Consider the following premises. forall x_2: W(x_2) <-> S(x_2). exists x_2: S(x_2) <-> W(x_2). Can we infer forall x_2: ~(S(x_2) <-> W(x_2)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.