% Mizar problem: t4_dirort,dirort,252,66 
fof(t4_dirort,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ( ~ v3_struct_0(k7_analort(A,B,C))
                  & v1_dirort(k7_analort(A,B,C))
                  & l1_analoaf(k7_analort(A,B,C)) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_analoaf,d1_dirort,dt_g1_analoaf,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k7_analort,dt_l1_analoaf,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_analoaf,dt_u1_struct_0,existence_l1_analoaf,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc2_analort,free_g1_analoaf,rc1_analoaf,rc1_dirort,rc2_analoaf,redefinition_m2_relset_1,t2_dirort]),
    [file(dirort,t4_dirort)]).

fof(abstractness_v1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => ( v1_analoaf(A)
       => A = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) ) ),
    file(analoaf,v1_analoaf),
    []).

fof(d1_dirort,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v1_dirort(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))
                             => ( r2_analoaf(A,B,B,D,F)
                                & r2_analoaf(A,B,D,F,F)
                                & ~ ( r2_analoaf(A,B,D,C,E)
                                    & r2_analoaf(A,B,D,E,C)
                                    & B != D
                                    & C != E )
                                & ~ ( r2_analoaf(A,B,D,C,E)
                                    & r2_analoaf(A,B,D,C,F)
                                    & ~ r2_analoaf(A,B,D,E,F)
                                    & ~ r2_analoaf(A,B,D,F,E) )
                                & ( r2_analoaf(A,B,D,C,E)
                                 => r2_analoaf(A,D,B,E,C) )
                                & ( ( r2_analoaf(A,B,D,C,E)
                                    & r2_analoaf(A,B,D,E,F) )
                                 => r2_analoaf(A,B,D,C,F) )
                                & ~ ( r2_analoaf(A,B,C,D,E)
                                    & ~ r2_analoaf(A,D,E,B,C)
                                    & ~ r2_analoaf(A,D,E,C,B) ) ) ) ) ) ) )
          & ! [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))
                          & D != E
                          & r2_analoaf(A,D,E,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))
                          & D != E
                          & r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ),
    file(dirort,d1_dirort),
    []).

fof(dt_g1_analoaf,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
     => ( v1_analoaf(g1_analoaf(A,B))
        & l1_analoaf(g1_analoaf(A,B)) ) ) ),
    file(analoaf,g1_analoaf),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k7_analort,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( v1_analoaf(k7_analort(A,B,C))
        & l1_analoaf(k7_analort(A,B,C)) ) ) ),
    file(analort,k7_analort),
    []).

fof(dt_l1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => l1_struct_0(A) ) ),
    file(analoaf,l1_analoaf),
    []).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_rlvect_1,axiom,(
    ! [A] : 
      ( l2_rlvect_1(A)
     => l1_rlvect_1(A) ) ),
    file(rlvect_1,l2_rlvect_1),
    []).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_u1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => m2_relset_1(u1_analoaf(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ),
    file(analoaf,u1_analoaf),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_analoaf,axiom,(
    ? [A] : l1_analoaf(A) ),
    file(analoaf,l1_analoaf),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_rlvect_1,axiom,(
    ? [A] : l2_rlvect_1(A) ),
    file(rlvect_1,l2_rlvect_1),
    []).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc2_analort,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k7_analort(A,B,C))
        & v1_analoaf(k7_analort(A,B,C)) ) ) ),
    file(analort,fc2_analort),
    []).

fof(free_g1_analoaf,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
     => ! [C,D] : 
          ( g1_analoaf(A,B) = g1_analoaf(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(analoaf,g1_analoaf),
    []).

fof(rc1_analoaf,axiom,(
    ? [A] : 
      ( l1_analoaf(A)
      & v1_analoaf(A) ) ),
    file(analoaf,rc1_analoaf),
    []).

fof(rc1_dirort,axiom,(
    ? [A] : 
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_dirort(A) ) ),
    file(dirort,rc1_dirort),
    []).

fof(rc2_analoaf,axiom,(
    ? [A] : 
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_analoaf(A) ) ),
    file(analoaf,rc2_analoaf),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(t2_dirort,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ( ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(k7_analort(A,B,C)))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(k7_analort(A,B,C)))
                         => ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(k7_analort(A,B,C)))
                             => ! [G] : 
                                  ( m1_subset_1(G,u1_struct_0(k7_analort(A,B,C)))
                                 => ! [H] : 
                                      ( m1_subset_1(H,u1_struct_0(k7_analort(A,B,C)))
                                     => ( r2_analoaf(k7_analort(A,B,C),D,D,F,H)
                                        & r2_analoaf(k7_analort(A,B,C),D,F,H,H)
                                        & ~ ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
                                            & r2_analoaf(k7_analort(A,B,C),D,F,G,E)
                                            & D != F
                                            & E != G )
                                        & ~ ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
                                            & r2_analoaf(k7_analort(A,B,C),D,F,E,H)
                                            & ~ r2_analoaf(k7_analort(A,B,C),D,F,G,H)
                                            & ~ r2_analoaf(k7_analort(A,B,C),D,F,H,G) )
                                        & ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
                                         => r2_analoaf(k7_analort(A,B,C),F,D,G,E) )
                                        & ( ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
                                            & r2_analoaf(k7_analort(A,B,C),D,F,G,H) )
                                         => r2_analoaf(k7_analort(A,B,C),D,F,E,H) )
                                        & ~ ( r2_analoaf(k7_analort(A,B,C),D,E,F,G)
                                            & ~ r2_analoaf(k7_analort(A,B,C),F,G,D,E)
                                            & ~ r2_analoaf(k7_analort(A,B,C),F,G,E,D) ) ) ) ) ) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(k7_analort(A,B,C)))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(k7_analort(A,B,C)))
                         => ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(k7_analort(A,B,C)))
                             => ? [G] : 
                                  ( m1_subset_1(G,u1_struct_0(k7_analort(A,B,C)))
                                  & F != G
                                  & r2_analoaf(k7_analort(A,B,C),F,G,D,E) ) ) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(k7_analort(A,B,C)))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(k7_analort(A,B,C)))
                         => ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(k7_analort(A,B,C)))
                             => ? [G] : 
                                  ( m1_subset_1(G,u1_struct_0(k7_analort(A,B,C)))
                                  & F != G
                                  & r2_analoaf(k7_analort(A,B,C),D,E,F,G) ) ) ) ) ) ) ) ) ) ),
    file(dirort,t2_dirort),
    []).