fof(l5_tdgroup,theorem,(
    v13_vectsp_1(k1_vectsp_1) ),
    inference(mizar_proof,[status(thm)],[d28_vectsp_1,t3_tdgroup]),
    [file(tdgroup,l5_tdgroup),interesting(1.00)]).

fof(t3_tdgroup,theorem,(
    ! [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) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rlvect_1,d3_rlvect_1,d9_binop_2]),
    [file(tdgroup,t3_tdgroup),interesting(0.80)]).

fof(t22_tdgroup,theorem,(
    ! [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)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_tdgroup,d8_tdgroup,d7_realset2]),
    [file(tdgroup,t22_tdgroup),interesting(0.73)]).

fof(t2_tdgroup,theorem,(
    ! [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 ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rlvect_1,d9_binop_2]),
    [file(tdgroup,t2_tdgroup),interesting(0.68)]).

fof(t15_tdgroup,theorem,(
    ! [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) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlvect_1,t16_rlvect_1,t10_rlvect_1,t10_tdgroup]),
    [file(tdgroup,t15_tdgroup),interesting(0.63)]).

fof(t14_tdgroup,theorem,(
    ! [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) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_tdgroup,d6_rlvect_1,d6_rlvect_1,t10_tdgroup,d6_rlvect_1,d6_rlvect_1,t21_rlvect_1,t10_tdgroup]),
    [file(tdgroup,t14_tdgroup),interesting(0.61)]).

fof(t17_tdgroup,theorem,(
    ! [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) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tdgroup,t10_tdgroup]),
    [file(tdgroup,t17_tdgroup),interesting(0.60)]).

fof(t16_tdgroup,theorem,(
    ! [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) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_tdgroup,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,t21_rlvect_1,t10_tdgroup]),
    [file(tdgroup,t16_tdgroup),interesting(0.58)]).

fof(t18_tdgroup,theorem,(
    ! [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 ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_tdgroup,d6_rlvect_1,d6_rlvect_1,t16_rlvect_1,t10_rlvect_1,d6_rlvect_1,t16_rlvect_1,t10_rlvect_1,d28_vectsp_1,d6_rlvect_1,t16_rlvect_1,t10_rlvect_1]),
    [file(tdgroup,t18_tdgroup),interesting(0.57)]).

fof(t13_tdgroup,theorem,(
    ! [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 ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_tdgroup,t21_rlvect_1]),
    [file(tdgroup,t13_tdgroup),interesting(0.56)]).

fof(t19_tdgroup,theorem,(
    ! [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) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_tdgroup,t10_tdgroup]),
    [file(tdgroup,t19_tdgroup),interesting(0.56)]).

fof(t10_tdgroup,theorem,(
    ! [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) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_tdgroup,d4_tdgroup,d4_tdgroup,d6_tdgroup]),
    [file(tdgroup,t10_tdgroup),interesting(0.38)]).

fof(t20_tdgroup,theorem,(
    ! [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) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_tdgroup,d2_analoaf,d2_analoaf,d6_tdgroup,t13_tdgroup,t14_tdgroup,t15_tdgroup,t16_tdgroup,t17_tdgroup,t18_tdgroup,t19_tdgroup]),
    [file(tdgroup,t20_tdgroup),interesting(0.33)]).

fof(t12_tdgroup,theorem,(
    ~ ! [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 ) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_tdgroup]),
    [file(tdgroup,t12_tdgroup),interesting(0.30)]).

fof(t21_tdgroup,theorem,(
    ! [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) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_tdgroup,d7_realset2]),
    [file(tdgroup,t21_tdgroup),interesting(0.17)]).

fof(d28_vectsp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v13_vectsp_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ( k2_rlvect_1(A,B,B) = k1_rlvect_1(A)
             => B = k1_rlvect_1(A) ) ) ) ) ),
    file(vectsp_1,d28_vectsp_1),
    [interesting(0.00)]).

