Consider the following premises. forall x_14: P_9(x_14) <-> P_10(x_14). forall x_14: P_10(x_14) -> P_14(x_14). w <-> P_9(g_2). forall x_14: ~Q_14(x_14). forall x_14: P_14(x_14) -> Q_14(x_14). Can we infer w 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(g_2) via universal instantiation. Finally, from w <-> P_9(g_2), ~P_9(g_2) we can infer ~w via biconditional elimination, which contradicts w. Therefore, the answer is no.