Consider the following premises. forall z_2: U(z_2) -> T(z_2). exists z_2: U(z_2). forall z_2: U(z_2) or ~T(z_2). Can we infer forall z_2: ~T(z_2) from them?
 From forall z_2: U(z_2) or ~T(z_2) we can infer forall z_2: T(z_2) -> U(z_2). From forall z_2: T(z_2) -> U(z_2), forall z_2: U(z_2) -> T(z_2) we can infer forall z_2: T(z_2) <-> U(z_2). From forall z_2: T(z_2) <-> U(z_2) we can infer forall z_2: U(z_2) -> T(z_2). Finally, from forall z_2: U(z_2) -> T(z_2), exists z_2: U(z_2) we can infer exists z_2: T(z_2), which contradicts forall z_2: ~T(z_2). Therefore, the answer is no.