You can't prove that something does not exist if you can't directly inspect it. "Free will" falls into this pit where it has a fuzzy definition in the first place and can't be directly looked at in any way. Plus, we already know that much of human functions are not based on Free will (how most of our organs function for one), but it's also trivial to show that there is a clear difference between something based on simple rules like a robot or a very simple animal form and human behavior (which we constantly need to study to understand its complexity). If there was no such thing akin to Free Will we would have cracked human psychology for centuries already.
Biology is driven by complex but precisely known rules (from molecular dynamics down to quark-gluon interactions). That doesn't mean we know how biology works , not even for a single person, because it's complex. Psychology attempts to do something much harder, understand the behavior of entire populations of nervous systems. Both are complex, but in principle not uncomputable.
And there's a definition of free will: that actions of humans axiomatically cannot be precomputed.
> but it's also trivial to show that there is a clear difference between something based on simple rules like a robot or a very simple animal form and human behavior
Where do you draw the line between a "very simple animal" and "non-simple animal"? Because there enough animals that have the behavioral patterns completely matching these of humans.
Human behavior is not particularly exceptional, unless you'd want to refer to our activities causing a new extinction.
