% Mizar problem: t8_projpl_1,projpl_1,265,57 
fof(t8_projpl_1,conjecture,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_incsp_1(A))
             => ~ ( v1_incproj(A)
                  & v2_incproj(A)
                  & v3_incproj(A)
                  & v4_incproj(A)
                  & v5_incproj(A)
                  & l1_incsp_1(A)
                  & r1_incsp_1(A,B,C)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_incsp_1(A))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_incsp_1(A))
                         => ~ ( r3_incproj(A,D,E,C)
                              & r1_incproj(B,D,E) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d5_incproj,d7_incproj,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,t8_projred1]),
    [file(projpl_1,t8_projpl_1)]).

fof(d5_incproj,axiom,(
    ! [A,B,C] : 
      ( r1_incproj(A,B,C)
    <=> ( A != B
        & B != C
        & C != A ) ) ),
    file(incproj,d5_incproj),
    []).

fof(d7_incproj,axiom,(
    ! [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))
                 => ( r3_incproj(A,B,C,D)
                  <=> ( r1_incsp_1(A,B,D)
                      & r1_incsp_1(A,C,D) ) ) ) ) ) ) ),
    file(incproj,d7_incproj),
    []).

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(t8_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,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_incsp_1(A))
                 => ? [E] : 
                      ( m1_subset_1(E,u1_incsp_1(A))
                      & r1_incsp_1(A,E,D)
                      & E != B
                      & E != C ) ) ) ) ) ),
    file(projred1,t8_projred1),
    []).