Consider the following premises. forall z_4: S(z_4) -> R(z_4). exists z_4: R(z_4) -> U(z_4). forall z_4: U(z_4) -> S(z_4). Can we infer forall z_4: ~(U(z_4) <-> S(z_4)) from them?
 From forall z_4: S(z_4) -> R(z_4), exists z_4: R(z_4) -> U(z_4) we can infer exists z_4: S(z_4) -> U(z_4). Finally, from forall z_4: U(z_4) -> S(z_4), exists z_4: S(z_4) -> U(z_4) we can infer exists z_4: U(z_4) <-> S(z_4), which contradicts forall z_4: ~(U(z_4) <-> S(z_4)). Therefore, the answer is no.