に違(ちが)いないThere is no doubt that, I'm sure

Both に相違ない and に違いない express a high degree of certainty, often translated as 'no doubt' or 'surely', but differ in tone and formality. に相違ない is more formal and used in writing or official contexts, e.g. '彼が犯人に相違ない' ('There is no doubt he is the culprit'). に違いない is more common in conversation and conveys strong personal conviction, e.g. 'あの人は日本人に違いない' ('That person must be Japanese').

Both ～というのは事実だ and に違いない make confident statements, but differ in implied certainty. ～というのは事実だ affirms something as a fact, e.g. 負けたというのは事実だ ('It's a fact that we lost'). に違いない expresses strong conviction, but not absolute certainty, e.g. 彼は疲れているに違いない ('He must be tired').

に違いない and に決まっている both express strong conviction, but differ in tone and basis of judgment. に違いない implies a strong conclusion drawn from evidence or context, e.g. '何かあったに違いない' ('Something must have happened'). に決まっている conveys more assertive confidence, often based on common sense or the obvious, e.g. '美味しいに決まっている' ('Of course it tastes good').