Consider the following premises. forall y: T_1(y) -> U(y). forall y: U(y) -> U_3(y). forall y: U(y) -> T_1(y). forall y: R(y) -> P(y). forall y: U_3(y) -> R(y). Can we infer forall y: T_1(y) -> P(y) from them?
 From forall y: U_3(y) -> R(y), forall y: R(y) -> P(y) we can infer forall y: U_3(y) -> P(y). From forall y: U(y) -> T_1(y), forall y: T_1(y) -> U(y) we can infer forall y: U(y) <-> T_1(y). From forall y: U(y) <-> T_1(y) we can infer forall y: T_1(y) -> U(y). From forall y: T_1(y) -> U(y), forall y: U(y) -> U_3(y) we can infer forall y: T_1(y) -> U_3(y). Finally, from forall y: T_1(y) -> U_3(y), forall y: U_3(y) -> P(y) we can infer forall y: T_1(y) -> P(y). Therefore, the answer is yes.