SET007 Axioms: SET007+235.ax


%------------------------------------------------------------------------------
% File     : SET007+235 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : A Construction of an Abstract Space of Congruence of Vectors
% 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    : tdgroup [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   36 (   8 unit)
%            Number of atoms       :  415 (  27 equality)
%            Maximal formula depth :   23 (   9 average)
%            Number of connectives :  417 (  38 ~  ;   0  |; 183  &)
%                                         (   8 <=>; 188 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   20 (   1 propositional; 0-5 arity)
%            Number of functors    :   11 (   1 constant; 0-3 arity)
%            Number of variables   :  177 (   0 singleton; 164 !;  13 ?)
%            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(fc1_tdgroup,axiom,
    ( ~ v3_struct_0(k1_vectsp_1)
    & v1_rlvect_1(k1_vectsp_1)
    & v3_rlvect_1(k1_vectsp_1)
    & v4_rlvect_1(k1_vectsp_1)
    & v5_rlvect_1(k1_vectsp_1)
    & v6_rlvect_1(k1_vectsp_1)
    & v13_vectsp_1(k1_vectsp_1)
    & v1_tdgroup(k1_vectsp_1) )).

fof(rc1_tdgroup,axiom,(
    ? [A] :
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v13_vectsp_1(A)
      & v1_tdgroup(A) ) )).

fof(fc2_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( ~ v3_struct_0(k2_tdgroup(A))
        & v1_analoaf(k2_tdgroup(A)) ) ) )).

fof(rc2_tdgroup,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_analoaf(A)
      & v2_tdgroup(A) ) )).

fof(t1_tdgroup,axiom,(
    $true )).

fof(t2_tdgroup,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k1_vectsp_1))
     => ? [B] :
          ( m1_subset_1(B,u1_struct_0(k1_vectsp_1))
          & k4_rlvect_1(k1_vectsp_1,B,B) = A ) ) )).

fof(t3_tdgroup,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k1_vectsp_1))
     => ( k4_rlvect_1(k1_vectsp_1,A,A) = k1_rlvect_1(k1_vectsp_1)
       => A = k1_rlvect_1(k1_vectsp_1) ) ) )).

fof(d1_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v1_tdgroup(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & k2_rlvect_1(A,C,C) = B ) ) ) ) )).

fof(t4_tdgroup,axiom,(
    $true )).

fof(t5_tdgroup,axiom,(
    $true )).

fof(t6_tdgroup,axiom,(
    $true )).

fof(t7_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ( ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v13_vectsp_1(A)
          & v1_tdgroup(A)
          & l1_rlvect_1(A) )
      <=> ( ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ? [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                  & k4_rlvect_1(A,C,C) = B ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ( k4_rlvect_1(A,B,B) = k1_rlvect_1(A)
               => B = k1_rlvect_1(A) ) ) ) ) ) )).

fof(d2_tdgroup,axiom,(
    $true )).

fof(d3_tdgroup,axiom,(
    $true )).

fof(d4_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
         => ( B = k1_tdgroup(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r2_hidden(k4_tarski(k4_tarski(C,D),k4_tarski(E,F)),B)
                            <=> k2_rlvect_1(A,C,F) = k2_rlvect_1(A,D,E) ) ) ) ) ) ) ) ) )).

fof(d5_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => k2_tdgroup(A) = g1_analoaf(u1_struct_0(A),k1_tdgroup(A)) ) )).

fof(t8_tdgroup,axiom,(
    $true )).

fof(t9_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ( u1_struct_0(k2_tdgroup(A)) = u1_struct_0(A)
        & u1_analoaf(k2_tdgroup(A)) = k1_tdgroup(A) ) ) )).

fof(d6_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_tdgroup(A,B,C,D,E)
                      <=> r2_hidden(k4_tarski(k4_tarski(B,C),k4_tarski(D,E)),u1_analoaf(k2_tdgroup(A))) ) ) ) ) ) ) )).

fof(t10_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_tdgroup(A,B,C,D,E)
                      <=> k2_rlvect_1(A,B,E) = k2_rlvect_1(A,C,D) ) ) ) ) ) ) )).

fof(t11_tdgroup,axiom,(
    ~ ! [A] :
        ( m1_subset_1(A,u1_struct_0(k1_vectsp_1))
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k1_vectsp_1))
           => A = B ) ) )).

fof(t12_tdgroup,axiom,(
    ~ ! [A] :
        ( ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v13_vectsp_1(A)
          & v1_tdgroup(A)
          & l1_rlvect_1(A) )
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => B = C ) ) ) )).

fof(t13_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_tdgroup(A,B,C,D,D)
                   => B = C ) ) ) ) ) )).

fof(t14_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_tdgroup(A,B,C,D,E)
                                  & r1_tdgroup(A,F,G,D,E) )
                               => r1_tdgroup(A,B,C,F,G) ) ) ) ) ) ) ) ) )).

