I think there is something wrong with premise three. The premise contains the assumption that only the present exists. If the past does not exist in the present, then it is not true that the past exist in the present. Since it is now the present, then it is not true that the past exists. This might be a defensible position, but it is not very attractive. The view would entail denying the existence of the holocaust for example. It is widely accepted that the Nazi Holocaust is in the past. But if the past does not exist, it means that the holocaust does not exist. So as well as being metaphysically unattractive, such a view is actually illegal in some countries.
If this feels like word play and some kind of logical fun and games, then consider more deeply. How short is the present? How is the present located? A way to answer the first question would be to list journal articles that you consider to be contemporary. What is the most recent philosophy paper that you consider to be in the past? What are you doing now? The problem here is that there does not seem to be a minimum unit that is non arbitrary, and if you just take a one dimensional point on a time line, then premise three means that nothing with any duration exists at all.
When talking about cosmology some people like to say in a tone of wonder that when we look at the stars, we are looking at events that took place thousands of years ago. According to premise three, this means that we are looking at events that do not exist. People will also say in this context, that this star that we see here may no longer exist, since it may have collapsed in the time it took the light to travel to earth. We would then get something like this pair of claims:
1. This star we now perceive used to exist
2. This star does not now exist.
The conclusion is
3. What we now perceive does not now exist.

This seems fine, but it does not seem to follow that the object that we are picking out by ostensive definition "That star (pointing at the star)" does not exist"; this cannot follow because we are picking out the thing by ostension. And we are not pointing into our visual cortex but out at the night sky in the direction of the star.