Consider the following premises. p -> P_9(a_5). Q_9(a_5) or p. forall x_9: P_9(x_9) <-> Q_9(x_9). Can we infer ~P_9(a_5) from them?
 From 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). From forall x_9: Q_9(x_9) -> P_9(x_9) we can infer Q_9(a_5) -> P_9(a_5). Finally, from Q_9(a_5) -> P_9(a_5), p -> P_9(a_5), Q_9(a_5) or p we can infer P_9(a_5), which contradicts ~P_9(a_5). Therefore, the answer is no.