I don't believe this works in general. If you have a set of tiles that connect to neither the horse nor to an exit, they can still keep each other reachable in this formulation.

Yes, this is the major challenge with solving them with SAT. You can make your solver check and reject these horseless pockets (incrementally rejecting solutions with new clauses), which might be the easiest method, since you might need iteration for maximizing anyways (bare SAT doesn't do "maximize"). To correctly track the flood-fill flow from the horse, you generally need a constraint like reachable(x,y,t) = reachable(nx,ny,t-1) ^ walkable(x,y), and reachable(x,y,0)=is_horse_cell, which adds N^2 additional variables to each cell.

You can more precisely track flows and do maximization with ILP, but that often loses conflict-driven clause learning advantages.

Good point. I don't think the puzzles do this and if they would, I would run a pre-solve pass over the puzzle first to flood fill such horseless pockets up with water, no?

It's not quite that easy. For the simplest example, look at https://enclose.horse/play/dlctud, where the naive solution will waste two walls to fence in the large area. Obviously, you can construct puzzles that have lots of these "bait" areas.

Like the other comment suggested, running a loop where you keep adding constraints that eliminate invalid solutions will probably work for any puzzle that a human would want to solve.

Oh I see what you mean now, indeed:

    Score: 7
    ~~~~~~
    ~····~
    ~·~~·~
    .#..#.
    ......
    ..#...
    .#H#..
    ..#...

However, I think that you do not need 'time' based variables in the form of

    reachable(x,y,t) = reachable(nx,ny,t-1)

Enforcing connectivity through single-commodity flows is IMO better to enforce flood fill (also introduces additional variables but is typically easier to solve with CP heuristics):

    Score: 2
    ~~~~~~
    ~....~
    ~.~~.~
    ......
    ......
    ..##..
    .#H·#.
    ..##..

Cool puzzle!

You are talking like this is the first time judges have been blocked for political reasons. See Horst Dreier in 2008 as a high-profile example.

The detailed results are in the links at the bottom of the post.

That's only if you are using pure predicates. From a quick glance, the code makes liberal use of assert, retract, and the cut operator, so you can't write a query that solves the problem automatically.

Up and down quarks have names that make perfect sense, they are derived from the isospin which in turn derives from spin (spin-1/2 was the only other well-known object in physics that had the same symmetry properties). Which one is up and which one is down is the only arbitrary choice.

Using "positive" and "negative" would have been a disaster. What charge does a positive antiquark have?