Consider the following premises. forall y_3: T(y_3) -> S_3(y_3). forall y_3: W_4(y_3) -> T(y_3). forall y_3: S_3(y_3) -> T(y_3). Can we infer exists y_3: ~(W_4(y_3) -> S_3(y_3)) from them?
 From forall y_3: S_3(y_3) -> T(y_3), forall y_3: T(y_3) -> S_3(y_3) we can infer forall y_3: S_3(y_3) <-> T(y_3). From forall y_3: S_3(y_3) <-> T(y_3) we can infer forall y_3: T(y_3) -> S_3(y_3). Finally, from forall y_3: W_4(y_3) -> T(y_3), forall y_3: T(y_3) -> S_3(y_3) we can infer forall y_3: W_4(y_3) -> S_3(y_3), which contradicts exists y_3: ~(W_4(y_3) -> S_3(y_3)). Therefore, the answer is no.