% Mizar problem: t7_projpl_1,projpl_1,253,42 
fof(t7_projpl_1,conjecture,(
    ! [A] : 
      ( l1_incsp_1(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,u2_incsp_1(A))
             => ! [C] : 
                  ( m1_subset_1(C,u2_incsp_1(A))
                 => B = C ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[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,t5_projred1]),
    [file(projpl_1,t7_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(t5_projred1,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,u2_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,C)
                      & r1_incsp_1(A,B,D)
                      & r1_incsp_1(A,B,E)
                      & C != D
                      & D != E
                      & E != C ) ) ) ) ) ),
    file(projred1,t5_projred1),
    []).