Consider the following premises. p. ~q_2. p_4 -> q_2. p_12 -> ~p. Can we infer p_4 from them? If possible, name the inference rules being used at each step.
 From p_12 -> ~p, p we can infer ~p_12 via modus tollens. Finally, from p_4 -> q_2, ~q_2 we can infer ~p_4 via modus tollens, which contradicts p_4. Therefore, the answer is no.