Consider the following premises. forall y_3: W_2(y_3) -> T(y_3). forall y_3: T(y_3) -> W_2(y_3). exists y_3: W_2(y_3) -> T(y_3). Can we infer forall y_3: ~(T(y_3) <-> W_2(y_3)) from them?
That contradicts the premises. Therefore the answer is no.