Aaaah! :)
My math books say booleans can't be true and false in the same time.
I made a mistake assuming that the identity function just because it
exists somewhere as an object in the memory is of a boolean type and
as such it's boolean value is true. Well, everybody here - thank you!

Just for the record: The type of:
- function 'identity' is "function with type signature: Any -> Any"
- functions: 'true?, false?, not'  is "function with type signature:
Any -> Boolean"

So following evaluations are perfectly valid:
(true? identity) -> false
(false? identity) -> false
(not identity) -> false

These functions should not be expected produce the boolean opposite of
each other's result, even if it's a bit strange at the first glance.

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