Consider the following premises. s_2 -> r_18. w_4 or s_2. p -> ~w. ~r_18. w_4 -> r_18. Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From w_4 -> r_18, s_2 -> r_18, w_4 or s_2 we can infer r_18 via disjunction elimination. From r_18 we can infer r_18 or w via addition. From r_18 or w, ~r_18 we can infer w via disjunctive syllogism. Finally, from p -> ~w, w we can infer ~p via modus tollens. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.