Paradox - Between a situation or statement seems strange or impossible together

Example sentences: 

1. Paradoxically, both actors fans got together for the current issue.
2. Paradox between myth and science are never identical.
3. The statement made by the physician and the victim are paradoxically different.
4. Submitted expenses bill and the total expenses have always been paradoxical.
5. Many software applications terms and conditions are paradoxically different from the real implementation.