Consider the following premises. forall y_3: Q_2(y_3) or W(y_3). forall y_3: ~U(y_3). forall y_3: U(y_3) <-> W(y_3). exists y_3: ~Q_2(y_3) or P(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: U(y_3) <-> W(y_3), forall y_3: ~U(y_3) we can infer forall y_3: ~W(y_3) via universal biconditional elimination. From forall y_3: Q_2(y_3) or W(y_3), exists y_3: ~Q_2(y_3) or P(y_3) we can infer exists y_3: W(y_3) or P(y_3) via existential resolution. Finally, from exists y_3: W(y_3) or P(y_3), forall y_3: ~W(y_3) we can infer exists y_3: P(y_3) via existential disjunctive syllogism, which contradicts forall y_3: ~P(y_3). Therefore, the answer is no.