% Mizar problem: t7_projdes1,projdes1,46,16 
fof(t7_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) )
     => ! [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))
                     => ( ( r1_collsp(A,B,C,E)
                          & r1_collsp(A,B,D,E) )
                       => ( r1_collsp(A,B,C,D)
                          | B = E ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d7_anproj_2,d8_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,t1_projdes1]),
    [file(projdes1,t7_projdes1)]).

fof(d7_anproj_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_collsp(A) )
     => ( v2_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))
                   => ( r1_collsp(A,B,C,B)
                      & r1_collsp(A,B,B,C)
                      & r1_collsp(A,B,C,C) ) ) ) ) ) ) ),
    file(anproj_2,d7_anproj_2),
    []).

fof(d8_anproj_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_collsp(A) )
     => ( v3_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))
                           => ( ( r1_collsp(A,B,C,D)
                                & r1_collsp(A,B,C,E)
                                & r1_collsp(A,B,C,F) )
                             => ( B = C
                                | r1_collsp(A,D,E,F) ) ) ) ) ) ) ) ) ) ),
    file(anproj_2,d8_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(t1_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))
                 => ( r1_collsp(A,B,C,D)
                   => ( r1_collsp(A,C,D,B)
                      & r1_collsp(A,D,B,C)
                      & r1_collsp(A,C,B,D)
                      & r1_collsp(A,B,D,C)
                      & r1_collsp(A,D,C,B) ) ) ) ) ) ) ),
    file(projdes1,t1_projdes1),
    []).