Consider the following premises. p_4 -> u_4. ~u_4. p_4. Can we infer t_2 from them? If possible, name the inference rules being used at each step.
 From p_4 -> u_4, ~u_4 we can infer ~p_4 via modus tollens. From p_4 we can infer p_4 or t_2 via addition. Finally, from p_4 or t_2, ~p_4 we can infer t_2 via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.