Consider the following premises. forall x_14: ~Q_10(x_14). forall x_14: P_14(x_14) -> Q_14(x_14). r_3 <-> P_14(a_5). forall x_14: Q_14(x_14) -> R_14(x_14). forall x_14: R_14(x_14) -> Q_10(x_14). Can we infer r_3 from them? If possible, name the inference rules being used at each step.
 From forall x_14: P_14(x_14) -> Q_14(x_14), forall x_14: Q_14(x_14) -> R_14(x_14) we can infer forall x_14: P_14(x_14) -> R_14(x_14) via universal transitivity. From forall x_14: R_14(x_14) -> Q_10(x_14), forall x_14: ~Q_10(x_14) we can infer forall x_14: ~R_14(x_14) via universal modus tollens. From forall x_14: P_14(x_14) -> R_14(x_14), forall x_14: ~R_14(x_14) we can infer forall x_14: ~P_14(x_14) via universal modus tollens. From forall x_14: ~P_14(x_14) we can infer ~P_14(a_5) via universal instantiation. Finally, from r_3 <-> P_14(a_5), ~P_14(a_5) we can infer ~r_3 via biconditional elimination, which contradicts r_3. Therefore, the answer is no.