```ucl
module main {
    type time_t;
    var light_on : boolean;
    var door_open : boolean;
    var time : time_t;

    init {
        light_on = false;
        door_open = false;
        time = 0;
    }

    next(door_open_prime : boolean) {
        if (door_open || door_open_prime) {     // A door is opened
            light_on' = true;
            time' = 0;
        } else if (time >= 30) {                // 30 seconds after all doors are closed
            light_on' = false;
        } else {                                // Counting 30 seconds while all doors are closed
            light_on' = light_on;
            time' = time + 1;
        }
    }

    // Safety property: light should be on any time a door is open
    property light_on_when_door_open {
        door_open -> light_on;
    }

    // Safety property: light should turn off only 30 seconds after all doors are closed
    property light_off_after_delay {
        (time >= 30) && !door_open -> !light_on;
    }
}
```

In this code:
- We define a UCLID5 `module` named `main` with three variables: `light_on` (boolean representing the dome light status), `door_open` (boolean representing any door being open), and `time` (time since last door was closed).
- The `init` block sets initial conditions: light off, no door open, and time reset.
- The `next` block defines the state transition based on whether any door is opened or all are closed.
- Two safety properties ensure that the light behaves as required: 
  - `light_on_when_door_open` ensures the light is on whenever a door is open.
  - `light_off_after_delay` ensures the light turns off only 30 seconds after all doors are closed and no new door openings occur during that interval.

This captures the behavior specified for the dome light of the automobile.