Consider the following premises. forall x_8: P_8(x_8). forall x_8: P_8(x_8) -> Q_8(x_8). forall x_8: Q_8(x_8) -> U_1(x_8). forall x_8: Q_3(x_8). Can we infer U_1(e_1) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) -> Q_8(x_8), forall x_8: Q_8(x_8) -> U_1(x_8) we can infer forall x_8: P_8(x_8) -> U_1(x_8) via universal transitivity. From forall x_8: P_8(x_8) -> U_1(x_8), forall x_8: P_8(x_8) we can infer forall x_8: U_1(x_8) via universal modus ponens. From forall x_8: U_1(x_8), forall x_8: Q_3(x_8) we can infer forall x_8: U_1(x_8) and Q_3(x_8) via universal conjunction. From forall x_8: U_1(x_8) and Q_3(x_8) we can infer U_1(e_1) and Q_3(e_1) via universal instantiation. Finally, from U_1(e_1) and Q_3(e_1) we can infer U_1(e_1) via simplification. Therefore, the answer is yes.