The expression に相違ない (にそういない) means "there is no doubt that…" or "it is certain that…". It is used to express a strong conviction or assertion that something is true. It is the formal, literary equivalent of にちがいない違いない (にちがいない), which is far more common in everyday speech and writing.
に相違ない attaches to the same forms as に違いない:
Verb (plain form)
い-adjective
な-adjective + である
Noun + である
This expression is highly formal and literary. It is commonly found in written language such as legal documents, academic papers, essays, novels, and formal speeches. In casual conversation, にちがいない違いない is used instead.
The speaker uses に相違ない when they have strong evidence or reasoning to support their conclusion, and they wish to state it with authority and certainty.
Both にそういない相違ない and にちがいない違いない express the same meaning – strong certainty. The only difference is register: に相違ない is formal/literary while に違いない is used in both spoken and written Japanese. In practice, learners should recognize に相違ない but will use に違いない far more often.