Godel's completeness theorem applies to first-order predicate logic, which is not powerful enough on its own even to express, let alone prove, 1+1=2. First orde

Godel's completeness theorem applies to first-order predicate logic, which is not powerful enough on its own even to express, let alone prove, 1+1=2. First order logic is best thought of as a framework on which other, useful logics may be built. And as soon as you add enough power to first-order-logic to capture Peano arithmetic, you run into incompleteness. C++ behavior is almost certainly more complex than Peano arithmetic.