Consider the following premises. R_3(i_2). forall x_5: R_3(x_5) <-> S(x_5). Can we infer exists x_5: S(x_5) from them? If possible, name the inference rules being used at each step.
 From R_3(i_2) we can infer exists x_5: R_3(x_5) via existential generalization. From forall x_5: R_3(x_5) <-> S(x_5) we can infer forall x_5: R_3(x_5) -> S(x_5) via universal biconditional elimination. Finally, from forall x_5: R_3(x_5) -> S(x_5), exists x_5: R_3(x_5) we can infer exists x_5: S(x_5) via existential modus ponens. Therefore, the answer is yes.