How do I trace the ACL2 rewriter? I would really like to know what's going on inside the prover. Is it advisable to seek out this type of information or should I just follow The Method?
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Here are some relevant trace forms, authored by Matt Kaufmann:
Then run your proof you want trace
Open up the trace file, my-trace-file in this example, in your favorite text editor.
With regards to your second question, 80% or more of ACL2 experts would say that, no, you don't need to know what's going on with the rewriter. I happen to disagree with them, which is why I've written this Q&A (as I will reference it myself indirectly via Google). You should also look into options like "break-rewrite" and "dmr". See ACL2 documentation topic "debugging" for more information.