(** {1 The Scottish private club puzzle} *)

(* The club follows six rules:

 - every non-scottish members wear red socks

 - every member wears a kilt or doesn't wear socks

 - the married members don't go out on sunday

 - a member goes out on sunday if and only if he is scottish

 - every member who wears a kilt is scottish and married

 - every scottish member wears a kilt

Problem: prove that there is nobody in this club!

*)

theory ScottishClubProblem

  predicate is_scottish
  predicate wears_red_socks
  predicate wears_kilt
  predicate is_married
  predicate goes_out_on_sunday

  axiom R1: not is_scottish -> wears_red_socks

  axiom R2: wears_kilt \/ not wears_red_socks

  axiom R3: is_married -> not goes_out_on_sunday

  axiom R4: goes_out_on_sunday <-> is_scottish

  axiom R5: wears_kilt -> is_scottish /\ is_married

  axiom R6: is_scottish -> wears_kilt

  goal ThereIsNobodyInTheClub: false

end

