Consider the following premises. Sarah is not writing a letter or it is snowing. If Sarah works, then it is raining. If it is cold, then it is raining. For all x_13, x_13 will make tea or x_13 will write a letter. For all x_13, x_13 will not make tea or x_13 will work. If it snows, then it is cold. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that for all x_13, x_13 will make tea or x_13 will write a letter, and that for all x_13, x_13 will not make tea or x_13 will work we can infer that for all x_13, x_13 will write a letter or x_13 will work via universal resolution. From the fact that if it snows, then it is cold, and that if it is cold, then it is raining we can infer that if it snows, then it is raining via transitivity. From the fact that for all x_13, x_13 will write a letter or x_13 will work we can infer that Sarah is writing a letter or Sarah is working via universal instantiation. From the fact that Sarah is writing a letter or Sarah is working, and that Sarah is not writing a letter or it is snowing we can infer that Sarah is working or it is snowing via resolution. Finally, from the fact that if Sarah works, then it is raining, that if it snows, then it is raining, and that Sarah is working or it is snowing we can infer that it is raining via disjunction elimination, which contradicts that It is not raining. Therefore, the answer is no.