Consider the following premises. forall z: Q(z) -> S_3(z). ~S_3(a_7). S_3(a_7) -> Q(a_7). Can we infer ~Q(a_7) from them? If possible, name the inference rules being used at each step.
 From forall z: Q(z) -> S_3(z) we can infer Q(a_7) -> S_3(a_7) via universal instantiation. From S_3(a_7) -> Q(a_7), Q(a_7) -> S_3(a_7) we can infer S_3(a_7) <-> Q(a_7) via biconditional introduction. Finally, from S_3(a_7) <-> Q(a_7), ~S_3(a_7) we can infer ~Q(a_7) via biconditional elimination. Therefore, the answer is yes.