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Yes, that's part of my argument.
My character has a +19 on Perception (I think) so I should be able to know there's an invisible someone in the room with me, although adding to the DC because of combat is reasonable (maybe a +2 for being distracted, and even another +2 if I'm focused on combatants across the room and the invisible someone is behind me).
My point to the GM is simply that there should've been a reactive check available. Being able to show that with a roll of 20 my character can detect "a group of goblins moving across hard rock two weeks ago" would go a long ways towards showing that my character should at least have the chance of detecting an invisible someone.
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