% Mizar problem: t1_projdes1,projdes1,32,5 
fof(t1_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)) ) ) ) ) ) )  =>  (! [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(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(t4_collsp, axiom,  (! [A] :  ( ( ~ (v2_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)) =>  (r1_collsp(A, B, C, D) =>  (r1_collsp(A, C, B, D) & r1_collsp(A, B, D, C)) ) ) ) ) ) ) ) ) ) ).
