Consider the following premises. exists z: R(z) -> U_4(z). forall z: R(z) <-> U(z). forall z: U_4(z) -> U(z). Can we infer forall z: ~(U_4(z) <-> R(z)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.