<s>
Nqthm	B-Application
is	O
a	O
theorem	B-Application
prover	I-Application
sometimes	O
referred	O
to	O
as	O
the	O
Boyer	B-Application
–	I-Application
Moore	I-Application
theorem	I-Application
prover	I-Application
.	O
</s>
<s>
It	O
was	O
a	O
precursor	O
to	O
ACL2	B-Application
.	O
</s>
<s>
Their	O
goal	O
was	O
to	O
make	O
a	O
fully	O
automatic	O
,	O
logic-based	O
theorem	B-Application
prover	I-Application
.	O
</s>
<s>
They	O
used	O
a	O
variant	O
of	O
Pure	B-Application
LISP	B-Language
as	O
the	O
working	O
logic	O
.	O
</s>
<s>
Definitions	O
are	O
formed	O
as	O
totally	O
recursive	O
functions	O
,	O
the	O
system	O
makes	O
extensive	O
use	O
of	O
rewriting	O
and	O
an	O
induction	B-Algorithm
heuristic	O
that	O
is	O
used	O
when	O
rewriting	O
and	O
something	O
that	O
they	O
called	O
symbolic	O
evaluation	O
fails	O
.	O
</s>
<s>
The	O
system	O
was	O
built	O
on	O
top	O
of	O
Lisp	B-Language
and	O
had	O
some	O
very	O
basic	O
knowledge	O
in	O
what	O
was	O
called	O
"	O
Ground-zero	O
"	O
,	O
the	O
state	O
of	O
the	O
machine	O
after	O
bootstrapping	O
it	O
onto	O
a	O
Common	O
Lisp	B-Language
implementation	O
.	O
</s>
<s>
The	O
formulation	O
of	O
the	O
theorem	O
is	O
also	O
given	O
in	O
a	O
Lisp-like	O
syntax	O
:	O
</s>
<s>
There	O
are	O
macros	O
for	O
LaTeX	B-Application
that	O
can	O
transform	O
the	O
Lisp	B-Language
structure	O
into	O
more	O
or	O
less	O
readable	O
mathematical	O
language	O
.	O
</s>
<s>
We	O
will	O
appeal	O
to	O
induction	B-Algorithm
.	O
</s>
<s>
Two	O
inductions	B-Algorithm
are	O
suggested	O
by	O
terms	O
in	O
the	O
conjecture	O
,	O
</s>
<s>
LESSP	O
in	O
each	O
induction	B-Algorithm
step	I-Algorithm
of	O
the	O
scheme	O
.	O
</s>
<s>
A	O
more	O
powerful	O
version	O
,	O
called	O
PC-Nqthm	O
(	O
Proof-checker	O
Nqthm	B-Application
)	O
was	O
developed	O
by	O
Matt	O
Kaufmann	O
.	O
</s>
<s>
This	O
is	O
a	O
great	O
help	O
,	O
as	O
the	O
system	O
has	O
an	O
unproductive	O
tendency	O
to	O
wander	O
down	O
infinite	O
chains	O
of	O
inductive	B-Algorithm
proofs	I-Algorithm
.	O
</s>
<s>
The	O
Boyer-Moore	B-Application
Theorem	I-Application
Prover	I-Application
and	O
Its	O
Interactive	O
Enhancement	O
,	O
with	O
M	O
.	O
Kaufmann	O
and	O
R	O
.	O
S	O
.	O
Boyer	O
,	O
Computers	O
and	O
Mathematics	O
with	O
Applications	O
,	O
29(2 )	O
,	O
1995	O
,	O
pp.27	O
–	O
62	O
.	O
</s>
<s>
In	O
2005	O
Robert	O
S	O
.	O
Boyer	O
,	O
Matt	O
Kaufmann	O
,	O
and	O
J	O
Strother	O
Moore	O
received	O
the	O
ACM	O
Software	O
System	O
Award	O
for	O
their	O
work	O
on	O
the	O
Nqthm	B-Application
theorem	B-Application
prover	I-Application
.	O
</s>
