Consider the following premises. exists x_5: W(x_5) -> R(x_5). forall x_5: W(x_5) -> S_1(x_5). forall x_5: S_1(x_5) -> W(x_5). Can we infer forall x_5: ~(S_1(x_5) -> R(x_5)) from them?
That contradicts the premises. Therefore the answer is no.