Consider the following premises. forall y: ~Q_1(y). forall y: U(y) -> P_3(y). forall y: Q_1(y) or U(y). Can we infer exists y: ~P_3(y) from them? If possible, name the inference rules being used at each step.
 From forall y: Q_1(y) or U(y), forall y: ~Q_1(y) we can infer forall y: U(y) via universal disjunctive syllogism. Finally, from forall y: U(y) -> P_3(y), forall y: U(y) we can infer forall y: P_3(y) via universal modus ponens, which contradicts exists y: ~P_3(y). Therefore, the answer is no.