Consider the following premises. forall x_3: U_1(x_3) or ~R(x_3). exists x_3: U_1(x_3) <-> R(x_3). Can we infer exists x_3: R(x_3) -> U_1(x_3) from them? If possible, name the inference rules being used at each step.
 From forall x_3: U_1(x_3) or ~R(x_3) we can infer forall x_3: R(x_3) -> U_1(x_3) via universal rewriting. From exists x_3: U_1(x_3) <-> R(x_3) we can infer exists x_3: U_1(x_3) -> R(x_3) via existential biconditional elimination. From forall x_3: R(x_3) -> U_1(x_3), exists x_3: U_1(x_3) -> R(x_3) we can infer exists x_3: R(x_3) <-> U_1(x_3) via existential biconditional introduction. Finally, from exists x_3: R(x_3) <-> U_1(x_3) we can infer exists x_3: R(x_3) -> U_1(x_3) via existential biconditional elimination. Therefore, the answer is yes.