Consider the following premises. forall x: ~S(x). S(a) -> q_1. q_1 -> S(a). Can we infer ~q_1 from them? If possible, name the inference rules being used at each step.
 From forall x: ~S(x) we can infer ~S(a) via universal instantiation. From S(a) -> q_1, q_1 -> S(a) we can infer S(a) <-> q_1 via biconditional introduction. Finally, from S(a) <-> q_1, ~S(a) we can infer ~q_1 via biconditional elimination. Therefore, the answer is yes.