Consider the following premises. forall x_9: Q(x_9) <-> S_9(x_9). ~S_9(a_9). Q(a_9) -> S_9(a_9). Can we infer ~Q(a_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: Q(x_9) <-> S_9(x_9) we can infer Q(a_9) <-> S_9(a_9) via universal instantiation. From Q(a_9) <-> S_9(a_9) we can infer S_9(a_9) -> Q(a_9) via biconditional elimination. From Q(a_9) -> S_9(a_9), S_9(a_9) -> Q(a_9) we can infer Q(a_9) <-> S_9(a_9) via biconditional introduction. Finally, from Q(a_9) <-> S_9(a_9), ~S_9(a_9) we can infer ~Q(a_9) via biconditional elimination. Therefore, the answer is yes.