Consider the following premises. exists x: P_1(x) or ~T_1(x). forall x: ~P_1(x). forall x: P_1(x) -> T_1(x). Can we infer forall x: T_1(x) from them?
 From exists x: P_1(x) or ~T_1(x) we can infer exists x: T_1(x) -> P_1(x). From exists x: T_1(x) -> P_1(x), forall x: P_1(x) -> T_1(x) we can infer exists x: T_1(x) <-> P_1(x). Finally, from exists x: T_1(x) <-> P_1(x), forall x: ~P_1(x) we can infer exists x: ~T_1(x), which contradicts forall x: T_1(x). Therefore, the answer is no.