Consider the following premises. forall y: W(y) <-> T_3(y). forall y: W(y) or ~T_3(y). Can we infer exists y: ~(T_3(y) -> W(y)) from them?
 From forall y: W(y) <-> T_3(y) we can infer forall y: W(y) -> T_3(y). From forall y: W(y) or ~T_3(y) we can infer forall y: T_3(y) -> W(y). From forall y: T_3(y) -> W(y), forall y: W(y) -> T_3(y) we can infer forall y: T_3(y) <-> W(y). Finally, from forall y: T_3(y) <-> W(y) we can infer forall y: T_3(y) -> W(y), which contradicts exists y: ~(T_3(y) -> W(y)). Therefore, the answer is no.