Consider the following premises. forall y_1: P_3(y_1) -> T_2(y_1). forall y_1: T(y_1) or P_3(y_1). forall y_1: ~T(y_1). Can we infer forall y_1: P_3(y_1) -> T_2(y_1) from them?
That is one of the premises. Therefore, the answer is yes.