Consider the following premises. forall x_14: ~Q_14(x_14). forall x_14: P_14(x_14) -> Q_14(x_14). s -> P_14(f_1). forall x_14: P_14(x_14) <-> Q_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) we can infer forall x_14: Q_14(x_14) -> P_14(x_14) via universal biconditional elimination. From forall x_14: P_14(x_14) -> Q_14(x_14), forall x_14: Q_14(x_14) -> P_14(x_14) we can infer forall x_14: P_14(x_14) <-> Q_14(x_14) via universal biconditional introduction. 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 biconditional elimination. From forall x_14: ~P_14(x_14) we can infer ~P_14(f_1) via universal instantiation. Finally, from s -> P_14(f_1), ~P_14(f_1) we can infer ~s via modus tollens. Therefore, the answer is yes.