Consider the following premises. q. s_1 -> ~t. q -> q_14. ~q_14. Can we infer ~s_1 from them? If possible, name the inference rules being used at each step.
 From q -> q_14, ~q_14 we can infer ~q via modus tollens. From ~q we can infer ~q or t via addition. From ~q or t, q we can infer t via disjunctive syllogism. Finally, from s_1 -> ~t, t we can infer ~s_1 via modus tollens. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.