Find a feasible solution of the CNF expression in Exercise 1 using a DPL algorithm with clause learning. Branch on variables in the order x1,...,x5, and take the false branch first.
Exercise 1
A group of medications are commonly used to treat a form of cancer, but they can be taken only in certain combinations.
A patient who takes Medications 1 and 2 must take Medication 5 as well.
Medication 1 can be taken if and only 5 is not taken. At least one of Medications 3, 4, and 5 must be taken. If 5 is taken, then 3 or 4 must be taken. If 4 is taken, then 3 or 5 must be taken. Medication 3 must be taken if both 4 and 5 are taken.
Medication 3 cannot be taken without 4, and 5 cannot be taken without 1. Let xj be true when medication j is taken, and write these conditions in propositional form. Convert them to CNF without adding variables.