Consider the following premises. For all x_11, x_11 is excited if and only if x_11 will go running. For all x_11, x_11 is excited if and only if x_11 is a poet. For all x_11, if x_11 were a poet, then x_11 is running. 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 if is not true that x_11 is excited if and only if x_11 will go running.
 From the fact that for all x_11, x_11 is excited if and only if x_11 is a poet we can infer that for all x_11, if x_11 were excited, then x_11 is a poet via universal biconditional elimination. From the fact that for all x_11, x_11 is excited if and only if x_11 will go running we can infer that for all x_11, if x_11 goes running, then x_11 is excited via universal biconditional elimination. From the fact that for all x_11, if x_11 were excited, then x_11 is a poet, and that for all x_11, if x_11 were a poet, then x_11 is running we can infer that for all x_11, if x_11 were excited, then x_11 is running via universal transitivity. Finally, from the fact that for all x_11, if x_11 were excited, then x_11 is running, and that for all x_11, if x_11 goes running, then x_11 is excited we can infer that for all x_11, x_11 is excited if and only if x_11 will go running via universal biconditional introduction, which contradicts that There is at least one x_11 for which if is not true that x_11 is excited if and only if x_11 will go running. Therefore, the answer is no.