Consider the following premises. For all x_14, x_14 is sad or x_14 will not go running. For all x_14, if x_14 were sad, then x_14 is drinking water. For all x_14, if x_14 drinks water, then x_14 is listening to a song. There is at least one x_14 for which if x_14 were a soldier, then x_14 is running. For all x_14, if x_14 listens to a song, then x_14 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, if is not true that x_14 will listen to a song if and only if x_14 is a soldier.
 From the fact that for all x_14, if x_14 were sad, then x_14 is drinking water, and that for all x_14, if x_14 drinks water, then x_14 is listening to a song we can infer that for all x_14, if x_14 were sad, then x_14 is listening to a song via universal transitivity. From the fact that for all x_14, x_14 is sad or x_14 will not go running we can infer that for all x_14, if x_14 goes running, then x_14 is sad via universal rewriting. From the fact that for all x_14, if x_14 goes running, then x_14 is sad, and that for all x_14, if x_14 were sad, then x_14 is listening to a song we can infer that for all x_14, if x_14 goes running, then x_14 is listening to a song via universal transitivity. From the fact that there is at least one x_14 for which if x_14 were a soldier, then x_14 is running, and that for all x_14, if x_14 goes running, then x_14 is listening to a song we can infer that there is at least one x_14 for which if x_14 were a soldier, then x_14 is listening to a song via existential transitivity. Finally, from the fact that for all x_14, if x_14 listens to a song, then x_14 is a soldier, and that there is at least one x_14 for which if x_14 were a soldier, then x_14 is listening to a song we can infer that there is at least one x_14 for which x_14 will listen to a song if and only if x_14 is a soldier via existential biconditional introduction, which contradicts that For all x_14, if is not true that x_14 will listen to a song if and only if x_14 is a soldier. Therefore, the answer is no.