WordWeb Online

1. Immune to attack; incapable of being tampered with
   "an impregnable fortress";
   - inviolable, secure, strong, unassailable, unattackable
    
2. Capable of conceiving
   - conceptive
    
3. Incapable of being overcome, challenged or refuted
   "an impregnable argument"; "impregnable self-confidence";
   - inexpugnable

See also: fertile, invulnerable, unconquerable

Encyclopedia: Impregnable