Consider the following premises. exists x_6: P(x_6) or U(x_6). forall x_6: Q(x_6) or ~P(x_6). forall x_6: U(x_6) <-> Q(x_6). Can we infer forall x_6: ~Q(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: Q(x_6) or ~P(x_6) we can infer forall x_6: P(x_6) -> Q(x_6) via universal rewriting. From forall x_6: U(x_6) <-> Q(x_6) we can infer forall x_6: U(x_6) -> Q(x_6) via universal biconditional elimination. Finally, from forall x_6: P(x_6) -> Q(x_6), forall x_6: U(x_6) -> Q(x_6), exists x_6: P(x_6) or U(x_6) we can infer exists x_6: Q(x_6) via existential disjunction elimination, which contradicts forall x_6: ~Q(x_6). Therefore, the answer is no.