Consider the following premises. For all x_19, x_19 will not write a letter or x_19 is curious. There is at least one x_19 for which if x_19 were a writer, then x_19 is sleeping. For all x_19, x_19 will write a letter or x_19 is a writer. For all x_19, x_19 will not sleep. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_19 for which x_19 is curious or x_19 will play squash.
 From the fact that for all x_19, x_19 will write a letter or x_19 is a writer, and that for all x_19, x_19 will not write a letter or x_19 is curious we can infer that for all x_19, x_19 is a writer or x_19 is curious via universal resolution. From the fact that there is at least one x_19 for which if x_19 were a writer, then x_19 is sleeping, and that for all x_19, x_19 will not sleep we can infer that there is at least one x_19 for which x_19 is not a writer via existential modus tollens. From the fact that for all x_19, x_19 is a writer or x_19 is curious, and that there is at least one x_19 for which x_19 is not a writer we can infer that there is at least one x_19 for which x_19 is curious via existential disjunctive syllogism. Finally, from the fact that there is at least one x_19 for which x_19 is curious we can infer that there is at least one x_19 for which x_19 is curious or x_19 will play squash via existential addition. Therefore, the answer is yes.