Consider the following premises. forall x_10: U(x_10) -> ~R_10(x_10). forall x_10: P_10(x_10) -> R_10(x_10). forall x_10: P_10(x_10) or Q_10(x_10). exists x_10: U(x_10) -> Q_5(x_10). forall x_10: Q_10(x_10) -> R_10(x_10). forall x_10: Q_5(x_10) -> U(x_10). Can we infer forall x_10: Q_5(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> R_10(x_10), forall x_10: Q_10(x_10) -> R_10(x_10), forall x_10: P_10(x_10) or Q_10(x_10) we can infer forall x_10: R_10(x_10) via universal disjunction elimination. From exists x_10: U(x_10) -> Q_5(x_10), forall x_10: Q_5(x_10) -> U(x_10) we can infer exists x_10: U(x_10) <-> Q_5(x_10) via existential biconditional introduction. From forall x_10: U(x_10) -> ~R_10(x_10), forall x_10: R_10(x_10) we can infer forall x_10: ~U(x_10) via universal modus tollens. Finally, from exists x_10: U(x_10) <-> Q_5(x_10), forall x_10: ~U(x_10) we can infer exists x_10: ~Q_5(x_10) via existential biconditional elimination, which contradicts forall x_10: Q_5(x_10). Therefore, the answer is no.