Consider the following premises. forall x_10: Q_10(x_10) -> U_4(x_10). forall x_10: Q_1(x_10). forall x_10: U(x_10) -> Q_10(x_10). exists x_10: U(x_10). Can we infer exists x_10: Q_1(x_10) and U_4(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: U(x_10) -> Q_10(x_10), forall x_10: Q_10(x_10) -> U_4(x_10) we can infer forall x_10: U(x_10) -> U_4(x_10) via universal transitivity. From forall x_10: U(x_10) -> U_4(x_10), exists x_10: U(x_10) we can infer exists x_10: U_4(x_10) via existential modus ponens. Finally, from forall x_10: Q_1(x_10), exists x_10: U_4(x_10) we can infer exists x_10: Q_1(x_10) and U_4(x_10) via existential conjunction. Therefore, the answer is yes.