SET007 Axioms: SET007+406.ax


%------------------------------------------------------------------------------
% File     : SET007+406 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On Kolmogorov 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    : tsp_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   63 (   2 unit)
%            Number of atoms       :  519 (  24 equality)
%            Maximal formula depth :   22 (  10 average)
%            Number of connectives :  630 ( 174 ~  ;   9  |; 255  &)
%                                         (  22 <=>; 170 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   32 (   1 propositional; 0-3 arity)
%            Number of functors    :   11 (   0 constant; 1-3 arity)
%            Number of variables   :  160 (   0 singleton; 149 !;  11 ?)
%            Maximal term depth    :    3 (   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(cc1_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_t_0topsp(A) ) ) ) )).

fof(cc2_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & ~ v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A) ) ) ) )).

fof(rc1_tsp_1,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v2_t_0topsp(A) ) )).

fof(rc2_tsp_1,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & ~ v2_t_0topsp(A) ) )).

fof(cc3_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A) ) ) ) )).

fof(cc4_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & ~ v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A) ) ) ) )).

fof(cc5_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & v2_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & ~ v2_t_0topsp(A) ) ) ) )).

fof(cc6_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_tdlat_3(A)
          & v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & v3_realset2(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v2_tdlat_3(A)
          & v3_tdlat_3(A)
          & v4_tdlat_3(A)
          & v5_tdlat_3(A)
          & v2_t_0topsp(A) ) ) ) )).

fof(cc7_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & ~ v2_tdlat_3(A) ) ) ) )).

fof(cc8_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v3_tdlat_3(A)
          & v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v3_tdlat_3(A)
          & v4_tdlat_3(A)
          & v5_tdlat_3(A)
          & v2_t_0topsp(A) ) ) ) )).

fof(cc9_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A)
          & v3_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A)
          & ~ v2_t_0topsp(A) ) ) ) )).

fof(cc10_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A)
          & v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A)
          & ~ v2_tdlat_3(A)
          & ~ v3_tdlat_3(A) ) ) ) )).

fof(rc3_tsp_1,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & ~ v2_tdlat_3(A)
      & v2_t_0topsp(A) ) )).

fof(rc4_tsp_1,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & ~ v1_tdlat_3(A)
      & ~ v2_t_0topsp(A) ) )).

fof(rc5_tsp_1,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_t_0topsp(B) ) ) )).

fof(rc6_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_tex_2(B,A)
          & v2_t_0topsp(B) ) ) )).

fof(cc11_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v3_struct_0(B)
           => ( ~ v3_struct_0(B)
              & v2_t_0topsp(B) ) ) ) ) )).

fof(cc12_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v2_t_0topsp(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)
              & ~ v2_t_0topsp(B) ) ) ) ) )).

fof(cc13_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v2_t_0topsp(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_t_0topsp(B) )
           => ( ~ v3_struct_0(B)
              & v2_tex_2(B,A) ) ) ) ) )).

fof(rc7_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v2_t_0topsp(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & ~ v2_t_0topsp(B) ) ) )).

fof(d1_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ( m1_tsp_1(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
                 => ( v3_pre_topc(C,B)
                  <=> ? [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                        & v3_pre_topc(D,A)
                        & C = k3_xboole_0(D,u1_struct_0(B)) ) ) ) ) ) ) ) )).

fof(t1_tsp_1,axiom,(
    $true )).

fof(t2_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_tsp_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v3_pre_topc(C,A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                     => ~ ( v3_pre_topc(D,B)
                          & D = k3_xboole_0(C,u1_struct_0(B)) ) ) ) ) ) ) )).

fof(d2_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ( m2_tsp_1(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
                 => ( v4_pre_topc(C,B)
                  <=> ? [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                        & v4_pre_topc(D,A)
                        & C = k3_xboole_0(D,u1_struct_0(B)) ) ) ) ) ) ) ) )).

fof(t3_tsp_1,axiom,(
    $true )).

fof(t4_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m2_tsp_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v4_pre_topc(C,A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                     => ~ ( v4_pre_topc(D,B)
                          & D = k3_xboole_0(C,u1_struct_0(B)) ) ) ) ) ) ) )).

