I would say a different problem:

There's many definitions of "thinking".

AI and brains can do some, AI and brains definitely provably cannot do others, some others are untestable at present, and nobody really knows enough about what human brains do to be able to tell if or when some existing or future AI can do whatever is needed for the stuff we find special about ourselves.

A lot of people use different definitions, and respond to anyone pointing this out by denying the issue and claiming their own definition is the only sensible one and "obviously" everyone else (who isn't a weird pedant) uses it.

Statements like "it is bound by the laws of physics" are not "verifiable" by your definition, and yet we safely assume it is true of everything. Everything except the human brain, that is, for which wild speculation that it may be supernatural is seemingly considered rational discussion so long as it satisfies people's needs to believe that they are somehow special in the universe.

Do you think that thinking is undefinable ? If thinking is definable, then all statements about it aren't unverifiable.

Is this some self refuting sentence?

Is reasoning undefined? That's what usually meant by "thinking".