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Can you briefly explain what the definition is of a 'property' and why 'existing' doesn't fit in it? The way I use the word property I don't see how it wouldn't apply to 'existing' or any other adjective for that matter

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So what exactly a property is would also naturally be up for debate, but an example property would be say having a mass of 13kg. Or being pink. Most adjectives presumably are corresponding to properties, some would word my formulation as to exist is to be the subject of a predicate.

There are also relational properties, like being ten meters away from the Eiffel tower.

Some would call existence a second order property.

The Stanford encyclopedia of philosophy gives s good overview of the issues around existence. https://plato.stanford.edu/entries/existence/

Thanks for the link. It would seem to me that it's all a matter of how you define the word property. Since words are part of a natural language, there is no one given true definition, so one has to be chosen before starting an argument, like an axiom if you are mathematically inclined. But still, it doesn't feel relevant for the question at hand, which is, how to prove an existing Santa exists? This clearly is an instance of assuming the thesis before proving it. The same can be done for any property, like proving that a blue santa is blue. I suppose that the premise of proving that an "existing santa exists" is not really a stronger statement after all than the original question of whether just "santa exists".

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