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