% Mizar problem: t14_projdes1,projdes1,267,35 
fof(t14_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))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_collsp(A,B,C,D)
                                  & r1_projdes1(A,E,F,G,B)
                                  & r1_projdes1(A,E,F,G,C) )
                               => ( B = C
                                  | r1_projdes1(A,E,F,G,D) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d7_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,l16_projdes1,l20_projdes1,rc2_anproj_2,t10_projdes1,t11_projdes1,t12_projdes1,t14_collsp,t1_projdes1]),
    [file(projdes1,t14_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(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(l16_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))
                         => ( ( r1_projdes1(A,B,C,D,E)
                              & r1_projdes1(A,B,C,D,F) )
                           => ( r1_collsp(A,B,C,D)
                              | r1_projdes1(A,B,C,E,F) ) ) ) ) ) ) ) ) ),
    file(projdes1,l16_projdes1),
    []).

fof(l20_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))
                         => ( ( r1_collsp(A,B,C,D)
                              & r1_projdes1(A,E,F,B,C) )
                           => ( B = C
                              | r1_projdes1(A,E,F,B,D) ) ) ) ) ) ) ) ) ),
    file(projdes1,l20_projdes1),
    []).

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(t10_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))
                     => ( ~ ( ~ r1_collsp(A,B,C,D)
                            & ~ r1_collsp(A,C,D,E)
                            & ~ r1_collsp(A,D,E,B)
                            & ~ r1_collsp(A,E,B,C) )
                       => r1_projdes1(A,B,C,D,E) ) ) ) ) ) ) ),
    file(projdes1,t10_projdes1),
    []).

fof(t11_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))
                     => ( r1_projdes1(A,B,C,D,E)
                       => ( r1_projdes1(A,C,D,E,B)
                          & r1_projdes1(A,D,E,B,C)
                          & r1_projdes1(A,E,B,C,D)
                          & r1_projdes1(A,C,B,D,E)
                          & r1_projdes1(A,D,C,E,B)
                          & r1_projdes1(A,E,D,B,C)
                          & r1_projdes1(A,B,E,C,D)
                          & r1_projdes1(A,B,D,E,C)
                          & r1_projdes1(A,C,E,B,D)
                          & r1_projdes1(A,D,B,C,E)
                          & r1_projdes1(A,E,C,D,B)
                          & r1_projdes1(A,D,B,E,C)
                          & r1_projdes1(A,E,C,B,D)
                          & r1_projdes1(A,B,D,C,E)
                          & r1_projdes1(A,C,E,D,B)
                          & r1_projdes1(A,B,C,E,D)
                          & r1_projdes1(A,B,E,D,C)
                          & r1_projdes1(A,C,D,B,E)
                          & r1_projdes1(A,C,B,E,D)
                          & r1_projdes1(A,D,C,B,E)
                          & r1_projdes1(A,D,E,C,B)
                          & r1_projdes1(A,E,B,D,C)
                          & r1_projdes1(A,E,D,C,B) ) ) ) ) ) ) ) ),
    file(projdes1,t11_projdes1),
    []).

fof(t12_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))
                                 => ( ( r1_projdes1(A,B,C,D,E)
                                      & r1_projdes1(A,B,C,D,F)
                                      & r1_projdes1(A,B,C,D,G)
                                      & r1_projdes1(A,B,C,D,H) )
                                   => ( r1_collsp(A,B,C,D)
                                      | r1_projdes1(A,E,F,G,H) ) ) ) ) ) ) ) ) ) ) ),
    file(projdes1,t12_projdes1),
    []).

fof(t14_collsp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(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))
                         => ( ( r1_collsp(A,D,E,B)
                              & r1_collsp(A,D,E,C)
                              & r1_collsp(A,B,C,F) )
                           => ( B = C
                              | r1_collsp(A,D,E,F) ) ) ) ) ) ) ) ) ),
    file(collsp,t14_collsp),
    []).

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),
    []).