Consider the following premises. p. q_1. ~q_1. Can we infer p_2 and p from them? If possible, name the inference rules being used at each step.
 From q_1 we can infer q_1 or p_2 via addition. From q_1 or p_2, ~q_1 we can infer p_2 via disjunctive syllogism. Finally, from p_2, p we can infer p_2 and p via conjunction. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.