let (|EmptySet|_|) a = if Set.isEmpty a then Some () else None

let (|SetHead|_|) set =
    match set |> Set.toList with
    | head::_ -> Some head
    | _ -> None

let hasZeroSum set =
    let rec hasZeroSum sum set  =
        match set with
        | EmptySet -> false // Empty set doesn't count
        | SetHead head when (head + sum) = 0 -> // Is first element + current sum = 0? Success!
            true
        | _ ->
            // Try any (element + current sum) with rest of set
            set |> Set.exists (fun i ->
                set
                |> Set.remove i
                |> hasZeroSum (i + sum)
            )

    hasZeroSum 0 set


[<EntryPoint>]
let main argv =

    [10; 20; -5; -13; -3; 1; 56]
    |> Set.ofList
    |> hasZeroSum
    |> printfn "Has any zero sums? %A"

    0