Consider the following premises. forall x_13: U(x_13) <-> Q_13(x_13). forall x_13: P_13(x_13). forall x_13: U(x_13) -> Q(x_13). forall x_13: U(x_13) or ~P_13(x_13). Can we infer forall x_13: Q(x_13) from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13) we can infer forall x_13: P_13(x_13) or Q_13(x_13) via universal addition. From forall x_13: U(x_13) or ~P_13(x_13) we can infer forall x_13: P_13(x_13) -> U(x_13) via universal rewriting. From forall x_13: U(x_13) <-> Q_13(x_13) we can infer forall x_13: Q_13(x_13) -> U(x_13) via universal biconditional elimination. From forall x_13: P_13(x_13) -> U(x_13), forall x_13: Q_13(x_13) -> U(x_13), forall x_13: P_13(x_13) or Q_13(x_13) we can infer forall x_13: U(x_13) via universal disjunction elimination. Finally, from forall x_13: U(x_13) -> Q(x_13), forall x_13: U(x_13) we can infer forall x_13: Q(x_13) via universal modus ponens. Therefore, the answer is yes.