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:

  1. Choose two clauses that have exactly one pair of literals that are complementary (have different signs).

  2. Produce a new clause by deleting the complementary literals and combining the remaining literals.

  3. 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.)
This assumes that the premises are consistent.

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