Consider the following premises. forall x_1: W_1(x_1) -> S_3(x_1). exists x_1: S_3(x_1) -> W(x_1). forall x_1: W_1(x_1) or ~W(x_1). Can we infer forall x_1: ~(W_1(x_1) -> W(x_1)) from them?
That contradicts the premises. Therefore the answer is no.