Consider the following premises. For all y_3, if y_3 were a soldier, then y_3 is running. For all y_3, if y_3 were happy, then y_3 is a soldier. For all y_3, if y_3 were a soldier, then y_3 is happy. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_3 for which the fact that y_3 were happy does not imply that y_3 is running.
 From the fact that for all y_3, if y_3 were happy, then y_3 is a soldier, and that for all y_3, if y_3 were a soldier, then y_3 is happy we can infer that for all y_3, y_3 is happy if and only if y_3 is a soldier via universal biconditional introduction. From the fact that for all y_3, y_3 is happy if and only if y_3 is a soldier we can infer that for all y_3, if y_3 were happy, then y_3 is a soldier via universal biconditional elimination. Finally, from the fact that for all y_3, if y_3 were happy, then y_3 is a soldier, and that for all y_3, if y_3 were a soldier, then y_3 is running we can infer that for all y_3, if y_3 were happy, then y_3 is running via universal transitivity, which contradicts that There is at least one y_3 for which the fact that y_3 were happy does not imply that y_3 is running. Therefore, the answer is no.