Consider the following premises. forall x_12: U(x_12) <-> T_1(x_12). exists x_12: P(x_12) or U(x_12). forall x_12: ~P(x_12). Can we infer exists x_12: T_1(x_12) from them?
 From forall x_12: U(x_12) <-> T_1(x_12) we can infer forall x_12: U(x_12) -> T_1(x_12). From exists x_12: P(x_12) or U(x_12), forall x_12: ~P(x_12) we can infer exists x_12: U(x_12). Finally, from forall x_12: U(x_12) -> T_1(x_12), exists x_12: U(x_12) we can infer exists x_12: T_1(x_12). Therefore, the answer is yes.