Consider the following premises. forall z: S_3(z). forall z: ~W(z) or S(z). forall z: R_1(z) -> ~S_3(z). exists z: W(z) or R_1(z). Can we infer forall z: ~(S(z) or P_3(z)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.