<s>
CARINE	B-Application
(	O
Computer	O
Aided	O
Reasoning	O
Engine	O
)	O
is	O
a	O
first-order	O
classical	O
logic	O
automated	B-Application
theorem	I-Application
prover	I-Application
.	O
</s>
<s>
CARINE	B-Application
's	O
main	O
search	O
algorithm	O
is	O
semi-linear	B-Application
resolution	I-Application
(	O
SLR	O
)	O
which	O
is	O
based	O
on	O
an	O
iteratively-deepening	O
depth-first	O
search	O
(	O
also	O
known	O
as	O
depth-first	O
iterative-deepening	O
(	O
DFID	O
)	O
)	O
and	O
used	O
in	O
theorem	O
provers	O
like	O
THEO	O
.	O
</s>
<s>
Delayed	B-Application
Clause	I-Application
Construction	I-Application
is	O
a	O
stalling	O
strategy	O
that	O
enhances	O
a	O
theorem	O
prover	O
's	O
performance	O
by	O
reducing	O
the	O
work	O
to	O
construct	O
clauses	O
to	O
a	O
minimum	O
.	O
</s>
<s>
This	O
procedure	O
keeps	O
going	O
along	O
a	O
derivation	O
until	O
the	O
theorem	O
provers	O
reaches	O
a	O
point	O
where	O
it	O
decides	O
,	O
based	O
on	O
certain	O
criteria	O
and	O
heuristics	O
,	O
whether	O
to	O
construct	O
the	O
final	O
clause	O
in	O
the	O
derivation	O
(	O
and	O
probably	O
some	O
other	O
clause(s )	O
along	O
the	O
path	O
)	O
or	O
discard	O
the	O
whole	O
derivation	O
i.e.	O
,	O
deletes	O
from	O
memory	O
the	O
maintained	O
substitution	O
sets	O
and	O
whatever	O
information	O
stored	O
with	O
them	O
.	O
</s>
<s>
(	O
An	O
informal	O
definition	O
of	O
)	O
a	O
clause	O
in	O
theorem	B-Application
proving	I-Application
is	O
a	O
statement	O
that	O
can	O
result	O
in	O
a	O
true	O
or	O
false	O
answer	O
depending	O
on	O
the	O
evaluation	O
of	O
its	O
literals	O
.	O
</s>
<s>
A	O
clause	O
is	O
represented	O
as	O
a	O
disjunction	O
(	O
i.e.	O
,	O
OR	O
)	O
,	O
conjunction	O
(	O
i.e.	O
,	O
AND	O
)	O
,	O
set	O
,	O
or	O
multi-set	O
(	O
similar	O
to	O
a	O
set	O
but	O
can	O
contain	O
identical	O
elements	O
)	O
of	O
literals	O
.	O
</s>
<s>
Note	O
:	O
An	O
n-tuple	O
of	O
clause	O
attributes	O
is	O
similar	O
(	O
but	O
not	O
the	O
same	O
)	O
to	O
the	O
feature	O
vector	O
named	O
by	O
Stephan	B-Language
Schulz	I-Language
,	O
PhD	O
(	O
see	O
E	B-Language
equational	I-Language
theorem	I-Language
prover	I-Language
)	O
.	O
</s>