fof(t15_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ? [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                      & r1_tdgroup(A,B,C,D,E) ) ) ) ) ) )).

fof(t16_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_tdgroup(A,B,C,D,E)
                                  & r1_tdgroup(A,B,F,D,G) )
                               => r1_tdgroup(A,C,F,E,G) ) ) ) ) ) ) ) ) )).

fof(t17_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & r1_tdgroup(A,B,D,D,C) ) ) ) ) )).

fof(t18_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_tdgroup(A,B,C,C,D)
                          & r1_tdgroup(A,B,E,E,D) )
                       => C = E ) ) ) ) ) ) )).

fof(t19_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_tdgroup(A,B,C,D,E)
                       => r1_tdgroup(A,B,D,C,E) ) ) ) ) ) ) )).

fof(t20_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ( ~ ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => B = C ) )
       => ( ~ ! [B] :
                ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
                   => B = C ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
                     => ( r2_analoaf(k2_tdgroup(A),B,C,D,D)
                       => B = C ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k2_tdgroup(A)))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k2_tdgroup(A)))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k2_tdgroup(A)))
                                 => ( ( r2_analoaf(k2_tdgroup(A),B,C,F,G)
                                      & r2_analoaf(k2_tdgroup(A),D,E,F,G) )
                                   => r2_analoaf(k2_tdgroup(A),B,C,D,E) ) ) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
                     => ? [E] :
                          ( m1_subset_1(E,u1_struct_0(k2_tdgroup(A)))
                          & r2_analoaf(k2_tdgroup(A),B,C,D,E) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k2_tdgroup(A)))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k2_tdgroup(A)))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k2_tdgroup(A)))
                                 => ( ( r2_analoaf(k2_tdgroup(A),B,C,E,F)
                                      & r2_analoaf(k2_tdgroup(A),B,D,E,G) )
                                   => r2_analoaf(k2_tdgroup(A),C,D,F,G) ) ) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
                 => ? [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
                      & r2_analoaf(k2_tdgroup(A),B,D,D,C) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k2_tdgroup(A)))
                         => ( ( r2_analoaf(k2_tdgroup(A),B,C,C,D)
                              & r2_analoaf(k2_tdgroup(A),B,E,E,D) )
                           => C = E ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k2_tdgroup(A)))
                         => ( r2_analoaf(k2_tdgroup(A),B,C,D,E)
                           => r2_analoaf(k2_tdgroup(A),B,D,C,E) ) ) ) ) ) ) ) ) )).

fof(d7_tdgroup,axiom,(
    $true )).

fof(d8_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v2_tdgroup(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_analoaf(A,B,C,D,D)
                       => B = C ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_analoaf(A,B,C,F,G)
                                      & r2_analoaf(A,D,E,F,G) )
                                   => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & r2_analoaf(A,B,C,D,E) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_analoaf(A,B,C,E,F)
                                      & r2_analoaf(A,B,D,E,G) )
                                   => r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ? [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                      & r2_analoaf(A,B,D,D,C) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r2_analoaf(A,B,C,C,D)
                              & r2_analoaf(A,B,E,E,D) )
                           => C = E ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r2_analoaf(A,B,C,D,E)
                           => r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) )).

fof(t21_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( ( ~ ! [B] :
                ( m1_subset_1(B,u1_struct_0(A))
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => B = C ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_analoaf(A,B,C,D,D)
                       => B = C ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_analoaf(A,B,C,F,G)
                                      & r2_analoaf(A,D,E,F,G) )
                                   => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & r2_analoaf(A,B,C,D,E) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_analoaf(A,B,C,E,F)
                                      & r2_analoaf(A,B,D,E,G) )
                                   => r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ? [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                      & r2_analoaf(A,B,D,D,C) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r2_analoaf(A,B,C,C,D)
                              & r2_analoaf(A,B,E,E,D) )
                           => C = E ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r2_analoaf(A,B,C,D,E)
                           => r2_analoaf(A,B,D,C,E) ) ) ) ) ) )
      <=> ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_tdgroup(A)
          & l1_analoaf(A) ) ) ) )).

fof(t22_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ( ~ ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => B = C ) )
       => ( ~ v3_struct_0(k2_tdgroup(A))
          & ~ v3_realset2(k2_tdgroup(A))
          & v2_tdgroup(k2_tdgroup(A))
          & l1_analoaf(k2_tdgroup(A)) ) ) ) )).

fof(dt_k1_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => m2_relset_1(k1_tdgroup(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) )).

fof(dt_k2_tdgroup,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v1_analoaf(k2_tdgroup(A))
        & l1_analoaf(k2_tdgroup(A)) ) ) )).
%------------------------------------------------------------------------------