Consider the following premises. forall x_23: P_23(x_23). u <-> ~p_8. p_8 -> ~P_23(a_23). Can we infer ~u from them? If possible, name the inference rules being used at each step.
 From forall x_23: P_23(x_23) we can infer P_23(a_23) via universal instantiation. From p_8 -> ~P_23(a_23), P_23(a_23) we can infer ~p_8 via modus tollens. From u <-> ~p_8 we can infer ~p_8 -> u via biconditional elimination. Finally, from ~p_8 -> u, ~p_8 we can infer u via modus ponens, which contradicts ~u. Therefore, the answer is no.