Doing a four-way (set-inclusion) test, we can solve this by only considering eight possibilities:

This gives only one solution,
a = 6
b = 9
c = -3
d = -25
e = 5
f = -1
g = -7
h = -2
i = 8 ✅

All combinations are valid, which gives us 16 possible sign-solutions;
applied to the two number-solutions we already had gives us a grand total of 32 possibilities. 👍

Now we just have to find put which fulfil the grey-box condition.

4/

... er, the opposite (XNOR) 😅

Let's label our cells as
a b c F
d e f T
g h i T
T F T

c = not xor(a, b)
f = xor(d, e)
g = xor(a, d)
h = not xor(b, e)
i = xor(not xor(a, b), xor(d, e))

So we only need to consider the independent variables a, b, d, e.

3/

Next we have to find possible placements of negative factors.

We can solve this as a parity problem, encoding +ve as True and -ve as False.

If we look at possible combinations,
T • T = T
T • F = F
F • T = F
F • F = T
which matches the XOR operator 👍

2/

Ignoring negatives for the moment, factorization and comparison gets us two base solutions:

1/

The last solution I found was
1/12 + 1/20 + 1/30 + 1/72 + 1/90 + 1/110 + 1/156 + 1/182
+ 1/210 + 1/240 + 1/272 + 1/306 + 1/342 + 1/380 + 1/420
+ 1/462 + 1/600 + 1/650 + 1/702 + 1/756 + 1/812 + 1/870
+ 1/930 + 1/992 + 1/1056
= 1/4 🥳

or on one machine across 10,000 different sessions.

What would *really* help would be a better algorithm; but I can't picture what that would look like, I think I've got this one pretty well cinched down tight. 🤔

4/

I can get around that by making the solver reentrant; that would let me parallelize it across time or hardware.
I could run the basic solver until my state-table is ie a million entries, then split it into hundred-entry chunks and restart each on 10,000 different machines,

3/

I can try porting it to a different language (Julia or Rust) - but I suspect that 98% of the memory consumption is simply a huge table of partial solutions, which is a basic necessity for the solver.

2/

I rewrote my program on my desktop machine, refactored it, and tried to minimize memory usage.

That ran for 11 minutes and got me up to 188 solutions before locking my machine (Python using 28.3 GB of RAM) 😂.

1/

"Dumbest" isn't a huge problem - Americans survived Dubya mostly intact.

Unfortunately Trump is also the law-breaking-est president, and surrounded by idiot goons happy to break the law for him.