Consider the following premises. forall x_14: S(x_14) -> U(x_14). exists x_14: P_8(x_14) or S(x_14). forall x_14: ~P_8(x_14). forall x_14: U(x_14) -> S(x_14). Can we infer exists x_14: U(x_14) from them? If possible, name the inference rules being used at each step.
 From forall x_14: S(x_14) -> U(x_14), forall x_14: U(x_14) -> S(x_14) we can infer forall x_14: S(x_14) <-> U(x_14) via universal biconditional introduction. From exists x_14: P_8(x_14) or S(x_14), forall x_14: ~P_8(x_14) we can infer exists x_14: S(x_14) via existential disjunctive syllogism. From forall x_14: S(x_14) <-> U(x_14) we can infer forall x_14: S(x_14) -> U(x_14) via universal biconditional elimination. Finally, from forall x_14: S(x_14) -> U(x_14), exists x_14: S(x_14) we can infer exists x_14: U(x_14) via existential modus ponens. Therefore, the answer is yes.