Consider the following premises. forall y: S(y) -> W(y). exists y: T(y) -> S(y). forall y: W(y) -> R_4(y). forall y: R_4(y) -> T(y). Can we infer forall y: ~(R_4(y) <-> S(y)) from them? If possible, name the inference rules being used at each step.
 From forall y: R_4(y) -> T(y), exists y: T(y) -> S(y) we can infer exists y: R_4(y) -> S(y) via existential transitivity. From forall y: S(y) -> W(y), forall y: W(y) -> R_4(y) we can infer forall y: S(y) -> R_4(y) via universal transitivity. Finally, from exists y: R_4(y) -> S(y), forall y: S(y) -> R_4(y) we can infer exists y: R_4(y) <-> S(y) via existential biconditional introduction, which contradicts forall y: ~(R_4(y) <-> S(y)). Therefore, the answer is no.