% Mizar problem: t27_projdes1,projdes1,498,37 
fof(t27_projdes1,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & v2_anproj_2(A)
        & v3_anproj_2(A)
        & ~ v7_anproj_2(A)
        & l1_collsp(A) )
     => v5_anproj_2(A) ) ),
    inference(mizar_bg_added,[status(thm)],[d12_anproj_2,dt_l1_collsp,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_collsp,existence_l1_struct_0,existence_m1_subset_1,rc2_anproj_2,t26_projdes1]),
    [file(projdes1,t27_projdes1)]).

fof(d12_anproj_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & v2_anproj_2(A)
        & v3_anproj_2(A)
        & l1_collsp(A) )
     => ( v5_anproj_2(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))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] : 
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( ( r1_collsp(A,C,D,K)
                                                    & r1_collsp(A,F,G,K)
                                                    & r1_collsp(A,D,E,I)
                                                    & r1_collsp(A,G,H,I)
                                                    & r1_collsp(A,C,E,J)
                                                    & r1_collsp(A,F,H,J)
                                                    & r1_collsp(A,B,C,F)
                                                    & r1_collsp(A,B,D,G)
                                                    & r1_collsp(A,B,E,H) )
                                                 => ( B = F
                                                    | C = F
                                                    | B = G
                                                    | D = G
                                                    | B = H
                                                    | E = H
                                                    | r1_collsp(A,B,C,D)
                                                    | r1_collsp(A,B,C,E)
                                                    | r1_collsp(A,B,D,E)
                                                    | r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(anproj_2,d12_anproj_2),
    []).

fof(dt_l1_collsp,axiom,(
    ! [A] : 
      ( l1_collsp(A)
     => l1_struct_0(A) ) ),
    file(collsp,l1_collsp),
    []).

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_collsp,axiom,(
    ? [A] : l1_collsp(A) ),
    file(collsp,l1_collsp),
    []).

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(rc2_anproj_2,axiom,(
    ? [A] : 
      ( l1_collsp(A)
      & ~ v3_struct_0(A)
      & v2_collsp(A)
      & v3_collsp(A)
      & v4_collsp(A)
      & v2_anproj_2(A)
      & v3_anproj_2(A) ) ),
    file(anproj_2,rc2_anproj_2),
    []).

fof(t26_projdes1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & v2_anproj_2(A)
        & v3_anproj_2(A)
        & ~ v7_anproj_2(A)
        & l1_collsp(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))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ! [J] : 
                                          ( m1_subset_1(J,u1_struct_0(A))
                                         => ! [K] : 
                                              ( m1_subset_1(K,u1_struct_0(A))
                                             => ( ( r1_collsp(A,B,C,F)
                                                  & r1_collsp(A,B,D,G)
                                                  & r1_collsp(A,B,E,H)
                                                  & r1_collsp(A,C,D,I)
                                                  & r1_collsp(A,F,G,I)
                                                  & r1_collsp(A,D,E,J)
                                                  & r1_collsp(A,G,H,J)
                                                  & r1_collsp(A,C,E,K)
                                                  & r1_collsp(A,F,H,K) )
                                               => ( r1_collsp(A,B,C,D)
                                                  | r1_collsp(A,B,D,E)
                                                  | r1_collsp(A,B,C,E)
                                                  | C = F
                                                  | D = G
                                                  | B = F
                                                  | B = G
                                                  | B = H
                                                  | r1_collsp(A,J,K,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(projdes1,t26_projdes1),
    []).