While the Sikh Gurus criticized the hierarchy of the caste system, a caste system has historically existed amidst the Sikhs.
You are right when you say, that many Sikhs adhere to the caste system. That's a problem among Sikhs as everywhere in India.
But you are wrong when you say that this has anything to do with Sikh religion, because their Scripture and doctrines very very clearly refuse any kind of castes. Their founder, Guru Nanak, really hated that.
So Sikhs who are proud of their caste are bad Sikhs.
Consequently you are totally wrong when you say "Sikhs are the people who introduced the caste system into India." I've no words how wrong you are!
I know that from books but you can easily look it up on the web, honestly, for it is basic stuff.