% Mizar problem: l18_hessenbe,hessenbe,672,5 
fof(l18_hessenbe, conjecture,  (! [A] :  ( ( ~ (v2_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)) =>  (! [L] :  (m1_subset_1(L, u1_struct_0(A)) =>  ( (r1_collsp(A, B, C, J) &  (r1_collsp(A, E, F, J) &  (r1_collsp(A, C, D, H) &  (r1_collsp(A, F, G, H) &  (r1_collsp(A, B, D, I) &  (r1_collsp(A, E, G, I) &  (r1_collsp(A, K, B, E) &  (r1_collsp(A, K, C, F) &  (r1_collsp(A, K, D, G) &  (r1_collsp(A, K, C, L) & r1_collsp(A, B, D, L)) ) ) ) ) ) ) ) ) )  =>  (K=E |  (B=E |  (K=F |  (C=F |  (K=G |  (D=G |  (r1_collsp(A, K, B, C) |  (r1_collsp(A, K, B, D) |  (r1_collsp(A, K, C, D) |  (r1_collsp(A, K, H, J) |  (r1_collsp(A, H, J, L) | r1_collsp(A, H, I, J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_projdes1, axiom,  (! [A] :  (l1_collsp(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_collsp(A) &  (v3_collsp(A) &  (v4_collsp(A) &  (v2_anproj_2(A) &  (v3_anproj_2(A) &  ~ (v7_anproj_2(A)) ) ) ) ) ) )  =>  ( ~ (v2_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)) ) ) ) ) ) ) ) ) ) ) ).
fof(d14_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_collsp(A) &  (v3_collsp(A) &  (v4_collsp(A) &  (v2_anproj_2(A) &  (v3_anproj_2(A) & l1_collsp(A)) ) ) ) ) )  =>  (v7_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)) &  (r1_collsp(A, B, C, F) & r1_collsp(A, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_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)) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_l1_collsp, axiom,  (! [A] :  (l1_collsp(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_collsp, axiom,  (? [A] : l1_collsp(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(rc2_anproj_2, axiom,  (? [A] :  (l1_collsp(A) &  ( ~ (v2_struct_0(A))  &  (v2_collsp(A) &  (v3_collsp(A) &  (v4_collsp(A) &  (v2_anproj_2(A) & v3_anproj_2(A)) ) ) ) ) ) ) ).
fof(t13_hessenbe, axiom,  (! [A] :  ( ( ~ (v2_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)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ~ ( ( ~ (r1_collsp(A, B, C, E))  &  (r1_collsp(A, B, C, D) &  (r1_collsp(A, E, F, B) &  ( ~ (B=D)  &  ( ~ (B=F)  & r1_collsp(A, D, B, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_hessenbe, axiom,  (! [A] :  ( ( ~ (v2_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)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ( (r1_collsp(A, D, E, F) &  (r1_collsp(A, D, E, G) &  (r1_collsp(A, B, C, F) & r1_collsp(A, B, C, G)) ) )  =>  (B=C |  (D=E |  (r1_collsp(A, B, C, D) | F=G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_hessenbe, axiom,  (! [A] :  ( ( ~ (v2_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)) =>  ( (r1_collsp(A, B, C, D) &  (r1_collsp(A, E, F, G) &  (r1_collsp(A, B, F, J) &  (r1_collsp(A, E, C, J) &  (r1_collsp(A, B, G, I) &  (r1_collsp(A, D, E, I) &  (r1_collsp(A, C, G, H) & r1_collsp(A, D, F, H)) ) ) ) ) ) )  =>  (C=D |  (B=D |  (F=G |  (E=F |  (E=G |  (r1_collsp(A, B, C, E) | r1_collsp(A, H, I, J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_hessenbe, axiom,  (! [A] :  ( ( ~ (v2_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)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_hessenbe, axiom,  (! [A] :  ( ( ~ (v2_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=C | r1_collsp(A, B, D, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_hessenbe, axiom,  (! [A] :  ( ( ~ (v2_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, E))  &  (r1_collsp(A, B, C, D) &  ( ~ (B=D)  & r1_collsp(A, B, D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_hessenbe, axiom,  (! [A] :  ( ( ~ (v2_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, E) & r1_collsp(A, B, D, E))  =>  (r1_collsp(A, B, C, D) | B=E) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_hessenbe, axiom,  (! [A] :  ( ( ~ (v2_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)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ~ ( ( ~ (r1_collsp(A, F, B, D))  &  (r1_collsp(A, F, D, E) &  ( ~ (D=E)  &  (r1_collsp(A, C, E, G) &  (r1_collsp(A, F, B, C) &  ( ~ (F=C)  & G=D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_hessenbe, axiom,  (! [A] :  ( ( ~ (v2_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)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ( (r1_collsp(A, B, C, F) &  (r1_collsp(A, C, D, E) & r1_collsp(A, E, F, G)) )  =>  (r1_collsp(A, B, C, D) |  (F=B |  (F=C |  (E=C |  (E=D |  ( ~ (B=G)  &  ~ (D=G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
