Consider the following premises. forall y_2: W(y_2) -> S(y_2). forall y_2: U_3(y_2) -> W(y_2). forall y_2: S(y_2) -> W(y_2). exists y_2: ~S(y_2). Can we infer forall y_2: U_3(y_2) from them? If possible, name the inference rules being used at each step.
 From forall y_2: W(y_2) -> S(y_2), forall y_2: S(y_2) -> W(y_2) we can infer forall y_2: W(y_2) <-> S(y_2) via universal biconditional introduction. From forall y_2: W(y_2) <-> S(y_2), exists y_2: ~S(y_2) we can infer exists y_2: ~W(y_2) via existential biconditional elimination. Finally, from forall y_2: U_3(y_2) -> W(y_2), exists y_2: ~W(y_2) we can infer exists y_2: ~U_3(y_2) via existential modus tollens, which contradicts forall y_2: U_3(y_2). Therefore, the answer is no.