Consider the following premises. For all x_11, x_11 will cook or x_11 is not a soldier. For all x_11, x_11 is a soldier and x_11 will play squash. There is at least one x_11 for which if x_11 cooks, then x_11 is sad. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 is not sad.
 From the fact that for all x_11, x_11 will cook or x_11 is not a soldier we can infer that for all x_11, if x_11 were a soldier, then x_11 is cooking via universal rewriting. From the fact that for all x_11, if x_11 were a soldier, then x_11 is cooking, and that there is at least one x_11 for which if x_11 cooks, then x_11 is sad we can infer that there is at least one x_11 for which if x_11 were a soldier, then x_11 is sad via existential transitivity. From the fact that for all x_11, x_11 is a soldier and x_11 will play squash we can infer that for all x_11, x_11 is a soldier via universal simplification. Finally, from the fact that there is at least one x_11 for which if x_11 were a soldier, then x_11 is sad, and that for all x_11, x_11 is a soldier we can infer that there is at least one x_11 for which x_11 is sad via existential modus ponens, which contradicts that For all x_11, x_11 is not sad. Therefore, the answer is no.