Consider the following premises. It is late or Joseph is not a scientist. For all x_13, if x_13 were a poet, then x_13 is a scientist. For all x_13, if x_13 were a scientist, then x_13 is a poet. Can we infer the following from them? If Joseph were a poet, then it is late.
 From the fact that for all x_13, if x_13 were a poet, then x_13 is a scientist, and that for all x_13, if x_13 were a scientist, then x_13 is a poet we can infer that for all x_13, x_13 is a poet if and only if x_13 is a scientist. From the fact that for all x_13, x_13 is a poet if and only if x_13 is a scientist we can infer that Joseph is a poet if and only if Joseph is a scientist. From the fact that it is late or Joseph is not a scientist we can infer that if Joseph were a scientist, then it is late. From the fact that Joseph is a poet if and only if Joseph is a scientist we can infer that if Joseph were a poet, then Joseph is a scientist. Finally, from the fact that if Joseph were a poet, then Joseph is a scientist, and that if Joseph were a scientist, then it is late we can infer that if Joseph were a poet, then it is late. Therefore, the answer is yes.