Consider the following premises. forall x_11: ~P_11(x_11). forall x_11: ~T(x_11). forall x_11: P_11(x_11) or U_2(x_11). exists x_11: T(x_11) or U(x_11). Can we infer exists x_11: U(x_11) and U_2(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) or U_2(x_11), forall x_11: ~P_11(x_11) we can infer forall x_11: U_2(x_11) via universal disjunctive syllogism. From exists x_11: T(x_11) or U(x_11), forall x_11: ~T(x_11) we can infer exists x_11: U(x_11) via existential disjunctive syllogism. Finally, from exists x_11: U(x_11), forall x_11: U_2(x_11) we can infer exists x_11: U(x_11) and U_2(x_11) via existential conjunction. Therefore, the answer is yes.