% Mizar problem: t21_hessenbe,hessenbe,701,74 
fof(t21_hessenbe,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & v2_anproj_2(A)
        & v3_anproj_2(A)
        & v6_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,D,F,I)
                                                  & r1_collsp(A,C,E,I)
                                                  & r1_collsp(A,F,H,J)
                                                  & r1_collsp(A,E,G,J)
                                                  & r1_collsp(A,D,H,K)
                                                  & r1_collsp(A,C,G,K)
                                                  & r1_collsp(A,B,D,C)
                                                  & r1_collsp(A,B,F,E)
                                                  & r1_collsp(A,B,H,G) )
                                               => ( B = C
                                                  | D = C
                                                  | B = E
                                                  | F = E
                                                  | B = G
                                                  | H = G
                                                  | r1_collsp(A,B,D,F)
                                                  | r1_collsp(A,B,D,H)
                                                  | r1_collsp(A,B,F,H)
                                                  | r1_collsp(A,J,K,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_projdes1,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,l23_hessenbe,rc2_anproj_2,t3_hessenbe,t8_hessenbe]),
    [file(hessenbe,t21_hessenbe)]).

fof(cc1_projdes1,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)
          & ~ v7_anproj_2(A) )
       => ( ~ v3_struct_0(A)
          & v2_collsp(A)
          & v3_collsp(A)
          & v4_collsp(A)
          & v2_anproj_2(A)
          & v3_anproj_2(A)
          & v5_anproj_2(A)
          & ~ v7_anproj_2(A) ) ) ) ),
    file(projdes1,cc1_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(l23_hessenbe,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & v2_anproj_2(A)
        & v3_anproj_2(A)
        & v6_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,D,F,J)
                                                  & r1_collsp(A,C,E,J)
                                                  & r1_collsp(A,F,H,I)
                                                  & r1_collsp(A,E,G,I)
                                                  & r1_collsp(A,D,H,K)
                                                  & r1_collsp(A,C,G,K)
                                                  & r1_collsp(A,B,D,C)
                                                  & r1_collsp(A,B,F,E)
                                                  & r1_collsp(A,B,H,G) )
                                               => ( B = C
                                                  | D = C
                                                  | B = E
                                                  | F = E
                                                  | B = G
                                                  | H = G
                                                  | r1_collsp(A,B,D,F)
                                                  | r1_collsp(A,B,D,H)
                                                  | r1_collsp(A,B,F,H)
                                                  | r1_collsp(A,B,I,J)
                                                  | r1_collsp(A,I,K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(hessenbe,l23_hessenbe),
    []).

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(t3_hessenbe,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) )
     => ! [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(hessenbe,t3_hessenbe),
    []).

fof(t8_hessenbe,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) )
     => ! [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,B,C,E)
                          & B != E
                          & r1_collsp(A,B,E,D) ) ) ) ) ) ) ),
    file(hessenbe,t8_hessenbe),
    []).