Then clauses obtained by resolving clause 1 with a clause from 2 through
m + 1 other than clause i + 1 can be excluded from NH[/?i]. •
This theorem says that a forward AND-branch can also be treated indepen-
dently as a forward OR-branch.
Backward
AND-Branch
Reduction
LEMMA
3
Let CDB contain
l.PW-ß^v... νβ(χ,α„)
2.
Q(x
v
x
2
) & Q(x
2
,x
3
) -+R(x
v
x
3
).
Then clauses derived from 1 and 2 which contain more than one R are not
needed to compute Indef[/?(c7
,c2)].
•
The significant effect of Lemma 3 is illustrated with the following ex-
ample. Let CDB =
{\.P(x)^Q(x,a
l
)yQ(x,a
2
)
2.
Q(x
v
x
2
) & ...
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