Consider the following premises. For all x_11, x_11 is poor or x_11 is curious. For all x_11, x_11 will play squash or x_11 will work. For all x_11, if x_11 plays squash, then x_11 is playing tennis. For all x_11, if x_11 works, then x_11 is playing tennis. There is at least one x_11 for which x_11 is not poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 is curious.
We can infer this via the existential disjunctive syllogism rule. Therefore, the answer is yes.