Consider the following premises. exists x_13: P_13(x_13) or W(x_13). forall x_13: ~P_13(x_13). forall x_13: W(x_13) -> P(x_13). Can we infer forall x_13: ~(P(x_13) or T(x_13)) from them? If possible, name the inference rules being used at each step.
 From exists x_13: P_13(x_13) or W(x_13), forall x_13: ~P_13(x_13) we can infer exists x_13: W(x_13) via existential disjunctive syllogism. From forall x_13: W(x_13) -> P(x_13), exists x_13: W(x_13) we can infer exists x_13: P(x_13) via existential modus ponens. Finally, from exists x_13: P(x_13) we can infer exists x_13: P(x_13) or T(x_13) via existential addition, which contradicts forall x_13: ~(P(x_13) or T(x_13)). Therefore, the answer is no.