[verb (plain)] + に相違ない [i-adj] + に相違ない [na-adj] + (である) + に相違ない [noun] + (である) + に相違ない
に相違ない means "there is no doubt that", "must be". It goes after the plain form of a verb or an い-adjective, and straight after a noun or a な-adjective, often with である in between. It is the written, formal version of にちがいない違いない and means the same.
It states a conclusion the speaker has drawn from evidence and is sure of.
The two differ only in register. に相違ない belongs to essays, reports, novels and formal speeches. In conversation it sounds stiff, and にちがいない違いない is what you say.
On its own, そうい相違 means "a difference" or "a discrepancy". The polite そうい相違ありません at the foot of a form or a statement says the details above are correct.