Consider the following premises. u. p -> ~u. ~r_4 -> w. r_4 -> p. Can we infer ~w from them?
 From p -> ~u, u we can infer ~p. From r_4 -> p, ~p we can infer ~r_4. Finally, from ~r_4 -> w, ~r_4 we can infer w, which contradicts ~w. Therefore, the answer is no.