Consider the following premises. exists x_4: P_4(x_4) or T_2(x_4). forall x_4: ~P_4(x_4). Can we infer exists x_4: T_2(x_4) or U(x_4) from them? If possible, name the inference rules being used at each step.
 From exists x_4: P_4(x_4) or T_2(x_4), forall x_4: ~P_4(x_4) we can infer exists x_4: T_2(x_4) via existential disjunctive syllogism. Finally, from exists x_4: T_2(x_4) we can infer exists x_4: T_2(x_4) or U(x_4) via existential addition. Therefore, the answer is yes.