Consider the following premises. forall y_1: T(y_1) -> T_1(y_1). exists y_1: R(y_1) -> T_1(y_1). forall y_1: U_4(y_1). forall y_1: U_4(y_1) -> R(y_1). Can we infer exists y_1: T_1(y_1) from them? If possible, name the inference rules being used at each step.
 From forall y_1: U_4(y_1) we can infer forall y_1: U_4(y_1) or T(y_1) via universal addition. From forall y_1: U_4(y_1) -> R(y_1), exists y_1: R(y_1) -> T_1(y_1) we can infer exists y_1: U_4(y_1) -> T_1(y_1) via existential transitivity. Finally, from exists y_1: U_4(y_1) -> T_1(y_1), forall y_1: T(y_1) -> T_1(y_1), forall y_1: U_4(y_1) or T(y_1) we can infer exists y_1: T_1(y_1) via existential disjunction elimination. Therefore, the answer is yes.