Farmer's Theorem revisited - Veanes, Margus (Information Processing Letters, 2000)
The main result is that there is an integer n, such that second-order unification is undecidable in all non-monadic second-order term languages with at least n first-order variables, and even if the arguments of all second-order variables are ground terms of size bounded by n and the total number of variable occurrences is at most n.