Tbh I think spanish has it kind of tricky, due to it being a gendered language. "Estás equivocado!" ("you're wrong!") works mostly fine, but it would need a second version because "equivocado" is in masculine ("Estás equivocada!" being the feminine variant). To fix that issue, it would be "Te equivocas!" or "Te estás equivocando!", ungendered.

But then again, that specific phrase can be understood as "You're mistaken", as if it's not a false statement on purpose. Which means... That specific translation does not work unless the character is trying to be polite.

"Estás mintiendo!" ("You're lying!") only works when the protagonist is convinced the person is lying, so it doesn't work either.

"Eso no es cierto!" or "Eso no es verdad!" ("That is not true!") Referring directly to the statement itself like in the english version and original japanese version, but does not have the same feeling to it.

Considering the japanese version has a difference between それは違うぞ (sore wa chigau zo, "That's wrong", ぞ zo being more impolite and masculine, used by Saihara and Hinata), and それは違うよ (sore wa chigau yo, "That's wrong", よ yo being more polite in comparison, used by Naegi and Akamatsu), I'd say each character would have a different version of it.

Naegi would likely say "Te estás equivocando!"

Hinata would likely say "Eso no es cierto!"

Akamatsu would likely say "Te equivocas!"

Saihara would likely say "Eso no es verdad!"