Consider the following premises. forall y: R_3(y) -> ~S_2(y). forall y: S_2(y). forall y: R_3(y) <-> R(y). Can we infer forall y: ~R(y) from them? If possible, name the inference rules being used at each step.
 From forall y: R_3(y) -> ~S_2(y), forall y: S_2(y) we can infer forall y: ~R_3(y) via universal modus tollens. Finally, from forall y: R_3(y) <-> R(y), forall y: ~R_3(y) we can infer forall y: ~R(y) via universal biconditional elimination. Therefore, the answer is yes.