Without fear, I am going to state that both 「でない」 and 「ではない」 are "correct" negative forms of 「である」. Both are in wide use in our time.

That is, however, not to say that there exists a great amount of interchangeability between 「でない」 and 「ではない」.

「ではない」 is used most often in main clauses while 「でない」 is generally used in subordinate clauses.

Main Clause: "This is not pizza."

「これはピザではない。」 sounds more than natural and correct.

 

「これはピザでない。」 sounds very unnatural and inappropriate. Most native speakers would correct you right away if you said this.

Subordinate Clause: "You cannot be a model if you are not pretty."

「きれいでないと、モデルにはなれない。」 sounds perfectly natural and "correct".

 

「きれいではないと、モデルにはなれない。」 sounds just wrong and unnatural.

Without fear, I am going to state that both 「でない」 and 「ではない」 are "correct" negative forms of 「である」. Both are in wide use in our time.

That is, however, not to say that there exists a great amount of interchangeability between 「でない」 and 「ではない」.

「ではない」 is used most often in main clauses while 「でない」 is generally used in subordinate clauses.

Main Clause: "This is not pizza."

「これはピザではない。」 sounds more than natural and correct.

「これはピザでない。」 sounds very unnatural and inappropriate. Most native speakers would correct you right away if you said this.

Subordinate Clause: "You cannot be a model if you are not pretty."

「きれいでないと、モデルにはなれない。」 sounds perfectly natural and "correct".

「きれいではないと、モデルにはなれない。」 sounds just wrong and unnatural.