Consider the following premises. p <-> q_2. p_9 <-> p. p_2 -> q_2. Can we infer ~(p_2 -> p_9) from them?
 From p <-> q_2 we can infer q_2 -> p. From p_9 <-> p we can infer p -> p_9. From p_2 -> q_2, q_2 -> p we can infer p_2 -> p. Finally, from p_2 -> p, p -> p_9 we can infer p_2 -> p_9, which contradicts ~(p_2 -> p_9). Therefore, the answer is no.