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