Consider the following premises. t -> q. q -> q_3. t or ~r. Can we infer ~(r -> q_3) from them? If possible, name the inference rules being used at each step.
 From t -> q, q -> q_3 we can infer t -> q_3 via transitivity. From t or ~r we can infer r -> t via rewriting. Finally, from r -> t, t -> q_3 we can infer r -> q_3 via transitivity, which contradicts ~(r -> q_3). Therefore, the answer is no.