SET007 Axioms: SET007+358.ax


%------------------------------------------------------------------------------
% File     : SET007+358 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Duality Between Weakly Separated Subspaces of 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    : tsep_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   59 (   2 unit)
%            Number of atoms       :  589 (  35 equality)
%            Maximal formula depth :   20 (  11 average)
%            Number of connectives :  659 ( 129 ~  ;   4  |; 259  &)
%                                         (  21 <=>; 246 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   1 propositional; 0-3 arity)
%            Number of functors    :   15 (   0 constant; 1-3 arity)
%            Number of variables   :  227 (   0 singleton; 223 !;   4 ?)
%            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(t1_tsep_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)))
             => k6_subset_1(u1_struct_0(A),k3_subset_1(u1_struct_0(A),B),k3_subset_1(u1_struct_0(A),C)) = k6_subset_1(u1_struct_0(A),C,B) ) ) ) )).

fof(d1_tsep_2,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)))
             => ( r1_tsep_2(A,B,C)
              <=> ( r1_xboole_0(B,C)
                  & k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A) ) ) ) ) ) )).

fof(t2_tsep_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)))
             => ( r1_tsep_2(A,B,C)
              <=> ( r1_xboole_0(B,C)
                  & k4_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A) ) ) ) ) ) )).

fof(t3_tsep_2,axiom,(
    $true )).

fof(t4_tsep_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)))
             => ( r1_tsep_2(A,B,C)
               => ( B = k3_subset_1(u1_struct_0(A),C)
                  & C = k3_subset_1(u1_struct_0(A),B) ) ) ) ) ) )).

fof(t5_tsep_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)))
             => ( ( B = k3_subset_1(u1_struct_0(A),C)
                  | C = k3_subset_1(u1_struct_0(A),B) )
               => r1_tsep_2(A,B,C) ) ) ) ) )).

fof(t6_tsep_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)))
         => r1_tsep_2(A,B,k3_subset_1(u1_struct_0(A),B)) ) ) )).

fof(t7_tsep_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => r1_tsep_2(A,k1_pre_topc(A),k2_pre_topc(A)) ) )).

fof(t8_tsep_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)))
         => ~ r1_tsep_2(A,B,B) ) ) )).

fof(t9_tsep_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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r2_tsep_2(A,B,C)
                      & r2_tsep_2(A,C,D) )
                   => B = D ) ) ) ) ) )).

fof(t10_tsep_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)))
             => ( r2_tsep_2(A,B,C)
               => ( r2_tsep_2(A,k6_pre_topc(A,B),k1_tops_1(A,C))
                  & r2_tsep_2(A,k1_tops_1(A,B),k6_pre_topc(A,C)) ) ) ) ) ) )).

fof(t11_tsep_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)))
         => ( r2_tsep_2(A,k6_pre_topc(A,B),k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)))
            & r2_tsep_2(A,k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),k1_tops_1(A,B))
            & r2_tsep_2(A,k1_tops_1(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))
            & r2_tsep_2(A,k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)),k6_pre_topc(A,B)) ) ) ) )).

fof(t12_tsep_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)))
             => ( r2_tsep_2(A,B,C)
               => ( v3_pre_topc(B,A)
                <=> v4_pre_topc(C,A) ) ) ) ) ) )).

fof(t13_tsep_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)))
             => ( r2_tsep_2(A,B,C)
               => ( v4_pre_topc(B,A)
                <=> v3_pre_topc(C,A) ) ) ) ) ) )).

fof(t14_tsep_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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_tsep_2(A,B,C)
                          & r2_tsep_2(A,D,E) )
                       => r2_tsep_2(A,k5_subset_1(u1_struct_0(A),B,D),k4_subset_1(u1_struct_0(A),C,E)) ) ) ) ) ) ) )).

fof(t15_tsep_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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_tsep_2(A,B,C)
                          & r2_tsep_2(A,D,E) )
                       => r2_tsep_2(A,k4_subset_1(u1_struct_0(A),B,D),k5_subset_1(u1_struct_0(A),C,E)) ) ) ) ) ) ) )).

