Consider the following premises. forall x_10: S(x_10). forall x_10: T_4(x_10) -> R(x_10). forall x_10: W_4(x_10) -> R(x_10). exists x_10: T_4(x_10). Can we infer forall x_10: ~(R(x_10) and S(x_10)) from them? If possible, name the inference rules being used at each step.
 From exists x_10: T_4(x_10) we can infer exists x_10: T_4(x_10) or W_4(x_10) via existential addition. From forall x_10: T_4(x_10) -> R(x_10), forall x_10: W_4(x_10) -> R(x_10), exists x_10: T_4(x_10) or W_4(x_10) we can infer exists x_10: R(x_10) via existential disjunction elimination. Finally, from exists x_10: R(x_10), forall x_10: S(x_10) we can infer exists x_10: R(x_10) and S(x_10) via existential conjunction, which contradicts forall x_10: ~(R(x_10) and S(x_10)). Therefore, the answer is no.