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This appears to be more limited than what CBMC[1] (the C Bounded Model Checker) can do. CBMC can do function contracts. CBMC can prove memory safety and even the absence of memory leaks for non-trivial code bases that pass pointers all over the place that must eventually be freed. Applying all the annotations to make this happen though is like 10x the work of getting the program actually running in the first place. CBMC definitely makes C safer than even safe Rust for projects that can invest the time to use it. There is an experimental Rust front end to CBMC called Kani[2] that aims to verify unsafe Rust (thus making unsafe Rust become safe) but it is far from the speed and robustness of the C front end.
[1] https://github.com/diffblue/cbmc
[2] https://github.com/model-checking/kani