) ) ) ) )).

fof(t60_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tex_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( r2_hidden(C,k6_pre_topc(A,B))
                    & ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => ~ ( r2_hidden(D,B)
                            & k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,D) ) ) ) ) ) ) ) )).

fof(t61_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( ( v3_pre_topc(B,A)
                | v4_pre_topc(B,A) )
              & v4_tex_2(B,A)
              & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t62_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tex_2(B,A)
           => v1_tops_1(B,A) ) ) ) )).

fof(t64_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tex_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & r2_hidden(D,B)
                    & k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,D) ) ) ) ) ) )).

fof(t65_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( v3_tex_2(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( r1_tarski(B,C)
                      & v4_tex_2(C,A) ) ) ) ) ) )).

fof(t66_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v4_tex_2(B,A) ) ) )).

fof(t67_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_tdlat_3(B)
            & m1_pre_topc(B,A) )
         => ? [C] :
              ( ~ v3_struct_0(C)
              & v1_pre_topc(C)
              & m1_pre_topc(C,A)
              & m1_pre_topc(B,C)
              & v5_tex_2(C,A) ) ) ) )).

fof(t68_tex_2,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => v5_pre_topc(C,A,B) ) ) ) )).

fof(t69_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ! [B] :
            ( ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & l1_pre_topc(B) )
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
               => v5_pre_topc(C,A,B) ) )
       => v1_tdlat_3(A) ) ) )).

fof(t70_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_tdlat_3(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => v5_pre_topc(C,A,B) ) ) ) )).

fof(t71_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ! [B] :
            ( ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & l1_pre_topc(B) )
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                  & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
               => v5_pre_topc(C,B,A) ) )
       => v2_tdlat_3(A) ) ) )).

fof(t72_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v5_pre_topc(C,A,B)
              & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
              & v3_borsuk_1(C,A,B) ) ) ) )).

fof(t73_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => r1_borsuk_1(A,B) ) ) )).

fof(t74_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v5_tex_2(B,A)
            & m1_pre_topc(B,A) )
         => ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v5_pre_topc(C,A,B)
              & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
              & v3_borsuk_1(C,A,B) ) ) ) )).

fof(t75_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v5_tex_2(B,A)
            & m1_pre_topc(B,A) )
         => r1_borsuk_1(A,B) ) ) )).

fof(t76_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v5_tex_2(B,A)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_borsuk_1(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ( D = E
                         => k5_pre_topc(A,B,C,D) = k6_pre_topc(A,E) ) ) ) ) ) ) ) )).

fof(t77_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v5_tex_2(B,A)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_borsuk_1(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( D = E
                         => k5_pre_topc(A,B,C,k1_struct_0(B,D)) = k6_pre_topc(A,k1_struct_0(A,E)) ) ) ) ) ) ) ) )).

fof(t78_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_tdlat_3(B)
            & m1_pre_topc(B,A) )
         => ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v5_pre_topc(C,A,B)
              & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
              & v3_borsuk_1(C,A,B) ) ) ) )).

fof(t79_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_tdlat_3(B)
            & m1_pre_topc(B,A) )
         => r1_borsuk_1(A,B) ) ) )).

fof(s1_tex_2,axiom,
    ( ! [A] :
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_tex_2)))
       => ~ ( r2_hidden(A,f2_s1_tex_2)
            & ! [B] :
                ( m1_subset_1(B,u1_struct_0(f1_s1_tex_2))
               => ~ p1_s1_tex_2(A,B) ) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f2_s1_tex_2,u1_struct_0(f1_s1_tex_2))
        & m2_relset_1(A,f2_s1_tex_2,u1_struct_0(f1_s1_tex_2))
        & ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_tex_2)))
           => ( r2_hidden(B,f2_s1_tex_2)
             => p1_s1_tex_2(B,k1_funct_1(A,B)) ) ) ) )).

fof(dt_k1_tex_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k1_tex_2(A,B))
        & v1_pre_topc(k1_tex_2(A,B))
        & m1_pre_topc(k1_tex_2(A,B),A) ) ) )).

fof(t54_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,B) = k3_tarski(a_2_0_tex_2(A,B)) ) ) )).

fof(t63_tex_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tex_2(B,A)
           => k3_tarski(a_2_0_tex_2(A,B)) = u1_struct_0(A) ) ) ) )).

fof(fraenkel_a_2_0_tex_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v3_tdlat_3(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_tex_2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = k6_pre_topc(B,k1_struct_0(B,D))
            & r2_hidden(D,C) ) ) ) )).
%------------------------------------------------------------------------------