Consider the following premises. p_8 <-> q_2. p_8 -> q_16. q_2 <-> q_16. Can we infer ~(p_8 -> q_2) from them?
 From q_2 <-> q_16 we can infer q_16 -> q_2. Finally, from p_8 -> q_16, q_16 -> q_2 we can infer p_8 -> q_2, which contradicts ~(p_8 -> q_2). Therefore, the answer is no.