Consider the following premises. forall x_18: P_18(x_18). forall x_18: Q_18(x_18) -> P_18(x_18). forall x_18: P_18(x_18) -> Q_18(x_18). Can we infer ~Q_18(a_9) from them?
 From forall x_18: P_18(x_18) -> Q_18(x_18), forall x_18: Q_18(x_18) -> P_18(x_18) we can infer forall x_18: P_18(x_18) <-> Q_18(x_18). From forall x_18: P_18(x_18) <-> Q_18(x_18) we can infer forall x_18: P_18(x_18) -> Q_18(x_18). Finally, from forall x_18: P_18(x_18) -> Q_18(x_18), forall x_18: P_18(x_18) we can infer forall x_18: Q_18(x_18), which contradicts ~Q_18(a_9). Therefore, the answer is no.