Consider the following premises. forall x_1: Q(x_1) <-> U(x_1). forall x_1: R(x_1) or U(x_1). exists x_1: Q(x_1) <-> R(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: Q(x_1) <-> U(x_1) we can infer forall x_1: U(x_1) -> Q(x_1) via universal biconditional elimination. From exists x_1: Q(x_1) <-> R(x_1) we can infer exists x_1: R(x_1) -> Q(x_1) via existential biconditional elimination. Finally, from exists x_1: R(x_1) -> Q(x_1), forall x_1: U(x_1) -> Q(x_1), forall x_1: R(x_1) or U(x_1) we can infer exists x_1: Q(x_1) via existential disjunction elimination. Therefore, the answer is yes.