Consider the following premises. exists y_4: T_1(y_4) -> P(y_4). forall y_4: U_2(y_4) <-> T_4(y_4). forall y_4: U_2(y_4) -> T_1(y_4). forall y_4: P(y_4) -> T_4(y_4). Can we infer exists y_4: P(y_4) -> U_2(y_4) from them?
 From forall y_4: U_2(y_4) <-> T_4(y_4) we can infer forall y_4: T_4(y_4) -> U_2(y_4). From forall y_4: U_2(y_4) -> T_1(y_4), exists y_4: T_1(y_4) -> P(y_4) we can infer exists y_4: U_2(y_4) -> P(y_4). From forall y_4: P(y_4) -> T_4(y_4), forall y_4: T_4(y_4) -> U_2(y_4) we can infer forall y_4: P(y_4) -> U_2(y_4). From exists y_4: U_2(y_4) -> P(y_4), forall y_4: P(y_4) -> U_2(y_4) we can infer exists y_4: U_2(y_4) <-> P(y_4). Finally, from exists y_4: U_2(y_4) <-> P(y_4) we can infer exists y_4: P(y_4) -> U_2(y_4). Therefore, the answer is yes.