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