Consider the following premises. forall x_5: ~W(x_5). exists x_5: ~T(x_5) or P(x_5). forall x_5: P_5(x_5) or T(x_5). forall x_5: ~P_5(x_5) or W(x_5). Can we infer exists x_5: P(x_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: P_5(x_5) or T(x_5), forall x_5: ~P_5(x_5) or W(x_5) we can infer forall x_5: T(x_5) or W(x_5) via universal resolution. From forall x_5: T(x_5) or W(x_5), exists x_5: ~T(x_5) or P(x_5) we can infer exists x_5: W(x_5) or P(x_5) via existential resolution. Finally, from exists x_5: W(x_5) or P(x_5), forall x_5: ~W(x_5) we can infer exists x_5: P(x_5) via existential disjunctive syllogism. Therefore, the answer is yes.