Consider the following premises. p_7 or ~q_7. p_7 -> t. t -> p_4. Can we infer ~(q_7 -> p_4) from them? If possible, name the inference rules being used at each step.
 From p_7 or ~q_7 we can infer q_7 -> p_7 via rewriting. From q_7 -> p_7, p_7 -> t we can infer q_7 -> t via transitivity. Finally, from q_7 -> t, t -> p_4 we can infer q_7 -> p_4 via transitivity, which contradicts ~(q_7 -> p_4). Therefore, the answer is no.