Consider the following premises. exists x_11: P_5(x_11) <-> W(x_11). forall x_11: Q(x_11) <-> W(x_11). forall x_11: ~P_5(x_11). Can we infer forall x_11: Q(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: Q(x_11) <-> W(x_11) we can infer forall x_11: Q(x_11) -> W(x_11) via universal biconditional elimination. From exists x_11: P_5(x_11) <-> W(x_11), forall x_11: ~P_5(x_11) we can infer exists x_11: ~W(x_11) via existential biconditional elimination. Finally, from forall x_11: Q(x_11) -> W(x_11), exists x_11: ~W(x_11) we can infer exists x_11: ~Q(x_11) via existential modus tollens, which contradicts forall x_11: Q(x_11). Therefore, the answer is no.