Consider the following premises. forall y: Q(y) -> S_4(y). exists y: Q(y) <-> R_1(y). forall y: W_4(y) -> R_1(y). forall y: Q(y) -> W_4(y). Can we infer forall y: ~(R_1(y) -> S_4(y)) from them?
That contradicts the premises. Therefore the answer is no.