Consider the following premises. p_9 -> p_3. p_3 -> t. p_9 or ~t. Can we infer ~(p_3 -> p_9) from them? If possible, name the inference rules being used at each step.
 From p_9 or ~t we can infer t -> p_9 via rewriting. Finally, from p_3 -> t, t -> p_9 we can infer p_3 -> p_9 via transitivity, which contradicts ~(p_3 -> p_9). Therefore, the answer is no.