"am/is/are not" [Polite Syle]

Mr. Yamada is not a student.

Mr. Yamada is a student. --> やまださんはがくせいです。 /Yamda-san-wa gakusee-desu./
The uncontracted form of /desu/ is /de arimasu/. The affirmative and non-perfect form is /u/.

Key 1: The negative and non-perfect form in classical Japanese is /en/. The form of the polite style is /imas/, and the negative and non-perfect form in classical Japanese is also used in modern Japanese to take the polite sytle only as the complement.
Key 2: It follows from Key 1 that です of the affirmative and non-perfect clause is replaced with:
では                         ありません
de-wa                            arimas-en
being to-TOPIC            exist-NOT
to get the corresponding negative and non-perfect counterpart The form /de wa/ [being to-Topic] is contracted in the informal speech to:

じゃ
ja

N.B. 1. The form /desen/ is not a grammatical form. Why?
N.B. 2. The literal translation of the Japanese sentence is 'Talking about Yamada-san's being a student does not hold by inertia.' The verb /ar/ is 'hold or exist by inertia.'

1) やまださんはがくせいじゃありません。