Consider the following premises. forall z: U(z) -> R_3(z). forall z: R_3(z) -> U(z). forall z: U(z) <-> R_3(z). Can we infer exists z: ~(U(z) <-> R_3(z)) from them?
 From forall z: U(z) <-> R_3(z) we can infer forall z: U(z) -> R_3(z). From forall z: U(z) -> R_3(z), forall z: R_3(z) -> U(z) we can infer forall z: U(z) <-> R_3(z). From forall z: U(z) <-> R_3(z) we can infer forall z: R_3(z) -> U(z). Finally, from forall z: U(z) -> R_3(z), forall z: R_3(z) -> U(z) we can infer forall z: U(z) <-> R_3(z), which contradicts exists z: ~(U(z) <-> R_3(z)). Therefore, the answer is no.