Consider the following premises. forall y_4: S(y_4) -> U_4(y_4). forall y_4: U_4(y_4) <-> S(y_4). forall y_4: ~S(y_4). exists y_4: W(y_4) -> U_4(y_4). Can we infer forall y_4: W(y_4) from them? If possible, name the inference rules being used at each step.
 From forall y_4: U_4(y_4) <-> S(y_4) we can infer forall y_4: U_4(y_4) -> S(y_4) via universal biconditional elimination. From forall y_4: U_4(y_4) -> S(y_4), forall y_4: S(y_4) -> U_4(y_4) we can infer forall y_4: U_4(y_4) <-> S(y_4) via universal biconditional introduction. From forall y_4: U_4(y_4) <-> S(y_4), forall y_4: ~S(y_4) we can infer forall y_4: ~U_4(y_4) via universal biconditional elimination. Finally, from exists y_4: W(y_4) -> U_4(y_4), forall y_4: ~U_4(y_4) we can infer exists y_4: ~W(y_4) via existential modus tollens, which contradicts forall y_4: W(y_4). Therefore, the answer is no.