Consider the following premises. forall x: ~U(x) or P(x). forall x: W(x) or U(x). exists x: ~W(x). Can we infer exists x: T_1(x) or P(x) from them? If possible, name the inference rules being used at each step.
 From forall x: W(x) or U(x), exists x: ~W(x) we can infer exists x: U(x) via existential disjunctive syllogism. From exists x: U(x) we can infer exists x: U(x) or T_1(x) via existential addition. Finally, from exists x: U(x) or T_1(x), forall x: ~U(x) or P(x) we can infer exists x: T_1(x) or P(x) via existential resolution. Therefore, the answer is yes.