Consider the following premises. forall x_13: P(x_13) -> U(x_13). exists x_13: ~P_13(x_13) or R_12(x_13). forall x_13: P_13(x_13). forall x_13: T(x_13). forall x_13: R_12(x_13) -> U(x_13). Can we infer exists x_13: U(x_13) and T(x_13) from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13) we can infer forall x_13: P_13(x_13) or P(x_13) via universal addition. From forall x_13: P_13(x_13) or P(x_13), exists x_13: ~P_13(x_13) or R_12(x_13) we can infer exists x_13: P(x_13) or R_12(x_13) via existential resolution. From forall x_13: P(x_13) -> U(x_13), forall x_13: R_12(x_13) -> U(x_13), exists x_13: P(x_13) or R_12(x_13) we can infer exists x_13: U(x_13) via existential disjunction elimination. Finally, from exists x_13: U(x_13), forall x_13: T(x_13) we can infer exists x_13: U(x_13) and T(x_13) via existential conjunction. Therefore, the answer is yes.