Consider the following premises. forall x_9: Q_9(x_9) -> P_9(x_9). forall x_9: P_9(x_9) -> Q_9(x_9). forall x_9: P_9(x_9) or ~Q_9(x_9). Can we infer forall x_9: Q_9(x_9) <-> P_9(x_9) from them?
 From forall x_9: P_9(x_9) -> Q_9(x_9), forall x_9: Q_9(x_9) -> P_9(x_9) we can infer forall x_9: P_9(x_9) <-> Q_9(x_9). From forall x_9: P_9(x_9) or ~Q_9(x_9) we can infer forall x_9: Q_9(x_9) -> P_9(x_9). From forall x_9: P_9(x_9) <-> Q_9(x_9) we can infer forall x_9: P_9(x_9) -> Q_9(x_9). Finally, from forall x_9: Q_9(x_9) -> P_9(x_9), forall x_9: P_9(x_9) -> Q_9(x_9) we can infer forall x_9: Q_9(x_9) <-> P_9(x_9). Therefore, the answer is yes.