Consider the following premises. forall x_13: R(x_13). forall x_13: Q_5(x_13) -> Q_13(x_13). forall x_13: P_5(x_13) -> Q_5(x_13). forall x_13: P(x_13) <-> Q_13(x_13). forall x_13: R(x_13) -> P_5(x_13). Can we infer forall x_13: Q_13(x_13) from them? If possible, name the inference rules being used at each step.
 From forall x_13: P(x_13) <-> Q_13(x_13) we can infer forall x_13: P(x_13) -> Q_13(x_13) via universal biconditional elimination. From forall x_13: R(x_13) we can infer forall x_13: R(x_13) or P(x_13) via universal addition. From forall x_13: P_5(x_13) -> Q_5(x_13), forall x_13: Q_5(x_13) -> Q_13(x_13) we can infer forall x_13: P_5(x_13) -> Q_13(x_13) via universal transitivity. From forall x_13: R(x_13) -> P_5(x_13), forall x_13: P_5(x_13) -> Q_13(x_13) we can infer forall x_13: R(x_13) -> Q_13(x_13) via universal transitivity. Finally, from forall x_13: R(x_13) -> Q_13(x_13), forall x_13: P(x_13) -> Q_13(x_13), forall x_13: R(x_13) or P(x_13) we can infer forall x_13: Q_13(x_13) via universal disjunction elimination. Therefore, the answer is yes.