Consider the following premises. exists z: P_3(z) -> W(z). forall z: W(z) <-> R_1(z). forall z: R_1(z) -> P_3(z). Can we infer forall z: ~(R_1(z) <-> 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.