Suppose that we have formulas such as the following:
¬ A &or ¬ B &or C (same as A &and B &rarr C )
¬ C &or ¬ D &or E (same as C &and D &rarr E )
A desired conclusion, say E , is negated to form the hypothetical fact
¬ E ; then the following algorithm is executed:
This assumes that the premises are consistent.
- Choose two clauses that have exactly one pair of literals
that are complementary (have different signs).
- Produce a new clause by deleting the complementary literals
and combining the remaining literals.
- If the resulting clause is empty (``box''), stop; the theorem
is proved by contradiction. (If the negation of the theorem leads
to a contradiction, then the theorem must be true.)