When a man with recurrent dreams of being alone in an empty room finds out that the world he knows is just a creation of his imagination and that there’s another world where he lives and doesnt? recognize, he will get stuck in the middle with some huge identity problems.

"When he discovers the world is just a figment of his imagination, a stubborn computer nerd vow's to devise a mathematical equation to free him from his mental prison before his skeptical family has him committed."

Agreed with the above also try avoiding such vague descriptions as "...some huge identity problems." in a logline in general and as an obstacle description in particular.

Better to specify the actual problem or the identity he is struggling with, by this I mean; sexuality, race, religious persuasion, profession etc?

Hope this helps.

As FFF said. The logline posits a situation, but doesn't present a plot. What does he do when he finds out his 'real' world is an illusion? What becomes his objective goal? Who or what opposes that goal? What are the stakes? What is the worst thing that can happen to him, will happen to him, if he fails? (Identity crisis may be a complication, a consequence of his problem, but is that as bad as it gets for him?)