Consider the following premises. exists x_11: P_11(x_11) or Q_11(x_11). forall x_11: P_11(x_11) -> U(x_11). forall x_11: Q_11(x_11) -> U(x_11). forall x_11: T(x_11). Can we infer exists x_11: T(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) -> U(x_11), forall x_11: Q_11(x_11) -> U(x_11), exists x_11: P_11(x_11) or Q_11(x_11) we can infer exists x_11: U(x_11) via existential disjunction elimination. From forall x_11: T(x_11), exists x_11: U(x_11) we can infer exists x_11: T(x_11) and U(x_11) via existential conjunction. Finally, from exists x_11: T(x_11) and U(x_11) we can infer exists x_11: T(x_11) via existential simplification. Therefore, the answer is yes.