Consider the following premises. p <-> Q_2(e_3). forall x_18: P_18(x_18) <-> Q_18(x_18). p or s. forall x_18: ~Q_18(x_18). forall x_18: P_18(x_18) <-> Q_2(x_18). Can we infer s from them? If possible, name the inference rules being used at each step.
 From forall x_18: P_18(x_18) <-> Q_18(x_18), forall x_18: ~Q_18(x_18) we can infer forall x_18: ~P_18(x_18) via universal biconditional elimination. From forall x_18: P_18(x_18) <-> Q_2(x_18), forall x_18: ~P_18(x_18) we can infer forall x_18: ~Q_2(x_18) via universal biconditional elimination. From forall x_18: ~Q_2(x_18) we can infer ~Q_2(e_3) via universal instantiation. From p <-> Q_2(e_3), ~Q_2(e_3) we can infer ~p via biconditional elimination. Finally, from p or s, ~p we can infer s via disjunctive syllogism. Therefore, the answer is yes.