Consider the following premises. p_12 -> ~q_12. w or q. q_12. q -> q_1. w -> q_1. Can we infer ~q_1 from them? If possible, name the inference rules being used at each step.
 From p_12 -> ~q_12, q_12 we can infer ~p_12 via modus tollens. Finally, from w -> q_1, q -> q_1, w or q we can infer q_1 via disjunction elimination, which contradicts ~q_1. Therefore, the answer is no.