Consider the following premises. forall x_16: P_16(x_16). forall x_16: P_16(x_16) <-> Q_16(x_16). Can we infer ~Q_16(a_9) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) <-> Q_16(x_16) we can infer forall x_16: P_16(x_16) -> Q_16(x_16) via universal biconditional elimination. Finally, from forall x_16: P_16(x_16) -> Q_16(x_16), forall x_16: P_16(x_16) we can infer forall x_16: Q_16(x_16) via universal modus ponens, which contradicts ~Q_16(a_9). Therefore, the answer is no.