This is the search tree for the query on slide 52, with a change made to
the rule for niece on slide 51.

Fact base used:

male(tom).              %Male Clause 1.
male(fred).             %Male Clause 2.

female(jane).           %Female Clause 1.
female(betty).          %Female Clause 2.
female(mary).           %Female Clause 3.

sibling(betty,fred).    %Sibling Clause 1.
sibling(fred,betty).    %Sibling Clause 2.
sibling(mary,fred).     %Sibling Clause 3.
sibling(fred,mary).     %Sibling Clause 4.

parent(tom,jane).       %Parent Clause 1.
parent(mary,jane).      %Parent Clause 2.

uncle(X,Z) :- male(X),       %Uncle Clause.
              sibling(X,Y),
              parent(Y,Z).

niece(X,Y):- uncle(Y,X), female(X). %Niece Clause.


Query:  ?- niece(X,Y).

Complete search tree:


                        niece(X,Y)
                            |    \
                            |     no
                            |
                    uncle(Y,X), female(X)
                            |           \
                            |            no
                            |
                male(Y), sibling(Y,Y1), parent(Y1,X), female(X)
                /                          \                 \
               / Y = tom                    \ Y = fred        no
              /                              \
sibling(tom,Y1),parent(Y1,X),female(X)        \
            |                       sibling(fred,Y1),parent(Y1,X),female(X)
            |                        /                  \               \
            no                      / Y1 = betty         \ Y1 = mary     no
                                   /                      \
                    parent(betty,X),female(X)   parent(mary,X),female(X)
                                |                          |            \
                                |                          | X = jane    no
                                no                         |
                                                        female(jane)
                                                           |       \
                                                           |        no
                                                           |
                                                          yes
                                                        X = fred
                                                        Y = jane  ; (retry)