The key to understanding and usage of Formal Methods is to realize that it is a way of thinking at many different levels. You can choose whatever level seems intuitive and accessible to you.
The must-read paper On Formal Methods Thinking in Computer Science Education posits three levels which i have highlighted here - https://news.ycombinator.com/item?id=46298961
Carroll Morgan's classic (In-)Formal Methods: The Lost Art --- A Users’ Manual and his recent book on the same are also relevant here - https://news.ycombinator.com/item?id=45490017
See eg. "Draft-and-Prune: Improving the Reliability of Auto-formalization for Logical Reasoning" [1].
Every formal method has that problem (including the mentioned trivial ones like SAT and SMT).