intuition.
Qed.
(*  A private club has the following rules : * *  . rule 1 : Every non-scottish member wears red socks *  . rule 2 : Every member wears a kilt or doesn't wear red socks *  . rule 3 : The married members don't go out on sunday *  . rule 4 : A member goes out on sunday if and only if he is scottish *  . rule 5 : Every member who wears a kilt is scottish and married *  . rule 6 : Every scottish member wears a kilt * *  Actually, no one can be accepted ! *)
Section club.
Variable Scottish RedSocks WearKilt Married GoOutSunday : Prop.
Hypothesis rule1 : ~ Scottish -> RedSocks.
Hypothesis rule2 : WearKilt \/ ~ RedSocks.
Hypothesis rule3 : Married -> ~ GoOutSunday.
Hypothesis rule4 : GoOutSunday <-> Scottish.
Hypothesis rule5 : WearKilt -> Scottish /\ Married.
Hypothesis rule6 : Scottish -> WearKilt.

Lemma NoMember : False.
tauto.