Consider the following premises. w -> p_4. ~p_4. p_12 -> w. q. q_1 -> ~q. Can we infer q_1 from them? If possible, name the inference rules being used at each step.
 From w -> p_4, ~p_4 we can infer ~w via modus tollens. From p_12 -> w, ~w we can infer ~p_12 via modus tollens. Finally, from q_1 -> ~q, q we can infer ~q_1 via modus tollens, which contradicts q_1. Therefore, the answer is no.