Consider the following premises. exists y_3: R_2(y_3) <-> S(y_3). forall y_3: ~W_1(y_3). forall y_3: W_1(y_3) <-> S(y_3). Can we infer forall y_3: R_2(y_3) from them? If possible, name the inference rules being used at each step.
 From exists y_3: R_2(y_3) <-> S(y_3) we can infer exists y_3: R_2(y_3) -> S(y_3) via existential biconditional elimination. From forall y_3: W_1(y_3) <-> S(y_3), forall y_3: ~W_1(y_3) we can infer forall y_3: ~S(y_3) via universal biconditional elimination. Finally, from exists y_3: R_2(y_3) -> S(y_3), forall y_3: ~S(y_3) we can infer exists y_3: ~R_2(y_3) via existential modus tollens, which contradicts forall y_3: R_2(y_3). Therefore, the answer is no.