% Mizar problem: t22_projdes1,projdes1,960,5 
fof(t22_projdes1, conjecture,  (! [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))  & l1_collsp(A)) ) ) ) ) ) )  => v5_anproj_2(A)) ) ).
fof(d12_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(t21_projdes1, axiom,  (! [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))  & 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, H, B, C) &  (r1_collsp(A, H, D, E) &  (r1_collsp(A, H, F, G) &  (r1_collsp(A, B, D, I) &  (r1_collsp(A, C, E, I) &  (r1_collsp(A, D, F, K) &  (r1_collsp(A, E, G, K) &  (r1_collsp(A, B, F, J) & r1_collsp(A, C, G, J)) ) ) ) ) ) ) )  =>  (r1_collsp(A, H, B, D) |  (r1_collsp(A, H, D, F) |  (r1_collsp(A, H, B, F) |  (B=C |  (D=E |  (H=C |  (H=E |  (H=G | r1_collsp(A, K, J, I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
