Consider the following premises. q_3 -> u. q_1 -> q_3. w_3 -> q_1. Can we infer ~(w_3 -> u) from them?
 From w_3 -> q_1, q_1 -> q_3 we can infer w_3 -> q_3. Finally, from w_3 -> q_3, q_3 -> u we can infer w_3 -> u, which contradicts ~(w_3 -> u). Therefore, the answer is no.