Consider the following premises. forall x_14: P_14(x_14) -> Q_14(x_14). forall x_14: P_9(x_14) <-> P_10(x_14). s <-> P_9(a_5). forall x_14: ~Q_14(x_14). forall x_14: P_10(x_14) -> P_14(x_14). Can we infer ~s 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) we can infer forall x_14: ~P_14(x_14) via universal modus tollens. From forall x_14: P_10(x_14) -> P_14(x_14), forall x_14: ~P_14(x_14) we can infer forall x_14: ~P_10(x_14) via universal modus tollens. From forall x_14: P_9(x_14) <-> P_10(x_14), forall x_14: ~P_10(x_14) we can infer forall x_14: ~P_9(x_14) via universal biconditional elimination. From forall x_14: ~P_9(x_14) we can infer ~P_9(a_5) via universal instantiation. Finally, from s <-> P_9(a_5), ~P_9(a_5) we can infer ~s via biconditional elimination. Therefore, the answer is yes.