Cut and Fail in Prolog

it fails because fail must fail.

The cut removes alternatives, then forbids values that otherwise would be 'returned' by means of X binding. Try

a(X) :- b(X),c(X),fail.
...

you'll get

?- a(X).
X = 4.

example :

a(X):- b(X),!,fail. %is the same as \+ a(X):- b(X).

the merge of "!" and "fail" gives you the negative of a(X).

its called the Negation by Failure.