Consider the following premises. forall y_2: Q_2(y_2) -> T_3(y_2). forall y_2: T(y_2) -> Q_2(y_2). forall y_2: U_1(y_2) -> T(y_2). Can we infer exists y_2: ~(U_1(y_2) -> T_3(y_2)) from them? If possible, name the inference rules being used at each step.
 From forall y_2: T(y_2) -> Q_2(y_2), forall y_2: Q_2(y_2) -> T_3(y_2) we can infer forall y_2: T(y_2) -> T_3(y_2) via universal transitivity. Finally, from forall y_2: U_1(y_2) -> T(y_2), forall y_2: T(y_2) -> T_3(y_2) we can infer forall y_2: U_1(y_2) -> T_3(y_2) via universal transitivity, which contradicts exists y_2: ~(U_1(y_2) -> T_3(y_2)). Therefore, the answer is no.