Resolution

Suppose that we have formulas such as the following:
A
B
D
¬ A ∨ ¬ B ∨ C (same as A ∧ B → C )
¬ C ∨ ¬ D ∨ E (same as C ∧ D → 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.)