Which Drupal log file is available to proof when exactly some content was deleted and by whom?
Check out their http://example.com/admin/reports/dblog. You should have messages like this one:

Type        content
Date        Wednesday, June 5, 2013 - 09:11
User        admin
Location    http://localhost/node/1/delete
Referrer    http://localhost/node/1/delete
Message     page: deleted test.


For future, you can use hook_watchdog()


  This hook allows modules to route log events to custom destinations, such as SMS, Email, pager, syslog, ...etc.