Consider the following premises. forall x: Q(x) <-> W(x). exists x: ~Q(x). forall x: S(x) -> W(x). Can we infer exists x: ~S(x) from them? If possible, name the inference rules being used at each step.
 From forall x: Q(x) <-> W(x), exists x: ~Q(x) we can infer exists x: ~W(x) via existential biconditional elimination. Finally, from forall x: S(x) -> W(x), exists x: ~W(x) we can infer exists x: ~S(x) via existential modus tollens. Therefore, the answer is yes.