Consider the following premises. forall z: W_3(z) -> U(z). exists z: S_4(z) -> T(z). forall z: T(z) -> W_3(z). forall z: U(z) -> S_4(z). Can we infer forall z: ~(S_4(z) <-> W_3(z)) from them?
 From forall z: W_3(z) -> U(z), forall z: U(z) -> S_4(z) we can infer forall z: W_3(z) -> S_4(z). From exists z: S_4(z) -> T(z), forall z: T(z) -> W_3(z) we can infer exists z: S_4(z) -> W_3(z). Finally, from exists z: S_4(z) -> W_3(z), forall z: W_3(z) -> S_4(z) we can infer exists z: S_4(z) <-> W_3(z), which contradicts forall z: ~(S_4(z) <-> W_3(z)). Therefore, the answer is no.