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Generates a SMT LIB v2 encoding of the n-queens problem for SAT solvers
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import os | |
import sys | |
if len(sys.argv) < 2: | |
sys.exit('Usage: %s <problem size>' % sys.argv[0]) | |
def nl(f): | |
f.write('\n') | |
# Output file | |
filename = '%s_queens_SAT.smt2' % sys.argv[1] | |
f = open(filename, 'w') | |
N = int(sys.argv[1]) | |
print "Opening %s to write the SMT-LIB v2 encoding of the %i-queens problem" % (filename, N) | |
f.write(';; Generate the definitions of the variables\n') | |
for i in range(0, N): | |
for j in range(0,N): | |
f.write('(declare-const x%iy%i Bool)\n' % (i, j)) | |
f.write(';;Generate the "one queen by line" clauses\n\n') | |
for i in range(0,N): | |
f.write('(assert (or') | |
for j in range(0, N-1): | |
f.write(' x%iy%i ' % (i,j)) | |
f.write('x%iy%i' %(i, N-1)) | |
f.write('))') | |
f.write('\n') | |
f.write('\n;;Generate the "only one queen by line" clauses\n\n') | |
for i in range(0,N): | |
f.write('(assert (not (or') | |
for j in range(1, N): | |
for k in range(0,j): | |
f.write('(and x%iy%i x%iy%i)' %(i,j,i,k)) | |
f.write(')))') | |
nl(f) | |
nl(f) | |
f.write(';;Generate the "only one queen by column" clauses\n') | |
for i in range(0,N): | |
f.write('(assert (not (or') | |
for j in range(1, N): | |
for k in range(0,j): | |
f.write('(and x%iy%i x%iy%i)' %(j,i,k,i)) | |
f.write(')))') | |
nl(f) | |
nl(f) | |
f.write(';;Generate the "only one queen by diagonal" clauses\n') | |
for i in range(0,N-1): | |
f.write('(assert (not (or') | |
for j in range(0, N-i): | |
for k in range(1,N-j-i): | |
f.write(' (and x%iy%i x%iy%i)' %(j,i+j,j+k,i+j+k)) | |
f.write(')))') | |
nl(f) | |
for i in range(1,N-1): | |
f.write('(assert (not (or') | |
for j in range(0, N-i): | |
for k in range(1,N-j-i): | |
f.write(' (and x%iy%i x%iy%i)' %(i+j,j,i+j+k,j+k)) | |
f.write(')))') | |
nl(f) | |
for i in range(0,N-1): | |
f.write('(assert (not (or') | |
for j in range(0, N-i): | |
for k in range(1,N-j-i): | |
f.write(' (and x%iy%i x%iy%i)' %(j+k,i+j+k,j,i+j)) | |
f.write(')))') | |
nl(f) | |
for i in range(1,N-1): | |
f.write('(assert (not (or') | |
for j in range(0, N-i): | |
for k in range(1,N-j-i): | |
f.write(' (and x%iy%i x%iy%i)' %(i+j+k,j+k,i+j,j)) | |
f.write(')))') | |
nl(f) | |
nl(f) | |
f.write(";; Check if the generate model is satisfiable and output a model.\n") | |
f.write("(check-sat)\n") | |
f.write("(get-model)\n") | |
f.close() | |
# solution_filename = 's%i_queens.txt' % N | |
# os.system('z3 %s > %s' % (filename, solution_filename)) | |
# solution_file = open(solution_filename, 'r') |
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