Consider the following premises. exists z: S_4(z) -> W(z). forall z: S(z) -> S_4(z). forall z: R(z) -> S(z). forall z: W(z) -> R(z). Can we infer forall z: ~(R(z) <-> S_4(z)) from them?
 From forall z: R(z) -> S(z), forall z: S(z) -> S_4(z) we can infer forall z: R(z) -> S_4(z). From exists z: S_4(z) -> W(z), forall z: W(z) -> R(z) we can infer exists z: S_4(z) -> R(z). Finally, from forall z: R(z) -> S_4(z), exists z: S_4(z) -> R(z) we can infer exists z: R(z) <-> S_4(z), which contradicts forall z: ~(R(z) <-> S_4(z)). Therefore, the answer is no.