Consider the following premises. exists x_13: Q_13(x_13). forall x_13: S(x_13) or T_3(x_13). forall x_13: S(x_13) -> ~Q_13(x_13). forall x_13: U(x_13). Can we infer exists x_13: U(x_13) and T_3(x_13) from them? If possible, name the inference rules being used at each step.
 From forall x_13: S(x_13) -> ~Q_13(x_13), exists x_13: Q_13(x_13) we can infer exists x_13: ~S(x_13) via existential modus tollens. From forall x_13: S(x_13) or T_3(x_13), exists x_13: ~S(x_13) we can infer exists x_13: T_3(x_13) via existential disjunctive syllogism. Finally, from forall x_13: U(x_13), exists x_13: T_3(x_13) we can infer exists x_13: U(x_13) and T_3(x_13) via existential conjunction. Therefore, the answer is yes.