Consider the following premises. ~q_14. u_1 -> q_14. u_1. q -> ~q_10. Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From u_1 -> q_14, ~q_14 we can infer ~u_1 via modus tollens. From ~u_1 we can infer ~u_1 or q_10 via addition. From ~u_1 or q_10, u_1 we can infer q_10 via disjunctive syllogism. Finally, from q -> ~q_10, q_10 we can infer ~q via modus tollens. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.