Clearly we need tests that check for effectiveness at applying general mathematical, logical and relational operations, eg. set theory, relational algebra, firs

Clearly we need tests that check for effectiveness at applying general mathematical, logical and relational operations, eg. set theory, relational algebra, first and second order logic, type theory, the lambda calculus, recurrence and induction, etc., and the ability to use these to abstract over specifics and the ability to generalize. The upside is that these can all be generated and checked synthetically so large data sets are possible, in both formal and natural languages.