Consider the following premises. forall x_9: P_9(x_9) -> Q_9(x_9). forall x_8: P_9(x_8). forall x_9: Q_9(x_9) -> P_9(x_9). Can we infer ~Q_9(a_8) 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_8: P_9(x_8) we can infer P_9(a_8). From forall x_9: P_9(x_9) <-> Q_9(x_9) we can infer P_9(a_8) <-> Q_9(a_8). From P_9(a_8) <-> Q_9(a_8) we can infer P_9(a_8) -> Q_9(a_8). Finally, from P_9(a_8) -> Q_9(a_8), P_9(a_8) we can infer Q_9(a_8), which contradicts ~Q_9(a_8). Therefore, the answer is no.