Consider the following premises. forall x_13: Q_9(x_13) -> W(x_13). exists x_13: S(x_13) or Q_9(x_13). forall x_13: U(x_13). forall x_13: W(x_13) <-> S(x_13). Can we infer exists x_13: W(x_13) and U(x_13) from them? If possible, name the inference rules being used at each step.
 From forall x_13: W(x_13) <-> S(x_13) we can infer forall x_13: S(x_13) -> W(x_13) via universal biconditional elimination. From forall x_13: S(x_13) -> W(x_13), forall x_13: Q_9(x_13) -> W(x_13), exists x_13: S(x_13) or Q_9(x_13) we can infer exists x_13: W(x_13) via existential disjunction elimination. Finally, from exists x_13: W(x_13), forall x_13: U(x_13) we can infer exists x_13: W(x_13) and U(x_13) via existential conjunction. Therefore, the answer is yes.