I agree (though many here seem not to agree).For supporting a charge of trespassing in the moment, you are right, but the criminal trespass statute does make provision for preemptory charges of criminal trespassing, if the property owner/proprietor or their agent places a notice on the main entrance in a place likely to come to the notice of the public, then they don't have to confront you for you to already be guilty of criminal trespass.
I am not willing to be the test case on it. So I will comply with the signage.