Consider the following premises. exists x_14: P_8(x_14) or T_3(x_14). forall x_14: ~P_8(x_14). forall x_14: Q_14(x_14) -> S(x_14). forall x_14: P_14(x_14). forall x_14: P_14(x_14) -> Q_14(x_14). Can we infer forall x_14: ~(T_3(x_14) and S(x_14)) from them? If possible, name the inference rules being used at each step.
 From forall x_14: P_14(x_14) -> Q_14(x_14), forall x_14: P_14(x_14) we can infer forall x_14: Q_14(x_14) via universal modus ponens. From exists x_14: P_8(x_14) or T_3(x_14), forall x_14: ~P_8(x_14) we can infer exists x_14: T_3(x_14) via existential disjunctive syllogism. From forall x_14: Q_14(x_14) -> S(x_14), forall x_14: Q_14(x_14) we can infer forall x_14: S(x_14) via universal modus ponens. Finally, from exists x_14: T_3(x_14), forall x_14: S(x_14) we can infer exists x_14: T_3(x_14) and S(x_14) via existential conjunction, which contradicts forall x_14: ~(T_3(x_14) and S(x_14)). Therefore, the answer is no.