Consider the following premises. forall x_11: Q_9(x_11) or Q_11(x_11). forall x_11: P_11(x_11) or ~Q_11(x_11). forall x_11: P_11(x_11) <-> Q_9(x_11). Can we infer exists x: P_11(x) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) or ~Q_11(x_11) we can infer forall x_11: Q_11(x_11) -> P_11(x_11) via universal rewriting. From forall x_11: P_11(x_11) <-> Q_9(x_11) we can infer forall x_11: Q_9(x_11) -> P_11(x_11) via universal biconditional elimination. From forall x_11: Q_9(x_11) -> P_11(x_11), forall x_11: Q_11(x_11) -> P_11(x_11), forall x_11: Q_9(x_11) or Q_11(x_11) we can infer forall x_11: P_11(x_11) via universal disjunction elimination. From forall x_11: P_11(x_11) we can infer P_11(h) via universal instantiation. Finally, from P_11(h) we can infer exists x: P_11(x) via existential generalization. Therefore, the answer is yes.