Is existence a property? The way I became confounded was an example like this: a phoenix is a bird, it has feathers, and it is born from ashes, but it does not exist, whereas a penguin is a bird, has feathers, exists, and is born in snow. As in, existence and being born in snow are properties of penguins, but not of phoenixes. I feel there might be some mistake, but I certainly lack the expertise to puzzle through this on my own.
Why not think of it this way? The concept phoenix is the concept of a bird, with feathers, that arises from ashes, etc. The concept penguin is the concept of a bird, with feathers, that's (typically) born in a cold climate, etc. As it happens, the first of those concepts isn't fulfilled: nothing answers to the concept; there are no phoenixes; phoenixes don't exist. As it happens, the second concept is fulfilled: something answers to it; there are penguins; penguins exist. Both concepts exist, but only one of them is fulfilled. Our having the concepts phoenix and penguin doesn't imply that either concept is fulfilled, nor does it imply that there's any sense of 'exist' in which phoenixes (or for that matter penguins) exist.