% Mizar problem: t32_projpl_1,projpl_1,853,62 
fof(t32_projpl_1,conjecture,(
    ! [A] : 
      ( ( v1_incproj(A)
        & v2_incproj(A)
        & v3_incproj(A)
        & v4_incproj(A)
        & v5_incproj(A)
        & l1_incsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_incsp_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_incsp_1(A))
                     => ( ( r1_incsp_1(A,D,k1_projpl_1(A,B,C))
                          & r1_incsp_1(A,D,k1_projpl_1(A,B,E)) )
                       => ( D = B
                          | E = B
                          | B = C
                          | r1_incsp_1(A,E,k1_projpl_1(A,B,C)) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d9_incproj,dt_k1_projpl_1,dt_l1_incsp_1,dt_m1_subset_1,dt_u1_incsp_1,dt_u2_incsp_1,existence_l1_incsp_1,existence_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t16_projpl_1]),
    [file(projpl_1,t32_projpl_1)]).

fof(d9_incproj,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ( v1_incproj(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_incsp_1(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_incsp_1(A))
               => ! [D] : 
                    ( m1_subset_1(D,u2_incsp_1(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u2_incsp_1(A))
                       => ~ ( r1_incsp_1(A,B,D)
                            & r1_incsp_1(A,C,D)
                            & r1_incsp_1(A,B,E)
                            & r1_incsp_1(A,C,E)
                            & B != C
                            & D != E ) ) ) ) ) ) ) ),
    file(incproj,d9_incproj),
    []).

fof(dt_k1_projpl_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_incproj(A)
        & v2_incproj(A)
        & v3_incproj(A)
        & v4_incproj(A)
        & v5_incproj(A)
        & l1_incsp_1(A)
        & m1_subset_1(B,u1_incsp_1(A))
        & m1_subset_1(C,u1_incsp_1(A)) )
     => m1_subset_1(k1_projpl_1(A,B,C),u2_incsp_1(A)) ) ),
    file(projpl_1,k1_projpl_1),
    []).

fof(dt_l1_incsp_1,axiom,(
    $true ),
    file(incsp_1,l1_incsp_1),
    []).

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

fof(dt_u1_incsp_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ~ v1_xboole_0(u1_incsp_1(A)) ) ),
    file(incsp_1,u1_incsp_1),
    []).

fof(dt_u2_incsp_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ~ v1_xboole_0(u2_incsp_1(A)) ) ),
    file(incsp_1,u2_incsp_1),
    []).

fof(existence_l1_incsp_1,axiom,(
    ? [A] : l1_incsp_1(A) ),
    file(incsp_1,l1_incsp_1),
    []).

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

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

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

fof(t16_projpl_1,axiom,(
    ! [A] : 
      ( ( v1_incproj(A)
        & v2_incproj(A)
        & v3_incproj(A)
        & v4_incproj(A)
        & v5_incproj(A)
        & l1_incsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_incsp_1(A))
                 => ( B != C
                   => ( r1_incsp_1(A,B,k1_projpl_1(A,B,C))
                      & r1_incsp_1(A,C,k1_projpl_1(A,B,C))
                      & k1_projpl_1(A,B,C) = k1_projpl_1(A,C,B)
                      & ( ( r1_incsp_1(A,B,D)
                          & r1_incsp_1(A,C,D) )
                       => D = k1_projpl_1(A,B,C) ) ) ) ) ) ) ) ),
    file(projpl_1,t16_projpl_1),
    []).