% Mizar problem: t51_semi_af1,semi_af1,355,73 
fof(t51_semi_af1,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_semi_af1(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))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_semi_af1(A,B,C,E)
                                  & r1_semi_af1(A,B,D,F)
                                  & r1_semi_af1(A,B,D,G)
                                  & r2_analoaf(A,C,D,E,F)
                                  & r2_analoaf(A,C,D,E,F)
                                  & r2_analoaf(A,C,D,E,G) )
                               => ( r1_semi_af1(A,B,C,D)
                                  | F = G ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d2_semi_af1,dt_l1_analoaf,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_analoaf,existence_l1_struct_0,existence_m1_subset_1,rc1_semi_af1,t33_semi_af1]),
    [file(semi_af1,t51_semi_af1)]).

fof(d2_semi_af1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_semi_af1(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))
                 => ( r1_semi_af1(A,B,C,D)
                  <=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) ),
    file(semi_af1,d2_semi_af1),
    []).

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

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

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

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_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

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

fof(rc1_semi_af1,axiom,(
    ? [A] : 
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_semi_af1(A) ) ),
    file(semi_af1,rc1_semi_af1),
    []).

fof(t33_semi_af1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_semi_af1(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))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ( ( r2_analoaf(A,B,C,E,F)
                                      & r2_analoaf(A,B,D,E,G)
                                      & r2_analoaf(A,B,D,E,H)
                                      & r2_analoaf(A,C,D,F,G)
                                      & r2_analoaf(A,C,D,F,H) )
                                   => ( r2_analoaf(A,B,C,B,D)
                                      | G = H ) ) ) ) ) ) ) ) ) ) ),
    file(semi_af1,t33_semi_af1),
    []).