Consider the following premises. forall x_12: R(x_12) and Q_12(x_12). exists x_12: T_4(x_12) and U(x_12). Can we infer exists x_12: T_4(x_12) and R(x_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: R(x_12) and Q_12(x_12) we can infer forall x_12: R(x_12) via universal simplification. From exists x_12: T_4(x_12) and U(x_12) we can infer exists x_12: T_4(x_12) via existential simplification. Finally, from exists x_12: T_4(x_12), forall x_12: R(x_12) we can infer exists x_12: T_4(x_12) and R(x_12) via existential conjunction. Therefore, the answer is yes.