Consider the following premises. forall x_14: U(x_14) or ~Q_14(x_14). forall x_14: R_11(x_14) -> U(x_14). forall x_14: ~P_11(x_14) or R_11(x_14). exists x_14: P_11(x_14) or Q_14(x_14). Can we infer exists x_14: U(x_14) or U_3(x_14) from them? If possible, name the inference rules being used at each step.
 From forall x_14: U(x_14) or ~Q_14(x_14) we can infer forall x_14: Q_14(x_14) -> U(x_14) via universal rewriting. From exists x_14: P_11(x_14) or Q_14(x_14), forall x_14: ~P_11(x_14) or R_11(x_14) we can infer exists x_14: Q_14(x_14) or R_11(x_14) via existential resolution. From forall x_14: Q_14(x_14) -> U(x_14), forall x_14: R_11(x_14) -> U(x_14), exists x_14: Q_14(x_14) or R_11(x_14) we can infer exists x_14: U(x_14) via existential disjunction elimination. Finally, from exists x_14: U(x_14) we can infer exists x_14: U(x_14) or U_3(x_14) via existential addition. Therefore, the answer is yes.