% Mizar problem: t5_altcat_3,altcat_3,164,44 
fof(t5_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))
             => ! [D] : 
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ( v3_altcat_3(D,A,B,C)
                   => ( v1_altcat_3(D,A,B,C)
                      & v2_altcat_3(D,A,B,C) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d1_altcat_3,d2_altcat_3,d3_altcat_3,d5_altcat_3,dt_k1_altcat_1,dt_k1_altcat_3,dt_k5_altcat_1,dt_k8_altcat_1,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]),
    [file(altcat_3,t5_altcat_3)]).

fof(d1_altcat_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(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))
             => ! [D] : 
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_altcat_1(A,C,B))
                     => ( r1_altcat_3(A,B,C,D,E)
                      <=> k5_altcat_1(A,C,B,C,E,D) = k8_altcat_1(A,C) ) ) ) ) ) ) ),
    file(altcat_3,d1_altcat_3),
    []).

fof(d2_altcat_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(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))
             => ! [D] : 
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ( v1_altcat_3(D,A,B,C)
                  <=> ? [E] : 
                        ( m1_subset_1(E,k1_altcat_1(A,C,B))
                        & r1_altcat_3(A,B,C,D,E) ) ) ) ) ) ) ),
    file(altcat_3,d2_altcat_3),
    []).

fof(d3_altcat_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(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))
             => ! [D] : 
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ( v2_altcat_3(D,A,B,C)
                  <=> ? [E] : 
                        ( m1_subset_1(E,k1_altcat_1(A,C,B))
                        & r1_altcat_3(A,C,B,E,D) ) ) ) ) ) ) ),
    file(altcat_3,d3_altcat_3),
    []).

fof(d5_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))
             => ! [D] : 
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ( v3_altcat_3(D,A,B,C)
                  <=> ( k5_altcat_1(A,C,B,C,k1_altcat_3(A,B,C,D),D) = k8_altcat_1(A,C)
                      & k5_altcat_1(A,B,C,B,D,k1_altcat_3(A,B,C,D)) = k8_altcat_1(A,B) ) ) ) ) ) ) ),
    file(altcat_3,d5_altcat_3),
    []).

fof(dt_k1_altcat_1,axiom,(
    $true ),
    file(altcat_1,k1_altcat_1),
    []).

fof(dt_k1_altcat_3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ 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))
        & m1_subset_1(D,k1_altcat_1(A,B,C)) )
     => m1_subset_1(k1_altcat_3(A,B,C,D),k1_altcat_1(A,C,B)) ) ),
    file(altcat_3,k1_altcat_3),
    []).

fof(dt_k5_altcat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,k1_altcat_1(A,B,C))
        & m1_subset_1(F,k1_altcat_1(A,C,D)) )
     => m1_subset_1(k5_altcat_1(A,B,C,D,E,F),k1_altcat_1(A,B,D)) ) ),
    file(altcat_1,k5_altcat_1),
    []).

fof(dt_k8_altcat_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k8_altcat_1(A,B),k1_altcat_1(A,B,B)) ) ),
    file(altcat_1,k8_altcat_1),
    []).

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),
    []).