Consider the following premises. S(f) -> s_1. forall x_2: ~S(x_2). s_1 -> S(f). Can we infer s_1 from them? If possible, name the inference rules being used at each step.
 From forall x_2: ~S(x_2) we can infer ~S(f) via universal instantiation. From s_1 -> S(f), S(f) -> s_1 we can infer s_1 <-> S(f) via biconditional introduction. Finally, from s_1 <-> S(f), ~S(f) we can infer ~s_1 via biconditional elimination, which contradicts s_1. Therefore, the answer is no.