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You could study core.logic: https://github.com/clojure/core.logic/tree/master/src/main/c...
I swear I'd bookmarked a resource that was more analogous to #2, but you may want to have a look at The Little Prover: https://mitpress.mit.edu/books/little-prover
The relevant section of PAIP: https://github.com/norvig/paip-lisp/blob/master/docs/chapter...
Also worth exploring The Reasoned Schemer which teaches minikanren, which can be (and has been) implemented in many programming languages. It explores much of the same space as Prolog. I wrote most of a minikanren in Common Lisp while working through the book (someone else had already published a version to quicklisp which was better than what I made).