Consider the following premises. forall y_3: P(y_3) -> U(y_3). forall y_3: U(y_3) -> P_4(y_3). forall y_3: P(y_3). forall y_3: P_4(y_3) -> W(y_3). Can we infer exists y_3: ~W(y_3) from them? If possible, name the inference rules being used at each step.
 From forall y_3: U(y_3) -> P_4(y_3), forall y_3: P_4(y_3) -> W(y_3) we can infer forall y_3: U(y_3) -> W(y_3) via universal transitivity. From forall y_3: P(y_3) -> U(y_3), forall y_3: P(y_3) we can infer forall y_3: U(y_3) via universal modus ponens. Finally, from forall y_3: U(y_3) -> W(y_3), forall y_3: U(y_3) we can infer forall y_3: W(y_3) via universal modus ponens, which contradicts exists y_3: ~W(y_3). Therefore, the answer is no.