@sneer,
Whilst dogs are certainly intelligent they lack hands, therefore the tool-making we so associate with humanlike intelligence is pretty much denied to them. I'd also say their capacity for language is limited, whilst dogs are known to employ different growls, barks and whines to mean different things, this seems to be a small and instinctive vocabulary, not an adaptive one.
There's no real reason to expect that an ape couldn't acheive humanlike sapience, after all a certain species of ape already has done and bonobos are quite similar in terms of what they can grasp the basics of - adaptive learning and so on.
But the issue I would take with the OP is that it "will happen in the future". i don't think humanlike potentials of intellect are really that predictable, and don't seem really to be an end of evolutionary processes any more than any other adaptation to a niche. Many species have been about a lot longer than humans, and have done pretty well without intelligence that competes with that we can develop.