"The man is eating the chicken, not the rice."
Translation:Mannen äter kycklingen, inte riset.
I tend to think of 'inte' as equivalent to 'not' in English. My understanding is that it needs to come after a verb, but in this sentence the verb is already established so you don't have to repeat it. Or you could, but it would feel clunky like it does in English:
"He eats the chicken, not the rice", vs
"He eats the chicken, he does not eat the rice".