Consider the following premises. forall y: ~Q_3(y). forall y: W(y) <-> S(y). exists y: Q_4(y) <-> W(y). forall y: S(y) -> R(y). forall y: Q_3(y) -> R(y). forall y: R(y) -> Q_3(y). Can we infer forall y: Q_4(y) from them? If possible, name the inference rules being used at each step.
 From forall y: Q_3(y) -> R(y), forall y: R(y) -> Q_3(y) we can infer forall y: Q_3(y) <-> R(y) via universal biconditional introduction. From forall y: Q_3(y) <-> R(y), forall y: ~Q_3(y) we can infer forall y: ~R(y) via universal biconditional elimination. From forall y: S(y) -> R(y), forall y: ~R(y) we can infer forall y: ~S(y) via universal modus tollens. From forall y: W(y) <-> S(y), forall y: ~S(y) we can infer forall y: ~W(y) via universal biconditional elimination. Finally, from exists y: Q_4(y) <-> W(y), forall y: ~W(y) we can infer exists y: ~Q_4(y) via existential biconditional elimination, which contradicts forall y: Q_4(y). Therefore, the answer is no.