% Mizar problem: t29_altcat_3,altcat_3,1314,45 
fof(t29_altcat_3,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( v8_altcat_3(B,A)
                  & v8_altcat_3(C,A) )
               => r2_altcat_3(A,B,C) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d11_altcat_3,dt_l1_altcat_1,dt_l1_struct_0,dt_l2_altcat_1,dt_m1_subset_1,dt_u1_struct_0,existence_l1_altcat_1,existence_l1_struct_0,existence_l2_altcat_1,existence_m1_subset_1,reflexivity_r2_altcat_3,symmetry_r2_altcat_3,t26_altcat_3]),
    [file(altcat_3,t29_altcat_3)]).

fof(d11_altcat_3,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v8_altcat_3(B,A)
          <=> ( v6_altcat_3(B,A)
              & v7_altcat_3(B,A) ) ) ) ) ),
    file(altcat_3,d11_altcat_3),
    []).

fof(dt_l1_altcat_1,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => l1_struct_0(A) ) ),
    file(altcat_1,l1_altcat_1),
    []).

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

fof(dt_l2_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => l1_altcat_1(A) ) ),
    file(altcat_1,l2_altcat_1),
    []).

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_altcat_1,axiom,(
    ? [A] : l1_altcat_1(A) ),
    file(altcat_1,l1_altcat_1),
    []).

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

fof(existence_l2_altcat_1,axiom,(
    ? [A] : l2_altcat_1(A) ),
    file(altcat_1,l2_altcat_1),
    []).

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

fof(reflexivity_r2_altcat_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r2_altcat_3(A,B,B) ) ),
    file(altcat_3,r2_altcat_3),
    []).

fof(symmetry_r2_altcat_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r2_altcat_3(A,B,C)
       => r2_altcat_3(A,C,B) ) ) ),
    file(altcat_3,r2_altcat_3),
    []).

fof(t26_altcat_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( v6_altcat_3(B,A)
                  & v6_altcat_3(C,A) )
               => r2_altcat_3(A,B,C) ) ) ) ) ),
    file(altcat_3,t26_altcat_3),
    []).