Is there a contradiction in the Qur'an?

[R00tKiT]

The system of 19 proves that the Qur'an is the word of God.

Muhammad took the Quran as a revelation by God and wrote it himself on the paper.

Pen Surah 1: Nun, the pen, and what they write. 

Muhammad PBUH, in spite of his obvious eloquence, couldn't read or write, he was illiterate, according to the Qur'an itself ;

Say, “O people, I am the Messenger of God to you all—He to whom belongs the kingdom of the heavens and the earth. There is no god but He. He gives life and causes death.” So believe in God and His Messenger, the Unlettered Prophet, who believes in God and His words. And follow him, that you may be guided. (7/158).

So, one way his contemporaries could've directly discredited him was to spot him actually write something or get knowledge from books. This would invalidate the above mentioned verse of the Qur'an, and a fortiori his prophecy claim;