c pigeon-3: placing 4 pigeons into 3 holes c c File generated by 'pigeonhole', (c) Tjark Weber c c The SAT encoding of this problem is very straightforward. For each pigeon i c and each hole j we have a variable x_{n*(i-1)+j} which means that pigeon i c is placed in hole j. Then we have n+1 clauses which say that a pigeon has c to be placed in some hole. Then for each hole we have a set of clauses c ensuring that only one single pigeon is placed into that hole. c c This encoding leads to a total of (n+1) * n propositional variables and c (n+1) + n * (n * (n+1) / 2) clauses. c c The resulting SAT problem is unsatisfiable. c p cnf 12 22 1 2 3 0 4 5 6 0 7 8 9 0 10 11 12 0 -1 -4 0 -1 -7 0 -1 -10 0 -4 -7 0 -4 -10 0 -7 -10 0 -2 -5 0 -2 -8 0 -2 -11 0 -5 -8 0 -5 -11 0 -8 -11 0 -3 -6 0 -3 -9 0 -3 -12 0 -6 -9 0 -6 -12 0 -9 -12 0