Consider the following premises. forall x_14: P_14(x_14) <-> Q_14(x_14). exists x_14: P_8(x_14) or ~P_14(x_14). forall x_14: ~P_8(x_14). Can we infer forall x_14: Q_14(x_14) 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 exists x_14: P_8(x_14) or ~P_14(x_14) we can infer exists x_14: P_14(x_14) -> P_8(x_14) via existential rewriting. From forall x_14: Q_14(x_14) -> P_14(x_14), exists x_14: P_14(x_14) -> P_8(x_14) we can infer exists x_14: Q_14(x_14) -> P_8(x_14) via existential transitivity. Finally, from exists x_14: Q_14(x_14) -> P_8(x_14), forall x_14: ~P_8(x_14) we can infer exists x_14: ~Q_14(x_14) via existential modus tollens, which contradicts forall x_14: Q_14(x_14). Therefore, the answer is no.