Consider the following premises. For all x_11, x_11 will work or x_11 will not drink water. There is at least one x_11 for which x_11 will drink water and x_11 will make tea. 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 work.
 From the fact that for all x_11, x_11 will work or x_11 will not drink water we can infer that for all x_11, if x_11 drinks water, then x_11 is working via universal rewriting. From the fact that there is at least one x_11 for which x_11 will drink water and x_11 will make tea we can infer that there is at least one x_11 for which x_11 will drink water via existential simplification. Finally, from the fact that for all x_11, if x_11 drinks water, then x_11 is working, and that there is at least one x_11 for which x_11 will drink water we can infer that there is at least one x_11 for which x_11 will work via existential modus ponens. Therefore, the answer is yes.