What he believes he is is he is not.

Regarding cleft sentence structure; is the following grammatically correct and if it isn't then why?

What he believes he is is he is not.

Sample:
(?)Non-Cleft - Brian believes that he is not what others think he is.
Pseudo-Cleft - What Brian believes he is is he isn't what others think he is.

This is purely a question from a grammatical standpoint.


Grammar Source: https://wwwuser.gwdg.de/~msailer2/events/cogeti-handouts/Gerbl-cogeti.pdf (Page 67)