let rec simple_string_of_boolean_expression =
  function
    | Var i -> string_of_int i
    | Not (Var i) -> "¬" ^ string_of_int i
    | Not e -> "¬(" ^ (simple_string_of_boolean_expression e) ^ ")"
    | BinOp (l, o, r) -> (
        match l with
          | BinOp (_, lo, _) when lo <> o ->
            "(" ^ simple_string_of_boolean_expression l ^ ")"
          | _ -> simple_string_of_boolean_expression l
      ) ^ (string_of_binary_operator o) ^ (
        match r with
          | BinOp (_, ro, _) when ro <> o ->
            "(" ^ simple_string_of_boolean_expression r ^ ")"
          | _ -> simple_string_of_boolean_expression r
      )
;;