fof(d3_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v2_t_0topsp(A)
      <=> ( v3_struct_0(A)
          | ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ ( B != C
                      & ! [D] :
                          ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( v3_pre_topc(D,A)
                              & r2_hidden(B,D)
                              & ~ r2_hidden(C,D) ) )
                      & ! [D] :
                          ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( v3_pre_topc(D,A)
                              & ~ r2_hidden(B,D)
                              & r2_hidden(C,D) ) ) ) ) ) ) ) ) )).

fof(d4_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v2_t_0topsp(A)
      <=> ( v3_struct_0(A)
          | ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ ( B != C
                      & ! [D] :
                          ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( v4_pre_topc(D,A)
                              & r2_hidden(B,D)
                              & ~ r2_hidden(C,D) ) )
                      & ! [D] :
                          ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( v4_pre_topc(D,A)
                              & ~ r2_hidden(B,D)
                              & r2_hidden(C,D) ) ) ) ) ) ) ) ) )).

fof(d5_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_t_0topsp(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( B != C
                    & k6_pre_topc(A,k1_struct_0(A,B)) = k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) ) )).

fof(d6_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_t_0topsp(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( B != C
                    & r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C)))
                    & r2_hidden(C,k6_pre_topc(A,k1_struct_0(A,B))) ) ) ) ) ) )).

fof(d7_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_t_0topsp(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( B != C
                    & r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C)))
                    & r1_tarski(k6_pre_topc(A,k1_struct_0(A,C)),k6_pre_topc(A,k1_struct_0(A,B))) ) ) ) ) ) )).

fof(d8_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tsp_1(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
                        & ! [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( v3_pre_topc(E,A)
                                & r2_hidden(C,E)
                                & ~ r2_hidden(D,E) ) )
                        & ! [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( v3_pre_topc(E,A)
                                & ~ r2_hidden(C,E)
                                & r2_hidden(D,E) ) ) ) ) ) ) ) ) )).

fof(d9_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tsp_1(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
                        & ! [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( v4_pre_topc(E,A)
                                & r2_hidden(C,E)
                                & ~ r2_hidden(D,E) ) )
                        & ! [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( v4_pre_topc(E,A)
                                & ~ r2_hidden(C,E)
                                & r2_hidden(D,E) ) ) ) ) ) ) ) ) )).

fof(t5_tsp_1,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
                      & v1_tsp_1(C,A) )
                   => v1_tsp_1(D,B) ) ) ) ) ) )).

fof(t6_tsp_1,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)
           => ( v1_tsp_1(B,A)
            <=> v2_t_0topsp(A) ) ) ) ) )).

fof(t7_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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)
                  & v1_tsp_1(B,A) )
               => v1_tsp_1(C,A) ) ) ) ) )).

fof(t8_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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)))
             => ( ( v1_tsp_1(B,A)
                  | v1_tsp_1(C,A) )
               => v1_tsp_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t9_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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)))
             => ( ( v1_tsp_1(B,A)
                  & v1_tsp_1(C,A) )
               => ( ( ~ v3_pre_topc(B,A)
                    & ~ v3_pre_topc(C,A) )
                  | v1_tsp_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) )).

fof(t10_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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)))
             => ( ( v1_tsp_1(B,A)
                  & v1_tsp_1(C,A) )
               => ( ( ~ v4_pre_topc(B,A)
                    & ~ v4_pre_topc(C,A) )
                  | v1_tsp_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) )).

fof(t11_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tex_2(B,A)
           => v1_tsp_1(B,A) ) ) ) )).

fof(t12_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ~ ( v1_tex_4(B,A)
              & ~ v1_realset1(B)
              & v1_tsp_1(B,A) ) ) ) )).

fof(d10_tsp_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)))
         => ( v1_tsp_1(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
                        & k6_pre_topc(A,k1_struct_0(A,C)) = k6_pre_topc(A,k1_struct_0(A,D)) ) ) ) ) ) ) )).

fof(d11_tsp_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)))
         => ( v1_tsp_1(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
                        & r2_hidden(C,k6_pre_topc(A,k1_struct_0(A,D)))
                        & r2_hidden(D,k6_pre_topc(A,k1_struct_0(A,C))) ) ) ) ) ) ) )).

fof(d12_tsp_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)))
         => ( v1_tsp_1(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
                        & r2_hidden(C,k6_pre_topc(A,k1_struct_0(A,D)))
                        & r1_tarski(k6_pre_topc(A,k1_struct_0(A,D)),k6_pre_topc(A,k1_struct_0(A,C))) ) ) ) ) ) ) )).

fof(t13_tsp_1,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))) )
         => v1_tsp_1(B,A) ) ) )).

