Consider the following premises. exists z: ~U(z). forall z: T_2(z) <-> U(z). forall z: T_2(z) -> W_4(z). forall z: W_4(z) -> T_2(z). Can we infer exists z: ~W_4(z) from them?
 From forall z: T_2(z) <-> U(z), exists z: ~U(z) we can infer exists z: ~T_2(z). From forall z: T_2(z) -> W_4(z), forall z: W_4(z) -> T_2(z) we can infer forall z: T_2(z) <-> W_4(z). Finally, from forall z: T_2(z) <-> W_4(z), exists z: ~T_2(z) we can infer exists z: ~W_4(z). Therefore, the answer is yes.