Consider the following premises. forall y_3: Q_3(y_3) -> P(y_3). exists y_3: W(y_3) or Q_3(y_3). forall y_3: ~W(y_3). forall y_3: P(y_3) -> Q_3(y_3). Can we infer forall y_3: ~P(y_3) from them? If possible, name the inference rules being used at each step.
 From forall y_3: Q_3(y_3) -> P(y_3), forall y_3: P(y_3) -> Q_3(y_3) we can infer forall y_3: Q_3(y_3) <-> P(y_3) via universal biconditional introduction. From exists y_3: W(y_3) or Q_3(y_3), forall y_3: ~W(y_3) we can infer exists y_3: Q_3(y_3) via existential disjunctive syllogism. From forall y_3: Q_3(y_3) <-> P(y_3) we can infer forall y_3: Q_3(y_3) -> P(y_3) via universal biconditional elimination. Finally, from forall y_3: Q_3(y_3) -> P(y_3), exists y_3: Q_3(y_3) we can infer exists y_3: P(y_3) via existential modus ponens, which contradicts forall y_3: ~P(y_3). Therefore, the answer is no.