Is It or Isn't It?
-- -- -- ----- ---

The `Is A' relation follows some very simple rules.  For
example, if

	x is a Y
	Y is a Z
then
	x is a Z

Here x is a proper noun, like `Jill' or `Jack', denoting
a particular object, and Y and Z are generic nouns, like
`mammal' or `animal', denoting properties.  So the above
is like

	Jack is a mammal
	mammal is a animal

therefore

	Jack is a animal

all of which, of course, needs further editing to be
good English, but is good enough for the internal
thoughts of a computer.

You are given some data consisting of nothing but `is a'
relations in which all objects are named by single lower
case letters and all properties are named by single
upper case letters.  You are then asked questions like

	x is a Z?

which according to the above data has the answer `true'.
However, if you cannot deduce that something is true,
then it is not necessarily false, so given the above
data if you are asked

	x is a W?

the answer should be `unknown', and NOT `false'.


Input
-----

A sequence of test cases.

Each test begins with a sequence of data lines, each of
the form

	x is a Y

or the form

	X is a Y

where x can be replaced by any lower case letter and
X and Y can be replaced by any upper case letters.

Following the data lines is a sequence of question
lines, each of the form

	x is a Y?

or the form

	X is a Y?

where x can be replaced by any lower case letter and
X and Y can be replaced by any upper case letters.

The question lines are followed by a single end line
containing just `.', which ends the test case

The input terminates with an end of file.

To make input easy, each data line is exactly 8 charac-
ters, each question line exactly 9 characters, charac-
ters 2 through 7 of each line are ` is a ', characters
1 and 8 of each line are letters, and character 9 of
each question line is `?'.  Character 8 must be upper
case, while character 1 may be lower or upper case.

Also to make the algorithm easier, each test case will
be such that if you can deduce that `X is a Y' is true,
then you CANNOT also deduce that `Y is a X' is true.
Thus there are no `loops' in the deductions.


Example Input
------- -----

x is a P
P is a Q
Q is a R
R is a S
P is a M
M is a N
x is a P?
x is a S?
R is a P?
Q is a N?
.
B is a C
B is a D
B is a E
x is a D
C is a E?
E is a B?
x is a B?
.

Output
------

For each test case, a sequence of answer lines that
correspond to the test case question lines, followed by
a single end line containing nothing but `.'.

An answer line contains nothing but `true' or `unknown',
according to whether or not the statement in the corres-
ponding question line can be deduced from the data or
not.


Example Output
------- ------

true
true
unknown
unknown
.
unknown
unknown
unknown
.

File:	   isa.txt
Author:	   Bob Walton <walton@deas.harvard.edu>
Date:	   Mon Oct 17 00:00:54 EDT 2005

The authors have placed this file in the public domain;
they make no warranty and accept no liability for this
file.

RCS Info (may not be true date or author):

    $Author: walton $
    $Date: 2005/10/17 04:01:09 $
    $RCSfile: isa.txt,v $
    $Revision: 1.5 $