Consider the following premises. forall x_1: R(x_1) <-> Q(x_1). forall x_1: W_3(x_1) -> U_2(x_1). exists x_1: U_2(x_1) -> Q(x_1). forall x_1: Q_3(x_1) or R(x_1). forall x_1: ~Q_3(x_1) or W_3(x_1). Can we infer exists x_1: Q(x_1) from them? If possible, name the inference rules being used at each step.
 From forall x_1: W_3(x_1) -> U_2(x_1), exists x_1: U_2(x_1) -> Q(x_1) we can infer exists x_1: W_3(x_1) -> Q(x_1) via existential transitivity. From forall x_1: Q_3(x_1) or R(x_1), forall x_1: ~Q_3(x_1) or W_3(x_1) we can infer forall x_1: R(x_1) or W_3(x_1) via universal resolution. From forall x_1: R(x_1) <-> Q(x_1) we can infer forall x_1: R(x_1) -> Q(x_1) via universal biconditional elimination. Finally, from forall x_1: R(x_1) -> Q(x_1), exists x_1: W_3(x_1) -> Q(x_1), forall x_1: R(x_1) or W_3(x_1) we can infer exists x_1: Q(x_1) via existential disjunction elimination. Therefore, the answer is yes.