Consider the following premises. p_4 -> q_11. q_11 <-> q. q_11 -> p_4. Can we infer ~(p_4 -> q) from them?
 From p_4 -> q_11, q_11 -> p_4 we can infer p_4 <-> q_11. From q_11 <-> q we can infer q_11 -> q. From p_4 <-> q_11 we can infer p_4 -> q_11. Finally, from p_4 -> q_11, q_11 -> q we can infer p_4 -> q, which contradicts ~(p_4 -> q). Therefore, the answer is no.