Consider the following premises. forall x_11: P_11(x_11) -> W_3(x_11). forall x_11: P_11(x_11) or Q_11(x_11). forall x_11: Q_11(x_11) -> W_3(x_11). forall x_11: P_6(x_11) and Q_6(x_11). Can we infer P_6(h) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) -> W_3(x_11), forall x_11: Q_11(x_11) -> W_3(x_11), forall x_11: P_11(x_11) or Q_11(x_11) we can infer forall x_11: W_3(x_11) via universal disjunction elimination. From forall x_11: P_6(x_11) and Q_6(x_11) we can infer forall x_11: P_6(x_11) via universal simplification. From forall x_11: W_3(x_11), forall x_11: P_6(x_11) we can infer forall x_11: W_3(x_11) and P_6(x_11) via universal conjunction. From forall x_11: W_3(x_11) and P_6(x_11) we can infer W_3(h) and P_6(h) via universal instantiation. Finally, from W_3(h) and P_6(h) we can infer P_6(h) via simplification. Therefore, the answer is yes.