Consider the following premises. forall z: ~T_4(z). forall z: T_4(z) <-> W(z). forall z: W(z) <-> T_4(z). Can we infer exists z: W(z) from them?
 From forall z: W(z) <-> T_4(z) we can infer forall z: T_4(z) -> W(z). From forall z: T_4(z) <-> W(z) we can infer forall z: W(z) -> T_4(z). From forall z: W(z) -> T_4(z), forall z: T_4(z) -> W(z) we can infer forall z: W(z) <-> T_4(z). Finally, from forall z: W(z) <-> T_4(z), forall z: ~T_4(z) we can infer forall z: ~W(z), which contradicts exists z: W(z). Therefore, the answer is no.