Consider the following premises. q or ~q_2. ~q. Can we infer q_2 from them? If possible, name the inference rules being used at each step.
 From q or ~q_2 we can infer q_2 -> q via rewriting. Finally, from q_2 -> q, ~q we can infer ~q_2 via modus tollens, which contradicts q_2. Therefore, the answer is no.