Consider the following premises. forall y: U_2(y) -> ~Q_2(y). forall y: U_2(y) -> S_3(y). forall y: S_3(y) -> U_2(y). forall y: Q_2(y). S_3(c) or u. Can we infer ~u from them? If possible, name the inference rules being used at each step.
 From forall y: U_2(y) -> S_3(y), forall y: S_3(y) -> U_2(y) we can infer forall y: U_2(y) <-> S_3(y) via universal biconditional introduction. From forall y: U_2(y) -> ~Q_2(y), forall y: Q_2(y) we can infer forall y: ~U_2(y) via universal modus tollens. From forall y: U_2(y) <-> S_3(y), forall y: ~U_2(y) we can infer forall y: ~S_3(y) via universal biconditional elimination. From forall y: ~S_3(y) we can infer ~S_3(c) via universal instantiation. Finally, from S_3(c) or u, ~S_3(c) we can infer u via disjunctive syllogism, which contradicts ~u. Therefore, the answer is no.