Predicate Logic Paradox
Your base predicate states that there exists some real number that's larger than or equal to all other real numbers (i.e that there is a highest real number).

The inverse states that every real number has a number larger than it (i.e. that there is no highest real number).

Your test cases don't produce a paradox because feeding x=y into the first predicate means that you're no longer working with R+. If all you have in your test set is a single number, then of course there's a maximum value. All you show with this test is that:

In a set containing a single real number, there exists a highest value

All that having been said, I'm sure you'll get a better answer on math.stackexchange.com!