Consider the following premises. exists x_3: ~U(x_3). forall x_3: R(x_3) <-> Q(x_3). forall x_3: Q(x_3) <-> U(x_3). Can we infer exists x_3: ~R(x_3) from them? If possible, name the inference rules being used at each step.
 From forall x_3: Q(x_3) <-> U(x_3), exists x_3: ~U(x_3) we can infer exists x_3: ~Q(x_3) via existential biconditional elimination. Finally, from forall x_3: R(x_3) <-> Q(x_3), exists x_3: ~Q(x_3) we can infer exists x_3: ~R(x_3) via existential biconditional elimination. Therefore, the answer is yes.