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