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I do not have any background in mathematical logic, but I have studied computation and complexity theory. I have looked through some textbooks and there are distinctions between different kinds of logic (first or second order). I've gotten the impression that these automated deduction systems are useful in some domains but not others. To phrase the title question differently: is there anything a system like this cannot do (in theory) that a human can? Why?

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I don't understand what you exactly mean by " is there anything a system like this cannot do (in theory) that a human can?" The question seems too vague to me. – Kaveh Feb 16 at 6:41
Perhaps not the answer you're looking for, but still: The famous Von-Neumann machine (en.wikipedia.org/wiki/Von_Neumann_architecture) showed that the laws of classical physics can be simulated in a computer. If you believe that humans are limited to the laws of classical physics (and in a way, this may also include quantum computing), then anything that a human can do is also computable. So in this sense, humans are no more powerful than a TM. However, the answer you may be looking for is that some logics are known to be undecidable. See Godel's incompleteness theorem for details. – Shaull Feb 16 at 7:25
I agree that this question is far too broad. Please edit it to focus on one method or one problem. – Raphael♦ Feb 16 at 14:44

closed as not a real question by Raphael♦ Feb 16 at 14:44

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.