Consider the following premises. forall x_17: P_17(x_17) <-> Q_17(x_17). forall x_17: Q_17(x_17). Can we infer ~P_17(a_9) from them? If possible, name the inference rules being used at each step.
 From forall x_17: P_17(x_17) <-> Q_17(x_17) we can infer forall x_17: Q_17(x_17) -> P_17(x_17) via universal biconditional elimination. Finally, from forall x_17: Q_17(x_17) -> P_17(x_17), forall x_17: Q_17(x_17) we can infer forall x_17: P_17(x_17) via universal modus ponens, which contradicts ~P_17(a_9). Therefore, the answer is no.