SET007 Axioms: SET007+407.ax


%------------------------------------------------------------------------------
% File     : SET007+407 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Maximal Kolmogorov Subspaces of a Topological Space
% Version  : [Urb08] axioms.
% English  : As Stone Retracts of the Ambient Space

% 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_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   65 (   0 unit)
%            Number of atoms       :  606 (  52 equality)
%            Maximal formula depth :   14 (   9 average)
%            Number of connectives :  661 ( 120 ~  ;   4  |; 299  &)
%                                         (  17 <=>; 221 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   31 (   0 propositional; 1-3 arity)
%            Number of functors    :   19 (   0 constant; 1-4 arity)
%            Number of variables   :  196 (   0 singleton; 189 !;   7 ?)
%            Maximal term depth    :    5 (   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_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_tsp_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_t_0topsp(B) ) ) ) ) )).

fof(cc2_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v2_t_0topsp(B) )
           => ( ~ v3_struct_0(B)
              & ~ v2_tsp_2(B,A) ) ) ) ) )).

fof(cc3_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v2_tsp_2(B,A)
           => ( v2_pre_topc(B)
              & v1_tex_3(B,A) ) ) ) ) )).

fof(cc4_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v1_tex_3(B,A)
           => ( v2_pre_topc(B)
              & ~ v2_tsp_2(B,A) ) ) ) ) )).

fof(cc5_tsp_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_tsp_2(B,A) )
           => ( v2_pre_topc(B)
              & ~ v2_tex_2(B,A) ) ) ) ) )).

fof(cc6_tsp_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_tex_2(B,A) )
           => ( v2_pre_topc(B)
              & ~ v2_tsp_2(B,A) ) ) ) ) )).

fof(cc7_tsp_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_tsp_2(B,A) )
           => ( v2_pre_topc(B)
              & ~ v1_tsep_1(B,A) ) ) ) ) )).

fof(cc8_tsp_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_tsp_2(B,A) )
           => ( v2_pre_topc(B)
              & ~ v2_tex_2(B,A) ) ) ) ) )).

fof(cc9_tsp_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)
              & v1_borsuk_1(B,A) )
           => ( v2_pre_topc(B)
              & ~ v2_tsp_2(B,A) ) ) ) ) )).

fof(cc10_tsp_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_tsp_2(B,A) )
           => ( v2_pre_topc(B)
              & ~ v1_borsuk_1(B,A) ) ) ) ) )).

fof(rc1_tsp_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_tex_3(B,A)
          & v2_t_0topsp(B)
          & v2_tsp_2(B,A) ) ) )).

fof(d1_tsp_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_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
                        | r1_subset_1(k4_tex_4(A,C),k4_tex_4(A,D)) ) ) ) ) ) ) ) )).

fof(d2_tsp_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_tsp_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => k5_subset_1(u1_struct_0(A),B,k4_tex_4(A,C)) = k1_struct_0(A,C) ) ) ) ) ) )).

fof(d3_tsp_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_tsp_1(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_tex_4(D,A)
                            & k5_subset_1(u1_struct_0(A),B,D) = k1_struct_0(A,C) ) ) ) ) ) ) ) )).

fof(d4_tsp_2,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tsp_2(B,A)
          <=> ( v1_tsp_1(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_tsp_1(C,A)
                      & r1_tarski(B,C) )
                   => B = C ) ) ) ) ) ) )).

fof(t1_tsp_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
                      & v1_tsp_2(C,A) )
                   => v1_tsp_2(D,B) ) ) ) ) ) )).

fof(d5_tsp_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_tsp_2(B,A)
          <=> ( v1_tsp_1(B,A)
              & k3_tex_4(A,B) = u1_struct_0(A) ) ) ) ) )).

fof(t2_tsp_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_tsp_2(B,A)
           => v1_tops_1(B,A) ) ) ) )).

fof(t3_tsp_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_pre_topc(B,A) )
              & v1_tsp_2(B,A)
              & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t4_tsp_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))) )
         => ~ v1_tsp_2(B,A) ) ) )).

fof(t5_tsp_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_tsp_2(B,A)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( v4_pre_topc(C,A)
                 => C = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) ) ) )).

fof(t6_tsp_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_tsp_2(B,A)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( v3_pre_topc(C,A)
                 => C = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) ) ) )).

fof(t7_tsp_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_tsp_2(B,A)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => k6_pre_topc(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C))) ) ) ) ) )).