fof(t14_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v1_tsp_1(k1_struct_0(A,B),A) ) ) )).

fof(d13_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m2_tsp_1(B,A)
         => ( v2_t_0topsp(B)
          <=> ( v3_struct_0(B)
              | ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( m1_subset_1(C,u1_struct_0(B))
                          & m1_subset_1(D,u1_struct_0(B))
                          & C != D
                          & ! [E] :
                              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                             => ~ ( v3_pre_topc(E,A)
                                  & r2_hidden(C,E)
                                  & ~ r2_hidden(D,E) ) )
                          & ! [E] :
                              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                             => ~ ( v3_pre_topc(E,A)
                                  & ~ r2_hidden(C,E)
                                  & r2_hidden(D,E) ) ) ) ) ) ) ) ) ) )).

fof(d14_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m2_tsp_1(B,A)
         => ( v2_t_0topsp(B)
          <=> ( v3_struct_0(B)
              | ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( m1_subset_1(C,u1_struct_0(B))
                          & m1_subset_1(D,u1_struct_0(B))
                          & C != D
                          & ! [E] :
                              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                             => ~ ( v4_pre_topc(E,A)
                                  & r2_hidden(C,E)
                                  & ~ r2_hidden(D,E) ) )
                          & ! [E] :
                              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                             => ~ ( v4_pre_topc(E,A)
                                  & ~ r2_hidden(C,E)
                                  & r2_hidden(D,E) ) ) ) ) ) ) ) ) ) )).

fof(t15_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = u1_struct_0(B)
               => ( v1_tsp_1(C,A)
                <=> v2_t_0topsp(B) ) ) ) ) ) )).

fof(t16_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_t_0topsp(C)
                & m2_tsp_1(C,A) )
             => ( m2_tsp_1(B,C)
               => v2_t_0topsp(B) ) ) ) ) )).

fof(t17_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_t_0topsp(B)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m2_tsp_1(C,A) )
             => ( ~ r1_tsep_1(A,B,C)
               => v2_t_0topsp(k2_tsep_1(A,B,C)) ) ) ) ) )).

fof(t18_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_t_0topsp(B)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_t_0topsp(C)
                & m2_tsp_1(C,A) )
             => ( ( v1_tsep_1(B,A)
                  | v1_tsep_1(C,A) )
               => v2_t_0topsp(k1_tsep_1(A,B,C)) ) ) ) ) )).

fof(t19_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_t_0topsp(B)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_t_0topsp(C)
                & m2_tsp_1(C,A) )
             => ( ( v1_borsuk_1(B,A)
                  | v1_borsuk_1(C,A) )
               => v2_t_0topsp(k1_tsep_1(A,B,C)) ) ) ) ) )).

fof(t20_tsp_1,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))) )
         => ~ ( v1_tsp_1(B,A)
              & ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v1_pre_topc(C)
                    & v2_t_0topsp(C)
                    & m2_tsp_1(C,A) )
                 => B != u1_struct_0(C) ) ) ) ) )).

fof(t21_tsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v2_t_0topsp(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( ~ v1_tsp_1(B,A)
              & ! [C] :
                  ( ( v1_pre_topc(C)
                    & ~ v2_t_0topsp(C)
                    & m2_tsp_1(C,A) )
                 => B != u1_struct_0(C) ) ) ) ) )).

fof(dt_m1_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_tsp_1(B,A)
         => l1_pre_topc(B) ) ) )).

fof(existence_m1_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ? [B] : m1_tsp_1(B,A) ) )).

fof(redefinition_m1_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_tsp_1(B,A)
        <=> m1_pre_topc(B,A) ) ) )).

fof(dt_m2_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m2_tsp_1(B,A)
         => l1_pre_topc(B) ) ) )).

fof(existence_m2_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ? [B] : m2_tsp_1(B,A) ) )).

fof(redefinition_m2_tsp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m2_tsp_1(B,A)
        <=> m1_pre_topc(B,A) ) ) )).

fof(redefinition_v2_tsp_1,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_pre_topc(B,A) )
     => ( v2_tsp_1(B,A)
      <=> v2_t_0topsp(B) ) ) )).

fof(redefinition_v3_tsp_1,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_pre_topc(B,A) )
     => ( v3_tsp_1(B,A)
      <=> v2_t_0topsp(B) ) ) )).
%------------------------------------------------------------------------------