Consider the following premises. forall x_6: P_6(x_6) <-> P(x_6). exists x_6: ~P_6(x_6). forall x_6: P(x_6) or Q(x_6). Can we infer exists x_6: Q(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) <-> P(x_6), exists x_6: ~P_6(x_6) we can infer exists x_6: ~P(x_6) via existential biconditional elimination. Finally, from forall x_6: P(x_6) or Q(x_6), exists x_6: ~P(x_6) we can infer exists x_6: Q(x_6) via existential disjunctive syllogism. Therefore, the answer is yes.