- Monadic predicate logic (with identity) is decidable (Löwenheim-Skolem 1915, or more conveniently Boolos, Burgess, and Jeffrey 2007, Ch. 21). This tool lets you can check whether a formula is a theorem. If it's not a theorem, you will be shown a counter-example.
- You can run it in your browser.
- Blog post discussing how to efficiently check validity.
tadamcz/monadic-predicate
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