% Mizar problem: t56_parsp_2,parsp_2,1097,28 
fof(t56_parsp_2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                 => ( r3_parsp_2(A,B,C,D,D)
                   => B = C ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d4_parsp_2,dt_l1_parsp_1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_parsp_1,existence_l1_struct_0,existence_m1_subset_1,fc1_struct_0,rc1_xboole_0,rc2_parsp_1,rc2_xboole_0,rc3_struct_0,t34_parsp_2]),
    [file(parsp_2,t56_parsp_2)]).

fof(d4_parsp_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r3_parsp_2(A,B,C,D,E)
                      <=> ~ ( ~ ( B = C
                                & D = E )
                            & ! [F] : 
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ! [G] : 
                                    ( m1_subset_1(G,u1_struct_0(A))
                                   => ~ ( r2_parsp_2(A,F,G,B,C)
                                        & r2_parsp_2(A,F,G,D,E) ) ) ) ) ) ) ) ) ) ) ),
    file(parsp_2,d4_parsp_2),
    []).

fof(dt_l1_parsp_1,axiom,(
    ! [A] : 
      ( l1_parsp_1(A)
     => l1_struct_0(A) ) ),
    file(parsp_1,l1_parsp_1),
    []).

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_parsp_1,axiom,(
    ? [A] : l1_parsp_1(A) ),
    file(parsp_1,l1_parsp_1),
    []).

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(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_parsp_1,axiom,(
    ? [A] : 
      ( l1_parsp_1(A)
      & ~ v3_struct_0(A) ) ),
    file(parsp_1,rc2_parsp_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(t34_parsp_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_parsp_2(A,B,C,D,E)
                       => ( B != C
                          & C != D
                          & D != B
                          & B != E
                          & C != E
                          & D != E ) ) ) ) ) ) ) ),
    file(parsp_2,t34_parsp_2),
    []).