solve set theory problem given list of conditions

set_conditions_solver.jl

using Combinatorics
using IterTools

function calculate(U, sets)
    solution_set = Set()
    Threads.@threads for s in sets
        A,B,C =Set(s[1]),Set(s[2]),Set(s[3])
        conditions = [
        (A ∩ setdiff(U,B) ∩ setdiff(U,C)) == (setdiff(U,A) ∩ B ∩ C)
        Set(1) ⊆ ((A ∪ C) ∩ setdiff(B, C))
        symdiff(setdiff(U,A),B) ⊆ (B ∪ C)
        length(setdiff(B ∪ C,symdiff(setdiff(U,A),B))) == 3
        symdiff(setdiff(U, A ∪ B),setdiff(U,A ∪ C)) == Set([2,3])
        ]
        if all(conditions)
            push!(solution_set,Set([A,B,C]))
        end
    end
    solution_set
end

NUM_SETS = 3
U = Set(1:6)
pset = collect(powerset(collect(U)))[:2:end] # ignore empty set
sets = collect(chain([permutations(x) for x in subsets(pset, NUM_SETS)]...))
calculate(U,sets)