fof(t8_tsp_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_tsp_2(B,A)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => k1_tops_1(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k1_tops_1(A,C))) ) ) ) ) )).

fof(d6_tsp_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_tsp_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,k4_tex_4(A,C)) = k1_struct_0(A,D) ) ) ) ) ) )).

fof(t9_tsp_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_tsp_1(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( r1_tarski(B,C)
                      & v1_tsp_2(C,A) ) ) ) ) ) )).

fof(t10_tsp_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_tsp_2(B,A) ) ) )).

fof(d7_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_tsp_1(B,A)
         => ( v2_tsp_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( C = u1_struct_0(B)
                 => v1_tsp_2(C,A) ) ) ) ) ) )).

fof(t11_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [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_2(C,A)
                <=> v2_tsp_2(B,A) ) ) ) ) ) )).

fof(d8_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m2_tsp_1(B,A) )
         => ( v2_tsp_2(B,A)
          <=> ( v2_t_0topsp(B)
              & ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v2_t_0topsp(C)
                    & m2_tsp_1(C,A) )
                 => ( m2_tsp_1(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(t12_tsp_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))) )
         => ~ ( v1_tsp_2(B,A)
              & ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v1_pre_topc(C)
                    & m2_tsp_1(C,A) )
                 => ~ ( v2_tsp_2(C,A)
                      & B = u1_struct_0(C) ) ) ) ) ) )).

fof(t13_tsp_2,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] :
              ( v1_pre_topc(C)
              & m2_tsp_1(C,A)
              & m2_tsp_1(B,C)
              & v2_tsp_2(C,A) ) ) ) )).

fof(t14_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( D = C
                   => ( v3_pre_topc(D,B)
                    <=> ( v3_pre_topc(k3_tex_4(A,C),A)
                        & D = k3_xboole_0(k3_tex_4(A,C),u1_struct_0(B)) ) ) ) ) ) ) ) )).

fof(t15_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v3_pre_topc(C,A)
              <=> ( C = k3_tex_4(A,C)
                  & ? [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(t16_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( D = C
                   => ( v4_pre_topc(D,B)
                    <=> ( v4_pre_topc(k3_tex_4(A,C),A)
                        & D = k3_xboole_0(k3_tex_4(A,C),u1_struct_0(B)) ) ) ) ) ) ) ) )).

fof(t17_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v4_pre_topc(C,A)
              <=> ( C = k3_tex_4(A,C)
                  & ? [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(t18_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [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)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( D = u1_struct_0(B)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) )
                   => ( 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)) ) ) ) ) ) ) )).

fof(t19_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [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)) )
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_tex_4(A,D)) )
               => ( 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)) ) ) ) ) ) )).

fof(t20_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(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)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( D = u1_struct_0(B)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) )
                   => v3_borsuk_1(C,A,B) ) ) ) ) ) )).

fof(t21_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(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)) )
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_tex_4(A,D)) )
               => v3_borsuk_1(C,A,B) ) ) ) ) )).

fof(t22_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(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(t23_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => r1_borsuk_1(A,B) ) ) )).

fof(d9_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(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)) )
             => ( C = k1_tsp_2(A,B)
              <=> v3_borsuk_1(C,A,B) ) ) ) ) )).

fof(t24_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( C = D
                   => k5_pre_topc(A,B,k1_tsp_2(A,B),k6_pre_topc(B,k1_struct_0(B,D))) = k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) ) )).

fof(t25_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( C = D
                   => k5_pre_topc(A,B,k1_tsp_2(A,B),k1_struct_0(B,D)) = k4_tex_4(A,C) ) ) ) ) ) )).

fof(t26_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( D = C
                   => k5_pre_topc(A,B,k1_tsp_2(A,B),D) = k3_tex_4(A,C) ) ) ) ) ) )).

fof(d10_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(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)) )
             => ( C = k2_tsp_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( D = u1_struct_0(B)
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ) )).

fof(d11_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(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)) )
             => ( C = k3_tsp_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_tex_4(A,D)) ) ) ) ) ) )).

fof(t27_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_pre_topc(A,B,k3_tsp_2(A,B),k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),k3_tsp_2(A,B),C))) = k4_tex_4(A,C) ) ) ) )).

fof(t28_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_pre_topc(A,B,k3_tsp_2(A,B),k1_struct_0(A,C)) = k4_pre_topc(A,B,k3_tsp_2(A,B),k4_tex_4(A,C)) ) ) ) )).

