Consider the following premises. u -> w_4. w_4 -> u. w_4 -> r. Can we infer ~(u -> r) from them?
 From w_4 -> u, u -> w_4 we can infer w_4 <-> u. From w_4 <-> u we can infer u -> w_4. Finally, from u -> w_4, w_4 -> r we can infer u -> r, which contradicts ~(u -> r). Therefore, the answer is no.