Consider the following premises. forall x_1: U(x_1) -> W_3(x_1). exists x_1: S(x_1) or ~U(x_1). forall x_1: W_3(x_1) -> U(x_1). forall x_1: T(x_1) -> W_3(x_1). Can we infer forall x_1: ~(T(x_1) -> S(x_1)) from them?
That contradicts the premises. Therefore the answer is no.