Consider the following premises. exists x_20: P_20(x_20) or Q_20(x_20). forall x_20: P_20(x_20) -> S(x_20). forall x_20: Q_20(x_20) -> S(x_20). forall x_20: U_1(x_20). Can we infer exists x_20: U_1(x_20) or T(x_20) from them? If possible, name the inference rules being used at each step.
 From forall x_20: P_20(x_20) -> S(x_20), forall x_20: Q_20(x_20) -> S(x_20), exists x_20: P_20(x_20) or Q_20(x_20) we can infer exists x_20: S(x_20) via existential disjunction elimination. From forall x_20: U_1(x_20), exists x_20: S(x_20) we can infer exists x_20: U_1(x_20) and S(x_20) via existential conjunction. From exists x_20: U_1(x_20) and S(x_20) we can infer exists x_20: U_1(x_20) via existential simplification. Finally, from exists x_20: U_1(x_20) we can infer exists x_20: U_1(x_20) or T(x_20) via existential addition. Therefore, the answer is yes.