Consider the following premises. forall y_1: T_3(y_1) -> U(y_1). forall y_1: ~P_3(y_1) or W(y_1). forall y_1: U(y_1) -> T_3(y_1). forall y_1: P(y_1) or P_3(y_1). forall y_1: W(y_1) -> T_3(y_1). forall y_1: ~P(y_1) or U(y_1). Can we infer forall y_1: T_3(y_1) from them?
 From forall y_1: P(y_1) or P_3(y_1), forall y_1: ~P(y_1) or U(y_1) we can infer forall y_1: P_3(y_1) or U(y_1). From forall y_1: T_3(y_1) -> U(y_1), forall y_1: U(y_1) -> T_3(y_1) we can infer forall y_1: T_3(y_1) <-> U(y_1). From forall y_1: P_3(y_1) or U(y_1), forall y_1: ~P_3(y_1) or W(y_1) we can infer forall y_1: U(y_1) or W(y_1). From forall y_1: T_3(y_1) <-> U(y_1) we can infer forall y_1: U(y_1) -> T_3(y_1). Finally, from forall y_1: U(y_1) -> T_3(y_1), forall y_1: W(y_1) -> T_3(y_1), forall y_1: U(y_1) or W(y_1) we can infer forall y_1: T_3(y_1). Therefore, the answer is yes.