Consider the following premises. For all x_11, if x_11 were a police officer, then x_11 is sad. For all x_11, x_11 will not play squash or x_11 is a police officer. For all x_11, x_11 will cook if and only if x_11 is sad. There is at least one x_11 for which x_11 will play squash or x_11 will write a letter. For all x_11, if x_11 writes a letter, then x_11 is cooking. 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 will cook.
 From the fact that for all x_11, x_11 will cook if and only if x_11 is sad we can infer that for all x_11, if x_11 were sad, then x_11 is cooking via universal biconditional elimination. From the fact that for all x_11, if x_11 were a police officer, then x_11 is sad, and that for all x_11, if x_11 were sad, then x_11 is cooking we can infer that for all x_11, if x_11 were a police officer, then x_11 is cooking via universal transitivity. From the fact that there is at least one x_11 for which x_11 will play squash or x_11 will write a letter, and that for all x_11, x_11 will not play squash or x_11 is a police officer we can infer that there is at least one x_11 for which x_11 will write a letter or x_11 is a police officer via existential resolution. Finally, from the fact that for all x_11, if x_11 writes a letter, then x_11 is cooking, that for all x_11, if x_11 were a police officer, then x_11 is cooking, and that there is at least one x_11 for which x_11 will write a letter or x_11 is a police officer we can infer that there is at least one x_11 for which x_11 will cook via existential disjunction elimination. Therefore, the answer is yes.