Consider the following premises. forall x: R_1(x) or ~W(x). exists x: S_2(x) -> R(x). forall x: R(x) -> W_2(x). forall x: W_2(x) -> W(x). Can we infer forall x: ~(S_2(x) -> R_1(x)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.