Consider the following premises. q_10 -> q_4. q_10 -> w_4. w_4 <-> q_10. Can we infer ~(w_4 -> q_4) from them?
 From w_4 <-> q_10 we can infer w_4 -> q_10. From q_10 -> w_4, w_4 -> q_10 we can infer q_10 <-> w_4. From q_10 <-> w_4 we can infer w_4 -> q_10. Finally, from w_4 -> q_10, q_10 -> q_4 we can infer w_4 -> q_4, which contradicts ~(w_4 -> q_4). Therefore, the answer is no.