I can see where your confusion comes from. After all he is so smart but we rarely see him use his intellect to solve problems. But there are some stories that give us an idea of how much his intellect surpasses that of any human. Lex Luthor, Batman or any other.
In some of the first issues of New 52 Action Comics, we got to see how huge is his raw brain power.
1. In Action Comics there was a story were he wanted to get a glimps of Krypton using Earth's telescopes, has you know telescopes are nothing more than tools that actually allows us to see through time, and in that particular date he wanted to witness Krypton's day when it blew up. So with worldwide coordination and the use of pratically ever telescope on Earth pointing to the place in our galaxy where Krypton was, he was able to get a clear picture. But getting that image was has much a contribution of all those telescopes has it was from Superman. The telescopes provided the information, but it was stated in the comic by one of the scientists that the data being produced even with a quantum computer it would take years to process all the information, but Superman did it in a matter of seconds. And when he inserted the processed data that he had done with his brain, a clear image of Krypton's explosive end, was displayed in the main screen.
2. Again in Action Comics, when Lois was caught in an acident, Superman took her to the hospital, but the doctors, said that due to the extent of the damage there was nothing they could do, so Superman ran to the library, read every article on every field of medicine, and in less than 5 minutes he was doing the surgery on Lois by himself with little to almost no help from the surgeons in the operating room. One even stated that Superman had learned in less than 5 minutes what even a skilled surgeon took 10 years to learn. That and the fact that he did everything without even leaving a scar on Lois, but that was more because of his precise use of his heat vision.
3. And unlike previous versions where Jor-El sent Krypton's knowledge inside some crystal and a AI of his conciousness to teach Kal-El, in the New 52 the only knowledge he had was the information stored in his ship brainiac processor AI. So this version of Superman didn't get free access to a ton of knowledge from his race, in fact it has been hinted that everything he knows about kryptonian technology he mostly figured it out by himself. And seeing that tech was way superior to Earth's tech one can assume that he's way more smarter than he leads on, or to be more precise, what the writers make him to be.
4. His fortress is filled with alien tech, most of which is not even kryptonian. But in one of Superman issues he was cataloging the tech that he had learned from and puting it on display, and in another issue (during the H'el arc, if I'm not mistaken) someone asked him why he had so much alien tech on his fortress and he answered saying that it was mostly tech that he had adquired on his adventures in space and that once he studied it he had deemed it to dangerous to store it elsewhere. This of course we can assume that he studied the tech, understood it and made it sure that it could not fall in the wrong hands, and seeing that most of it are from dozens if not thousands of different civilizations, and doing it all by himself does show an incredible intelligence.
There are other examples. But are only small pieces here and there. Writers for some reason focuse only on his raw physical power and not so much on his mental capacity, which was stated by the Psycho Pirate to be the most powerful on Earth, and I quote "You have the most powerful mind on Earth. Filled with psionic energy, shining like a star. To bad you don't know how to use it" in here the Psycho Pirate was not only refering to Superman's incredible mind but also to psychic powers that he himself doesn't know he has.
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