smt
// Define the module for a traffic light
module traffic_light
{
  type state_t = enum { red, green }; // Possible states of the traffic light

  var light : state_t; // Current state of the traffic light

  // Initial state of the traffic light
  init {
    light = red; // Assume both traffic lights start at red for simplicity
  }

  // Transition function to change the state of the traffic light
  procedure toggle()
    modifies light;
  {
    if (light == red) {
      light = green;
    } else {
      light = red;
    }
  }

  // Define the next state based on an external action
  next {
    if (*) { // Non-deterministic choice
      call toggle();
    }
  }
}

// Main module to handle two traffic lights and check for deadlocks
module main
{
  // Create two instances of traffic lights
  instance traffic_light1 : traffic_light;
  instance traffic_light2 : traffic_light;

  // Define an action type for synchronization
  type action_t = enum { A, B, none }; // A and B for synchronization, none for no action

  var action : action_t; // Current action

  // Initialize the action to none
  init {
    action = none;
  }

  // Define the next state based on the current action
  next {
    case
      // Action A: traffic_light1 goes green, traffic_light2 goes red
      action == A : {
        assume (traffic_light1.light == red && traffic_light2.light == green);
        next(traffic_light1); // Toggle traffic_light1 to green
        next(traffic_light2); // Toggle traffic_light2 to red
      }
      // Action B: traffic_light1 goes red, traffic_light2 goes green
      action == B : {
        assume (traffic_light1.light == green && traffic_light2.light == red);
        next(traffic_light1); // Toggle traffic_light1 to red
        next(traffic_light2); // Toggle traffic_light2 to green
      }
      // No action, no change
      action == none : {}
    esac
    havoc action; // Allow any action in the next state
  }

  // Check for deadlock: both lights are red
  invariant no_deadlock : !(traffic_light1.light == red && traffic_light2.light == red);

  control {
    // Setup for bounded model checking
    v = unroll(5); // Unroll the transition system 5 times
    check; // Check all properties including invariants
    print_results; // Print the results of the checks
  }
}
