Barton Willis pointed out that the correct command should be
is(equals(x,z)). When I input the assumptions and use the 'is'
functions together with the 'equals' function I get the expected
result.
The article is old (2004). I tested other examples where Maxima get
wrong results in the article, they have come up right until now
(although I haven't tested them all).
Since I didn't know how to use the program properly, when I tested
that particular example I was convinced that it was a bug. Since I
find this software very useful I thought it would be nice for some of
the developers to look into these issues, that was the cause of my
initial email.
I see now that the matter is not as serious as I thought at first.
However I will continue to test their cases and I will use the bug
system in case I find a bug.
One thing I do find disappointing is that there doesn't seem to be a
straightforward way to solve inequalities in maxima (if I'm mistaken,
please do correct me).