fof(d12_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(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)) )
             => ( C = k4_tsp_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( D = u1_struct_0(B)
                     => ! [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                         => k5_subset_1(u1_struct_0(A),D,k3_tex_4(A,E)) = k4_pre_topc(A,B,C,E) ) ) ) ) ) ) ) )).

fof(t29_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k5_pre_topc(A,B,k4_tsp_2(A,B),k4_pre_topc(A,B,k4_tsp_2(A,B),C)) = k3_tex_4(A,C) ) ) ) )).

fof(t30_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_pre_topc(A,B,k4_tsp_2(A,B),C) = k4_pre_topc(A,B,k4_tsp_2(A,B),k3_tex_4(A,C)) ) ) ) )).

fof(t31_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,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)))
                 => k4_pre_topc(A,B,k4_tsp_2(A,B),k4_subset_1(u1_struct_0(A),C,D)) = k4_subset_1(u1_struct_0(B),k4_pre_topc(A,B,k4_tsp_2(A,B),C),k4_pre_topc(A,B,k4_tsp_2(A,B),D)) ) ) ) ) )).

fof(t32_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,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)))
                 => ( ( v3_pre_topc(C,A)
                      | v3_pre_topc(D,A) )
                   => k4_pre_topc(A,B,k4_tsp_2(A,B),k5_subset_1(u1_struct_0(A),C,D)) = k5_subset_1(u1_struct_0(B),k4_pre_topc(A,B,k4_tsp_2(A,B),C),k4_pre_topc(A,B,k4_tsp_2(A,B),D)) ) ) ) ) ) )).

fof(t33_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,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)))
                 => ( ( v4_pre_topc(C,A)
                      | v4_pre_topc(D,A) )
                   => k4_pre_topc(A,B,k4_tsp_2(A,B),k5_subset_1(u1_struct_0(A),C,D)) = k5_subset_1(u1_struct_0(B),k4_pre_topc(A,B,k4_tsp_2(A,B),C),k4_pre_topc(A,B,k4_tsp_2(A,B),D)) ) ) ) ) ) )).

fof(t34_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v3_pre_topc(C,A)
               => v3_pre_topc(k4_pre_topc(A,B,k4_tsp_2(A,B),C),B) ) ) ) ) )).

fof(t35_tsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_tsp_2(B,A)
            & m2_tsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v4_pre_topc(C,A)
               => v4_pre_topc(k4_pre_topc(A,B,k4_tsp_2(A,B),C),B) ) ) ) ) )).

fof(dt_k1_tsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_tsp_2(B,A)
        & m1_pre_topc(B,A) )
     => ( v1_funct_1(k1_tsp_2(A,B))
        & v1_funct_2(k1_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(k1_tsp_2(A,B),A,B)
        & m2_relset_1(k1_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) )).

fof(dt_k2_tsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_tsp_2(B,A)
        & m1_pre_topc(B,A) )
     => ( v1_funct_1(k2_tsp_2(A,B))
        & v1_funct_2(k2_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(k2_tsp_2(A,B),A,B)
        & m2_relset_1(k2_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) )).

fof(redefinition_k2_tsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_tsp_2(B,A)
        & m1_pre_topc(B,A) )
     => k2_tsp_2(A,B) = k1_tsp_2(A,B) ) )).

fof(dt_k3_tsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_tsp_2(B,A)
        & m1_pre_topc(B,A) )
     => ( v1_funct_1(k3_tsp_2(A,B))
        & v1_funct_2(k3_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(k3_tsp_2(A,B),A,B)
        & m2_relset_1(k3_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) )).

fof(redefinition_k3_tsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_tsp_2(B,A)
        & m1_pre_topc(B,A) )
     => k3_tsp_2(A,B) = k1_tsp_2(A,B) ) )).

fof(dt_k4_tsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_tsp_2(B,A)
        & m1_pre_topc(B,A) )
     => ( v1_funct_1(k4_tsp_2(A,B))
        & v1_funct_2(k4_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(k4_tsp_2(A,B),A,B)
        & m2_relset_1(k4_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) )).

fof(redefinition_k4_tsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_tsp_2(B,A)
        & m1_pre_topc(B,A) )
     => k4_tsp_2(A,B) = k1_tsp_2(A,B) ) )).
%------------------------------------------------------------------------------