fof(d2_rlvect_1,definition,(
    ! [A] : 
      ( l2_struct_0(A)
     => k1_rlvect_1(A) = u2_struct_0(A) ) ),
    file(rlvect_1,d2_rlvect_1),
    [interesting(0.00)]).

fof(d3_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ),
    file(rlvect_1,d3_rlvect_1),
    [interesting(0.00)]).

fof(d9_binop_2,definition,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
     => ( A = k33_binop_2
      <=> ! [B] : 
            ( m1_subset_1(B,k1_numbers)
           => ! [C] : 
                ( m1_subset_1(C,k1_numbers)
               => k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k9_binop_2(B,C) ) ) ) ) ),
    file(binop_2,d9_binop_2),
    [interesting(0.00)]).

fof(t11_tdgroup,theorem,(
    ~ ! [A] : 
        ( m1_subset_1(A,u1_struct_0(k1_vectsp_1))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(k1_vectsp_1))
           => A = B ) ) ),
    file(tdgroup,t11_tdgroup),
    [interesting(0.00)]).

fof(t1_tdgroup,theorem,(
    $true ),
    file(tdgroup,t1_tdgroup),
    [interesting(0.00)]).

fof(d8_tdgroup,definition,(
    ! [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) ) ) ) ) ) ) ) ) ),
    file(tdgroup,d8_tdgroup),
    [interesting(0.00)]).

fof(d7_realset2,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v3_realset2(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => B = C ) ) ) ) ),
    file(realset2,d7_realset2),
    [interesting(0.00)]).

fof(d6_tdgroup,definition,(
    ! [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))) ) ) ) ) ) ) ),
    file(tdgroup,d6_tdgroup),
    [interesting(0.00)]).

fof(d2_analoaf,definition,(
    ! [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))
             => ! [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_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),u1_analoaf(A)) ) ) ) ) ) ) ),
    file(analoaf,d2_analoaf),
    [interesting(0.00)]).

fof(d4_tdgroup,definition,(
    ! [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) ) ) ) ) ) ) ) ) ),
    file(tdgroup,d4_tdgroup),
    [interesting(0.00)]).

fof(t21_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(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))
                     => ( ( k2_rlvect_1(A,B,D) = k2_rlvect_1(A,B,E)
                          | k2_rlvect_1(A,D,B) = k2_rlvect_1(A,E,B) )
                       => D = E ) ) ) ) ) ) ),
    file(rlvect_1,t21_rlvect_1),
    [interesting(0.00)]).

fof(d6_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v4_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))
                   => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) ),
    file(rlvect_1,d6_rlvect_1),
    [interesting(0.00)]).

fof(t16_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A)
            & k2_rlvect_1(A,k5_rlvect_1(A,B),B) = k1_rlvect_1(A) ) ) ) ),
    file(rlvect_1,t16_rlvect_1),
    [interesting(0.00)]).

fof(t10_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
            & k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) ),
    file(rlvect_1,t10_rlvect_1),
    [interesting(0.00)]).

fof(d1_tdgroup,definition,(
    ! [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 ) ) ) ) ),
    file(tdgroup,d1_tdgroup),
    [interesting(0.00)]).

fof(t4_tdgroup,theorem,(
    $true ),
    file(tdgroup,t4_tdgroup),
    [interesting(0.00)]).

fof(t5_tdgroup,theorem,(
    $true ),
    file(tdgroup,t5_tdgroup),
    [interesting(0.00)]).

fof(t6_tdgroup,theorem,(
    $true ),
    file(tdgroup,t6_tdgroup),
    [interesting(0.00)]).

fof(t7_tdgroup,theorem,(
    ! [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) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tdgroup,d28_vectsp_1]),
    [file(tdgroup,t7_tdgroup),interesting(0.00)]).

fof(t8_tdgroup,theorem,(
    $true ),
    file(tdgroup,t8_tdgroup),
    [interesting(0.00)]).

fof(t9_tdgroup,theorem,(
    ! [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) ) ) ),
    file(tdgroup,t9_tdgroup),
    [interesting(0.00)]).