In German it's Künstliche Intelligenz, which is another one of those curious English/German correspondences where even parts of words line up--Kunst is "art" and künstlich is "artificial".
Nope, "synthetic" would be "syntetyczna". "Sztuczna" just means "artificial", a direct translation.
In Slovak it's "Umelá inteligencia", same as "umelá hmota" - generic term for any kind of plastic.