Consider the following premises. For all x_5, if x_5 were a soldier, then x_5 is writing a letter. There is at least one x_5 for which x_5 will not play tennis or x_5 will climb a mountain. For all x_5, if x_5 climbs a mountain, then x_5 is writing a letter. For all x_5, x_5 is a nurse or x_5 will play tennis. For all x_5, x_5 is not a nurse or x_5 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will not write a letter.
 From the fact that for all x_5, x_5 is a nurse or x_5 will play tennis, and that for all x_5, x_5 is not a nurse or x_5 is a soldier we can infer that for all x_5, x_5 will play tennis or x_5 is a soldier via universal resolution. From the fact that for all x_5, x_5 will play tennis or x_5 is a soldier, and that there is at least one x_5 for which x_5 will not play tennis or x_5 will climb a mountain we can infer that there is at least one x_5 for which x_5 is a soldier or x_5 will climb a mountain via existential resolution. Finally, from the fact that for all x_5, if x_5 were a soldier, then x_5 is writing a letter, that for all x_5, if x_5 climbs a mountain, then x_5 is writing a letter, and that there is at least one x_5 for which x_5 is a soldier or x_5 will climb a mountain we can infer that there is at least one x_5 for which x_5 will write a letter via existential disjunction elimination, which contradicts that For all x_5, x_5 will not write a letter. Therefore, the answer is no.