% Mizar problem: t107_semi_af1,semi_af1,989,45 
fof(t107_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))
                 => ( k2_semi_af1(A,B,C) = k2_semi_af1(A,D,C)
                   => B = D ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k2_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,t106_semi_af1,t81_semi_af1,t89_semi_af1]),
    [file(semi_af1,t107_semi_af1)]).

fof(dt_k2_semi_af1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v1_semi_af1(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_semi_af1(A,B,C),u1_struct_0(A)) ) ),
    file(semi_af1,k2_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(t106_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))
             => r3_semi_af1(A,B,C,C,k2_semi_af1(A,B,C)) ) ) ) ),
    file(semi_af1,t106_semi_af1),
    []).

fof(t81_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))
                         => ( ( r3_semi_af1(A,B,C,D,E)
                              & r3_semi_af1(A,B,C,D,F) )
                           => E = F ) ) ) ) ) ) ) ),
    file(semi_af1,t81_semi_af1),
    []).

fof(t89_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))
                     => ( r3_semi_af1(A,B,C,D,E)
                       => ( r3_semi_af1(A,D,E,B,C)
                          & r3_semi_af1(A,C,B,E,D)
                          & r3_semi_af1(A,B,D,C,E)
                          & r3_semi_af1(A,E,D,C,B)
                          & r3_semi_af1(A,C,E,B,D)
                          & r3_semi_af1(A,D,B,E,C)
                          & r3_semi_af1(A,E,C,D,B) ) ) ) ) ) ) ) ),
    file(semi_af1,t89_semi_af1),
    []).