Consider the following premises. forall z: R(z) -> U_1(z). forall z: ~U_1(z). forall z: W(z) <-> R(z). forall z: U_1(z) -> W(z). Can we infer exists z: W(z) from them?
 From forall z: W(z) <-> R(z) we can infer forall z: W(z) -> R(z). From forall z: W(z) -> R(z), forall z: R(z) -> U_1(z) we can infer forall z: W(z) -> U_1(z). From forall z: W(z) -> U_1(z), forall z: U_1(z) -> W(z) we can infer forall z: W(z) <-> U_1(z). Finally, from forall z: W(z) <-> U_1(z), forall z: ~U_1(z) we can infer forall z: ~W(z), which contradicts exists z: W(z). Therefore, the answer is no.