Consider the following premises. exists x_11: Q(x_11) and S(x_11). forall x_11: U(x_11) or ~Q(x_11). Can we infer exists x_11: U(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: U(x_11) or ~Q(x_11) we can infer forall x_11: Q(x_11) -> U(x_11) via universal rewriting. From exists x_11: Q(x_11) and S(x_11) we can infer exists x_11: Q(x_11) via existential simplification. Finally, from forall x_11: Q(x_11) -> U(x_11), exists x_11: Q(x_11) we can infer exists x_11: U(x_11) via existential modus ponens. Therefore, the answer is yes.