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