Consider the following premises. forall x_13: T(x_13) -> Q_4(x_13). forall x_13: Q_4(x_13) -> U_3(x_13). forall x_13: R_2(x_13) -> U_3(x_13). exists x_13: T(x_13) and Q_13(x_13). Can we infer exists x_13: U_3(x_13) from them? If possible, name the inference rules being used at each step.
 From exists x_13: T(x_13) and Q_13(x_13) we can infer exists x_13: T(x_13) via existential simplification. From forall x_13: T(x_13) -> Q_4(x_13), forall x_13: Q_4(x_13) -> U_3(x_13) we can infer forall x_13: T(x_13) -> U_3(x_13) via universal transitivity. From exists x_13: T(x_13) we can infer exists x_13: T(x_13) or R_2(x_13) via existential addition. Finally, from forall x_13: T(x_13) -> U_3(x_13), forall x_13: R_2(x_13) -> U_3(x_13), exists x_13: T(x_13) or R_2(x_13) we can infer exists x_13: U_3(x_13) via existential disjunction elimination. Therefore, the answer is yes.