I have an assignment to program and test functions to perform nested quantifiers operations.I have to use a predicate that is non-trivial, but I don't know what a non-trivial predicate is. Can anyone please tell me what it means?

I am not aware of a specific concept in C++ for "non-trivial predicates". I believe what your instructor meant was that he/she expects the predicate you write to employ complex functionality - a simple "sum" predicate that adds two integers won't do.

Best regards,
Lucian