Consider the following premises. forall x_9: ~Q_9(x_9). forall x_9: P_9(x_9) <-> Q_9(x_9). p <-> P_9(a_5). Can we infer ~p from them?
 From forall x_9: P_9(x_9) <-> Q_9(x_9), forall x_9: ~Q_9(x_9) we can infer forall x_9: ~P_9(x_9). From forall x_9: ~P_9(x_9) we can infer ~P_9(a_5). Finally, from p <-> P_9(a_5), ~P_9(a_5) we can infer ~p. Therefore, the answer is yes.