Consider the following premises. exists x_10: R_3(x_10) and Q_6(x_10). forall x_10: P_10(x_10). forall x_10: P_10(x_10) -> T_4(x_10). Can we infer exists x_10: R_3(x_10) and T_4(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> T_4(x_10), forall x_10: P_10(x_10) we can infer forall x_10: T_4(x_10) via universal modus ponens. From exists x_10: R_3(x_10) and Q_6(x_10) we can infer exists x_10: R_3(x_10) via existential simplification. Finally, from exists x_10: R_3(x_10), forall x_10: T_4(x_10) we can infer exists x_10: R_3(x_10) and T_4(x_10) via existential conjunction. Therefore, the answer is yes.