Consider the following premises. P_1(b) -> T(b). forall x_3: P_1(x_3) or ~T(x_3). ~P_1(b). Can we infer ~T(b) from them?
 From forall x_3: P_1(x_3) or ~T(x_3) we can infer forall x_3: T(x_3) -> P_1(x_3). From forall x_3: T(x_3) -> P_1(x_3) we can infer T(b) -> P_1(b). From P_1(b) -> T(b), T(b) -> P_1(b) we can infer P_1(b) <-> T(b). From P_1(b) <-> T(b) we can infer T(b) -> P_1(b). Finally, from T(b) -> P_1(b), ~P_1(b) we can infer ~T(b). Therefore, the answer is yes.