Linear Resolution
✷ can be obtained from K in K by linear resolution iff
there are K1, . . . , Km with K1 = K, Km = ✷, and for all 2 ≤ i ≤ m:
Ki is resolvent of Ki−1 and a clause from {K1, . . . , Ki−1} ∪ K.
Input Resolution
✷ can be obtained from K in K by input resolution iff
there are K1, . . . , Km with K1 = K, Km = ✷, and for all 2 ≤ i ≤ m:
Ki is resolvent of Ki−1 and a clause from K.
{p,q} {¬p,q} {p,¬q} {¬p,¬q} {q}
{p}
{¬q}
✷
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