Consider the following premises. exists z_2: ~T_3(z_2). forall z_2: T(z_2) <-> T_3(z_2). forall z_2: T(z_2) or ~U(z_2). Can we infer forall z_2: U(z_2) from them? If possible, name the inference rules being used at each step.
 From forall z_2: T(z_2) or ~U(z_2) we can infer forall z_2: U(z_2) -> T(z_2) via universal rewriting. From forall z_2: T(z_2) <-> T_3(z_2), exists z_2: ~T_3(z_2) we can infer exists z_2: ~T(z_2) via existential biconditional elimination. Finally, from forall z_2: U(z_2) -> T(z_2), exists z_2: ~T(z_2) we can infer exists z_2: ~U(z_2) via existential modus tollens, which contradicts forall z_2: U(z_2). Therefore, the answer is no.