Go to http://www.le.state.ut.us/~code/code.htm and read the actual code for yourself.
Most of the laws governing carry of firearms are found in 76-10-5xx, with the concealed weapons permit itself defined in 53-5-7xx, and the definition of "schools" found in 76-3-203.2.
Bear in mind that you will find VERY little about openly carrying a firearm. Rather, you will find that most prohibitions on carrying a firearm relate to concealed firearms or "loaded" firearms rather than OC firearms that are not "loaded.
The problem with proving what you can do to an LEO type is you won't find any law that says, "it is legal to openly carry a Utah unloaded gun even without a permit." What you have to do is show him that statute he thinks applies to you (such as the prohibition on carrying a loaded or concealed gun in 76-10-504/505 do NOT apply to you because your gun is neither concealed nor "loaded" as that term is defined. Or that while it is "loaded" you are not in violation because your permit exempts you from that prohibition while not imposing any burden on you to actually conceal. Put another way, if your gun were legally concealed pursuant to a permit, but not loaded would he think you in violation of the law for choosing not to load your gun?
In the unlikely event of a run in with a police officer who doesn't know the law, I suggest a low-key approach rather than being too forceful. Bottom line, he CAN arrest you for darn near anything and then you get to incur the cost and hassle of either convincing a DA not to charge you, or winning in court. And despite what may be shown on TV, cash awards for unlawful arrest are a LOT harder to get than you may think.
So unless you are VERY well prepared to wage such a suit, your best bet is to persuade the officer you are not in violation of the law so he doesn't arrest you. That is best done with a low-key, but firm approach, and maybe a suggestion that he might want to consult with his duty Sergeant or Lieutenant rather than make the call on this area of law himself.