Consider the following premises. forall y: ~W(y). forall y: U(y) -> T_2(y). forall y: W(y) <-> T_2(y). forall y: S(y) -> U(y). forall y: T_2(y) -> S(y). Can we infer forall y: ~U(y) from them? If possible, name the inference rules being used at each step.
 From forall y: T_2(y) -> S(y), forall y: S(y) -> U(y) we can infer forall y: T_2(y) -> U(y) via universal transitivity. From forall y: T_2(y) -> U(y), forall y: U(y) -> T_2(y) we can infer forall y: T_2(y) <-> U(y) via universal biconditional introduction. From forall y: W(y) <-> T_2(y), forall y: ~W(y) we can infer forall y: ~T_2(y) via universal biconditional elimination. Finally, from forall y: T_2(y) <-> U(y), forall y: ~T_2(y) we can infer forall y: ~U(y) via universal biconditional elimination. Therefore, the answer is yes.