Right solver for JuMP to find every solution of a linear system of equations with integer solutions

Specific Domains Optimization (Mathematical)
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Here’s a gist with a better approach:

https://gist.github.com/dpsanders/5cf6448b3ef3d280b6d70a8fefe34963

Basically integerize needs to be mixed in throughout the process, and we use Contractors instead of Separators.

(Separators are used when you want to find inner and outer approximations. We want only an outer approximation here.)

This new version produces the following results in a few seconds:

24-element Array{StaticArrays.SArray{Tuple{16},Int64,1,16},1}:
 [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1]
 [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 1, 0]
 [0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0]
 [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1]
 [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]
 ⋮
 [0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0]
 [0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0]
 [0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0]
 [0, 0, 2, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0]
 [0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0]

Do you know what the correct solutions are in this case?

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