The evolution of cancer can produce FI, quite a bit of it. So, therefore, we know intelligence is not the only source. I’m not sure, for that matter, you have even demonstrated intelligence can produce FI. See here: Computing the Functional Information in Cancer.
@Kirk what if the task you are undertaking is (logically or practically) impossible? What if it is like trying to make a perpetual motion machine? How would you know? Perhaps continuing to try is just waisting you effort. How would you be able to avoid that waiste?