Consider the following premises. forall y: R_2(y) -> T(y). exists y: W(y) <-> R_2(y). forall y: T(y) -> W(y). forall y: W(y) -> R_2(y). Can we infer forall y: ~(R_2(y) <-> W(y)) from them?
 From forall y: R_2(y) -> T(y), forall y: T(y) -> W(y) we can infer forall y: R_2(y) -> W(y). Finally, from forall y: W(y) -> R_2(y), forall y: R_2(y) -> W(y) we can infer forall y: W(y) <-> R_2(y), which contradicts forall y: ~(R_2(y) <-> W(y)). Therefore, the answer is no.