Consider the following premises. For all x_11, x_11 is excited if and only if x_11 will cook. For all x_11, if x_11 cooks, then x_11 is a poet. For all x_11, x_11 is excited if and only if x_11 is a lawyer. Can we infer the following from them? There is at least one x_11 for which the fact that x_11 were a lawyer does not imply that x_11 is a poet.
 From the fact that for all x_11, x_11 is excited if and only if x_11 will cook we can infer that for all x_11, if x_11 were excited, then x_11 is cooking. From the fact that for all x_11, x_11 is excited if and only if x_11 is a lawyer we can infer that for all x_11, if x_11 were a lawyer, then x_11 is excited. From the fact that for all x_11, if x_11 were a lawyer, then x_11 is excited, and that for all x_11, if x_11 were excited, then x_11 is cooking we can infer that for all x_11, if x_11 were a lawyer, then x_11 is cooking. Finally, from the fact that for all x_11, if x_11 were a lawyer, then x_11 is cooking, and that for all x_11, if x_11 cooks, then x_11 is a poet we can infer that for all x_11, if x_11 were a lawyer, then x_11 is a poet, which contradicts that There is at least one x_11 for which the fact that x_11 were a lawyer does not imply that x_11 is a poet. Therefore, the answer is no.