〜に相違ない
must be, surely, without doubt (formal)
Plain form (Noun, な-adj without だ) + に相違ない
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に相違ない means "there's no doubt that…", a confident conclusion: 犯人は彼に相違ない, "he must be the culprit".
It's the formal, written equivalent of に違いない (N3), and they're interchangeable. 相違 means "difference", so it's literally "there's no difference from…".
It appears in detective novels, formal reports and official documents. On forms, 上記の通り相違ありません means "I certify the above is correct".
Don't confuse it with に相当する, "equivalent to", which uses a similar-looking word. In conversation, に違いない or きっと〜だ is far more natural, so save に相違ない for formal writing, where a firm, impersonal conclusion is wanted.
Examples
犯人は彼に相違ない。
He must be the culprit.
これは本物に相違ない。
This is surely the real thing.
彼の言っていることは事実に相違ない。
What he's saying is undoubtedly true.
上記の内容は事実に相違ありません。
I certify that the above is true.
彼女は何か隠しているに相違ない。
She must be hiding something.