Consider the following premises. exists x_7: U_4(x_7) or ~P(x_7). forall x_7: P(x_7) and Q_3(x_7). Can we infer exists x_7: U_4(x_7) from them? If possible, name the inference rules being used at each step.
 From exists x_7: U_4(x_7) or ~P(x_7) we can infer exists x_7: P(x_7) -> U_4(x_7) via existential rewriting. From forall x_7: P(x_7) and Q_3(x_7) we can infer forall x_7: P(x_7) via universal simplification. Finally, from exists x_7: P(x_7) -> U_4(x_7), forall x_7: P(x_7) we can infer exists x_7: U_4(x_7) via existential modus ponens. Therefore, the answer is yes.