Consider the following premises. ~s. s. Can we infer p_4 or p_1 from them? If possible, name the inference rules being used at each step.
 From s we can infer s or p_4 via addition. From s or p_4, ~s we can infer p_4 via disjunctive syllogism. Finally, from p_4 we can infer p_4 or p_1 via addition. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.