fof(t16_tsep_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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_tsep_2(A,B,D)
                          & r2_tsep_2(A,C,E) )
                       => ( r2_tsep_1(A,B,C)
                        <=> r2_tsep_1(A,D,E) ) ) ) ) ) ) ) )).

fof(t17_tsep_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)))
             => ( r2_tsep_1(A,B,C)
              <=> r2_tsep_1(A,k3_subset_1(u1_struct_0(A),B),k3_subset_1(u1_struct_0(A),C)) ) ) ) ) )).

fof(t18_tsep_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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_tsep_2(A,B,D)
                          & r2_tsep_2(A,C,E)
                          & r1_connsp_1(A,B,C) )
                       => r2_tsep_1(A,D,E) ) ) ) ) ) ) )).

fof(t19_tsep_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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_tsep_2(A,B,D)
                          & r2_tsep_2(A,C,E)
                          & r1_xboole_0(B,C)
                          & r2_tsep_1(A,D,E) )
                       => r1_connsp_1(A,B,C) ) ) ) ) ) ) )).

fof(t20_tsep_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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_tsep_2(A,B,D)
                          & r2_tsep_2(A,C,E)
                          & k4_subset_1(u1_struct_0(A),D,E) = u1_struct_0(A)
                          & r2_tsep_1(A,D,E) )
                       => r1_connsp_1(A,B,C) ) ) ) ) ) ) )).

fof(t21_tsep_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)))
             => ( r2_tsep_2(A,B,C)
               => ( r2_tsep_1(A,B,C)
                <=> r1_connsp_1(A,B,C) ) ) ) ) ) )).

fof(t22_tsep_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)))
             => ( r2_tsep_1(A,B,C)
              <=> r1_connsp_1(A,k6_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),B,C),B),k6_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),B,C),C)) ) ) ) ) )).

fof(t23_tsep_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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r1_tarski(D,B)
                          & r1_tarski(E,C)
                          & k4_subset_1(u1_struct_0(A),D,E) = k4_subset_1(u1_struct_0(A),B,C)
                          & r2_tsep_1(A,D,E) )
                       => r2_tsep_1(A,B,C) ) ) ) ) ) ) )).

fof(t24_tsep_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)))
             => ( r2_tsep_1(A,B,C)
              <=> r1_connsp_1(A,k6_subset_1(u1_struct_0(A),B,k5_subset_1(u1_struct_0(A),B,C)),k6_subset_1(u1_struct_0(A),C,k5_subset_1(u1_struct_0(A),B,C))) ) ) ) ) )).

fof(t25_tsep_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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r1_tarski(D,B)
                          & r1_tarski(E,C)
                          & k5_subset_1(u1_struct_0(A),D,E) = k5_subset_1(u1_struct_0(A),B,C)
                          & r2_tsep_1(A,B,C) )
                       => r2_tsep_1(A,D,E) ) ) ) ) ) ) )).

fof(t26_tsep_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)))
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D)))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D)))
                         => ( ( E = B
                              & F = C )
                           => ( r1_connsp_1(A,B,C)
                            <=> r1_connsp_1(D,E,F) ) ) ) ) ) ) ) ) )).

fof(t27_tsep_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)))
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D)))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D)))
                         => ( ( E = k3_xboole_0(u1_struct_0(D),B)
                              & F = k3_xboole_0(u1_struct_0(D),C)
                              & r1_connsp_1(A,B,C) )
                           => r1_connsp_1(D,E,F) ) ) ) ) ) ) ) )).

fof(t28_tsep_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)))
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D)))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D)))
                         => ( ( E = B
                              & F = C )
                           => ( r2_tsep_1(A,B,C)
                            <=> r2_tsep_1(D,E,F) ) ) ) ) ) ) ) ) )).

fof(t29_tsep_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)))
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D)))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D)))
                         => ( ( E = k3_xboole_0(u1_struct_0(D),B)
                              & F = k3_xboole_0(u1_struct_0(D),C)
                              & r2_tsep_1(A,B,C) )
                           => r2_tsep_1(D,E,F) ) ) ) ) ) ) ) )).

fof(d2_tsep_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_pre_topc(C,A)
             => ( r3_tsep_2(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ( ( D = u1_struct_0(B)
                            & E = u1_struct_0(C) )
                         => r2_tsep_2(A,D,E) ) ) ) ) ) ) ) )).

