The shortest explanation of the Gödel Theorem

Gödel's incompleteness theorem in my interpretation states that in every logical system sufficiently developed to contain an infinite number of statements, there will be one whose truth or falsity is unprovable in the framework of this system. Such a system should contain proof algorithms, an alphabet, a set of possible words and a subset of true statements.
Full proof on 114 pages can be found in the book by B. Uspensky “Godel's theorem”
The theorem is of paramount importance for a number of mathematical disciplines, the exact sciences, and perhaps for philosophy. The actual translation itself is the shortest explanation .

There is a machine that prints all the true expressions in some language. It is not necessary that such a machine is actually an expression printer; suppose only the existence of logic determining the truth of statements. But suppose that the machine still prints the expression.

In particular, some expressions printed by a machine have this form.
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P*x ( x)
NP*x ( x)
PR*x ( xx)
NPR*x ( xx)

For example, NPR * FOO means that the machine never prints FOOFOO. NP * FOOFOO means the same. So far, so good.
Now consider the expression NPR * NPR * . This expression means that the machine will never print NPR * NPR *. Consider 2 possible options: NPR * NPR * will and will not be printed.
Printing a NPR * NPR * machine will print a false expression. However, if the machine never prints NPR * NPR *, then NPR * NPR * will be a true statement that will not be a printed machine.
Thus, either the machine prints a false expression, or does not print the true one.
In other words, the machine printing all true expressions prints and false ones as well.

This translation is complete. Do you find this evidence adequate? How about the accuracy of the translation? tried to be literal as liberties are not appropriate.