Consider the following premises. forall x_11: Q_11(x_11) -> P(x_11). forall x_11: ~W(x_11). forall x_11: P_11(x_11) or Q_11(x_11). exists x_11: P_11(x_11) -> P(x_11). forall x_11: W(x_11) or R(x_11). Can we infer forall x_11: ~(P(x_11) and R(x_11)) from them? If possible, name the inference rules being used at each step.
 From exists x_11: P_11(x_11) -> P(x_11), forall x_11: Q_11(x_11) -> P(x_11), forall x_11: P_11(x_11) or Q_11(x_11) we can infer exists x_11: P(x_11) via existential disjunction elimination. From forall x_11: W(x_11) or R(x_11), forall x_11: ~W(x_11) we can infer forall x_11: R(x_11) via universal disjunctive syllogism. Finally, from exists x_11: P(x_11), forall x_11: R(x_11) we can infer exists x_11: P(x_11) and R(x_11) via existential conjunction, which contradicts forall x_11: ~(P(x_11) and R(x_11)). Therefore, the answer is no.