fof(t30_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ( r3_tsep_2(A,B,C)
              <=> ( r1_tsep_1(A,B,C)
                  & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k1_tsep_1(A,B,C) ) ) ) ) ) )).

fof(t31_tsep_2,axiom,(
    $true )).

fof(t32_tsep_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) )
         => ~ r3_tsep_2(A,B,B) ) ) )).

fof(t33_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ( ( r4_tsep_2(A,B,C)
                      & r4_tsep_2(A,C,D) )
                   => g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D)) ) ) ) ) ) )).

fof(t34_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & m1_pre_topc(E,A) )
                     => ( ( r4_tsep_2(A,B,D)
                          & r4_tsep_2(A,C,E) )
                       => ( k1_tsep_1(A,D,E) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))
                        <=> r1_tsep_1(A,B,C) ) ) ) ) ) ) ) )).

fof(t35_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ( r4_tsep_2(A,B,C)
               => ( v1_tsep_1(B,A)
                <=> v1_borsuk_1(C,A) ) ) ) ) ) )).

fof(t36_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ( r4_tsep_2(A,B,C)
               => ( v1_borsuk_1(B,A)
                <=> v1_tsep_1(C,A) ) ) ) ) ) )).

fof(t37_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & m1_pre_topc(E,A) )
                     => ( ( r4_tsep_2(A,B,D)
                          & r4_tsep_2(A,C,E) )
                       => ( r1_tsep_1(A,B,C)
                          | r4_tsep_2(A,k2_tsep_1(A,B,C),k1_tsep_1(A,D,E)) ) ) ) ) ) ) ) )).

fof(t38_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & m1_pre_topc(E,A) )
                     => ( ( r4_tsep_2(A,D,B)
                          & r4_tsep_2(A,E,C) )
                       => ( r1_tsep_1(A,B,C)
                          | r4_tsep_2(A,k1_tsep_1(A,D,E),k2_tsep_1(A,B,C)) ) ) ) ) ) ) ) )).

fof(t39_tsep_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_pre_topc(C,A)
             => ! [D] :
                  ( m1_pre_topc(D,A)
                 => ! [E] :
                      ( m1_pre_topc(E,A)
                     => ( ( r3_tsep_2(A,B,D)
                          & r3_tsep_2(A,C,E)
                          & r4_tsep_1(A,B,C) )
                       => r4_tsep_1(A,D,E) ) ) ) ) ) ) )).

fof(t40_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & m1_pre_topc(E,A) )
                     => ( ( r4_tsep_2(A,B,D)
                          & r4_tsep_2(A,C,E)
                          & r3_tsep_1(A,B,C) )
                       => r4_tsep_1(A,D,E) ) ) ) ) ) ) )).

fof(t41_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & m1_pre_topc(E,A) )
                     => ( ( r4_tsep_2(A,B,D)
                          & r4_tsep_2(A,C,E)
                          & r1_tsep_1(A,B,C)
                          & r4_tsep_1(A,D,E) )
                       => r3_tsep_1(A,B,C) ) ) ) ) ) ) )).

fof(t42_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & m1_pre_topc(E,A) )
                     => ( ( r4_tsep_2(A,B,D)
                          & r4_tsep_2(A,C,E)
                          & k1_tsep_1(A,D,E) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))
                          & r4_tsep_1(A,D,E) )
                       => r3_tsep_1(A,B,C) ) ) ) ) ) ) )).

fof(t43_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ( r4_tsep_2(A,B,C)
               => ( r4_tsep_1(A,B,C)
                <=> r3_tsep_1(A,B,C) ) ) ) ) ) )).

fof(t44_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & m1_pre_topc(E,A) )
                     => ( ( m1_pre_topc(D,B)
                          & m1_pre_topc(E,C)
                          & k1_tsep_1(A,D,E) = k1_tsep_1(A,B,C)
                          & r4_tsep_1(A,D,E) )
                       => r4_tsep_1(A,B,C) ) ) ) ) ) ) )).

