https://www.reddit.com/r/algorithms/comments/rw6pow/i_have_a_set_of_arrays_which_im_having_trouble/hrdbypu/?context=3

solve.py

# pylint: disable=missing-module-docstring
# pylint: disable=missing-function-docstring,missing-class-docstring
# pylint: disable=invalid-name

import pprint

from pycryptosat import Solver

data = [
    [2, 5, 8, 11],
    [1, 5, 6, 7],
    [4, 5, 10, 12],
    [3, 5, 9, 13],
    [1, 2, 3, 4],
    [2, 7, 10, 13],
    [2, 6, 9, 12],
    [1, 11, 12, 13],
    [4, 7, 9, 11],
    [3, 6, 10, 11],
    [1, 8, 9, 10],
    [3, 7, 8, 12],
    [4, 6, 8, 13],
]

n = len(data[0]) - 1
m = len(data)

assert m == n * n + n + 1
assert max(max(sub) for sub in data) == m

s = Solver()


def get_id(r, c, item):
    return r * m * (n + 1) + c * m + item + 1


# Row constraints
for i in range(m):
    for x in data[i]:
        x -= 1
        elems = [get_id(i, j, x) for j in range(n + 1)]
        # At least one
        s.add_clause(elems)
        # At most one
        for e1 in elems:
            for e2 in elems:
                if e1 != e2:
                    s.add_clause([-e1, -e2])

# Column constraints
for x in range(m):
    for j in range(n + 1):
        # At most one
        for i1 in range(m):
            for i2 in range(m):
                if i1 != i2:
                    s.add_clause([-get_id(i1, j, x), -get_id(i2, j, x)])

# No two should occupy the same space
for i in range(m):
    for j in range(n + 1):
        # At most one
        for x1 in range(m):
            for x2 in range(m):
                if x1 != x2:
                    s.add_clause([-get_id(i, j, x1), -get_id(i, j, x2)])

sat, solution = s.solve()

ans = []

for i in range(m):
    row_ans = []
    for j in range(n + 1):
        for x in range(m):
            if solution[get_id(i, j, x)]:
                row_ans.append(x + 1)
    ans.append(row_ans)

pprint.pprint(ans)