Consider the following premises. forall x_3: Q_2(x_3) or R_2(x_3). forall x_3: Q_2(x_3) -> T(x_3). forall x_3: U_4(x_3) or ~T(x_3). exists x_3: R_2(x_3) -> U_4(x_3). Can we infer exists x_3: U_4(x_3) from them? If possible, name the inference rules being used at each step.
 From forall x_3: U_4(x_3) or ~T(x_3) we can infer forall x_3: T(x_3) -> U_4(x_3) via universal rewriting. From forall x_3: Q_2(x_3) -> T(x_3), forall x_3: T(x_3) -> U_4(x_3) we can infer forall x_3: Q_2(x_3) -> U_4(x_3) via universal transitivity. Finally, from forall x_3: Q_2(x_3) -> U_4(x_3), exists x_3: R_2(x_3) -> U_4(x_3), forall x_3: Q_2(x_3) or R_2(x_3) we can infer exists x_3: U_4(x_3) via existential disjunction elimination. Therefore, the answer is yes.