"invincible" is normally (though not exclusively) used to describe people. "insurmountable" is typically used of problems, challenges, etc. Neither word seems to fit your sentence very well.
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pakeefor example, That man saw a woman and he started to feel these "invincible desires", but he had to be chilly, because he was her teacher."invincible desires" is not impossible. It would mean that one cannot conquer the desires. It is not a common thing to say. There are other words that would be more commonly used. In your original sentence it feels some