Consider the following premises. forall x: T(x) -> R(x). exists x: U_2(x) -> W(x). forall x: U_2(x) or T(x). forall x: W(x) -> R(x). forall x: W_1(x). Can we infer exists x: W_1(x) and R(x) from them? If possible, name the inference rules being used at each step.
 From exists x: U_2(x) -> W(x), forall x: W(x) -> R(x) we can infer exists x: U_2(x) -> R(x) via existential transitivity. From exists x: U_2(x) -> R(x), forall x: T(x) -> R(x), forall x: U_2(x) or T(x) we can infer exists x: R(x) via existential disjunction elimination. Finally, from forall x: W_1(x), exists x: R(x) we can infer exists x: W_1(x) and R(x) via existential conjunction. Therefore, the answer is yes.