fof(t45_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & m1_pre_topc(E,A) )
                     => ( ( m1_pre_topc(D,B)
                          & m1_pre_topc(E,C)
                          & k2_tsep_1(A,D,E) = k2_tsep_1(A,B,C)
                          & r4_tsep_1(A,B,C) )
                       => ( r1_tsep_1(A,D,E)
                          | r4_tsep_1(A,D,E) ) ) ) ) ) ) ) )).

fof(t46_tsep_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) )
         => ! [C] :
              ( m1_pre_topc(C,A)
             => ! [D] :
                  ( m1_pre_topc(D,A)
                 => ! [E] :
                      ( m1_pre_topc(E,B)
                     => ! [F] :
                          ( m1_pre_topc(F,B)
                         => ( ( u1_struct_0(C) = u1_struct_0(E)
                              & u1_struct_0(D) = u1_struct_0(F) )
                           => ( r3_tsep_1(A,C,D)
                            <=> r3_tsep_1(B,E,F) ) ) ) ) ) ) ) ) )).

fof(t47_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ~ ( ~ r1_tsep_1(A,C,B)
                      & ~ r1_tsep_1(A,D,B)
                      & ? [E] :
                          ( m1_pre_topc(E,B)
                          & ? [F] :
                              ( m1_pre_topc(F,B)
                              & E = k2_tsep_1(A,C,B)
                              & F = k2_tsep_1(A,D,B)
                              & r3_tsep_1(A,C,D)
                              & ~ r3_tsep_1(B,E,F) ) ) ) ) ) ) ) )).

fof(t48_tsep_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) )
         => ! [C] :
              ( m1_pre_topc(C,A)
             => ! [D] :
                  ( m1_pre_topc(D,A)
                 => ! [E] :
                      ( m1_pre_topc(E,B)
                     => ! [F] :
                          ( m1_pre_topc(F,B)
                         => ( ( u1_struct_0(C) = u1_struct_0(E)
                              & u1_struct_0(D) = u1_struct_0(F) )
                           => ( r4_tsep_1(A,C,D)
                            <=> r4_tsep_1(B,E,F) ) ) ) ) ) ) ) ) )).

fof(t49_tsep_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) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ~ ( ~ r1_tsep_1(A,C,B)
                      & ~ r1_tsep_1(A,D,B)
                      & ? [E] :
                          ( m1_pre_topc(E,B)
                          & ? [F] :
                              ( m1_pre_topc(F,B)
                              & E = k2_tsep_1(A,C,B)
                              & F = k2_tsep_1(A,D,B)
                              & r4_tsep_1(A,C,D)
                              & ~ r4_tsep_1(B,E,F) ) ) ) ) ) ) ) )).

fof(symmetry_r1_tsep_2,axiom,(
    ! [A,B,C] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r1_tsep_2(A,B,C)
       => r1_tsep_2(A,C,B) ) ) )).

fof(symmetry_r2_tsep_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r2_tsep_2(A,B,C)
       => r2_tsep_2(A,C,B) ) ) )).

fof(irreflexivity_r2_tsep_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ r2_tsep_2(A,B,B) ) )).

fof(redefinition_r2_tsep_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r2_tsep_2(A,B,C)
      <=> r1_tsep_2(A,B,C) ) ) )).

fof(symmetry_r3_tsep_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_pre_topc(B,A)
        & m1_pre_topc(C,A) )
     => ( r3_tsep_2(A,B,C)
       => r3_tsep_2(A,C,B) ) ) )).

fof(symmetry_r4_tsep_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & m1_pre_topc(B,A)
        & ~ v3_struct_0(C)
        & m1_pre_topc(C,A) )
     => ( r4_tsep_2(A,B,C)
       => r4_tsep_2(A,C,B) ) ) )).

fof(irreflexivity_r4_tsep_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & m1_pre_topc(B,A)
        & ~ v3_struct_0(C)
        & m1_pre_topc(C,A) )
     => ~ r4_tsep_2(A,B,B) ) )).

fof(redefinition_r4_tsep_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & m1_pre_topc(B,A)
        & ~ v3_struct_0(C)
        & m1_pre_topc(C,A) )
     => ( r4_tsep_2(A,B,C)
      <=> r3_tsep_2(A,B,C) ) ) )).
%------------------------------------------------------------------------------