Consider the following premises. forall x_12: Q(x_12) <-> P(x_12). forall x_12: P_8(x_12) or Q_8(x_12). forall x_12: R_8(x_12) -> P(x_12). forall x_12: Q_8(x_12) -> R_8(x_12). forall x_12: P_8(x_12) -> R_8(x_12). Can we infer forall x_12: Q(x_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: Q(x_12) <-> P(x_12) we can infer forall x_12: P(x_12) -> Q(x_12) via universal biconditional elimination. From forall x_12: P_8(x_12) -> R_8(x_12), forall x_12: Q_8(x_12) -> R_8(x_12), forall x_12: P_8(x_12) or Q_8(x_12) we can infer forall x_12: R_8(x_12) via universal disjunction elimination. From forall x_12: R_8(x_12) -> P(x_12), forall x_12: R_8(x_12) we can infer forall x_12: P(x_12) via universal modus ponens. Finally, from forall x_12: P(x_12) -> Q(x_12), forall x_12: P(x_12) we can infer forall x_12: Q(x_12) via universal modus ponens. Therefore, the answer is yes.