One problem is that you are declaring the "solver" variable globally and it seems to confuse or-tools to reuse it many times. When moving it inside "isdetecting", then the (7,12) problem is solved much faster, in about 7 seconds (compared to 2:51 minutes for the original model). I haven't checked it for the larger problem, though.
Also, it might be good idea to test different labelings (instead of solver.INT_VAR_DEFAULT and solver.INT_VALUE_DEFAULT), though binary value tend to be not very sensitive to different labelings. See the code for another labeling.
def isdetecting(matrix):
solver = cs.Solver("scip") # <----
X = np.array([solver.IntVar(values) for i in range(matrix.shape[1])])
X1 = X.tolist()
for row in matrix:
x = X[row].tolist()
solver.Add(solver.Sum(x) == 0)
# db = solver.Phase(X1, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)
db = solver.Phase(X1, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_CENTER_VALUE)
solver.NewSearch(db)
count = 0
while (solver.NextSolution() and count < 2):
solution = [x.Value() for x in X1]
count += 1
solver.EndSearch()
if (count < 2):
print "FOUND"
return True
Edit: Here are constraints to remove the all-0 solutions as mentioned in the comments. What I know of, it require a separate list. It now takes a little longer (10.4s vs 7s).
X1Abs = [solver.IntVar(values, 'X1Abs[%i]' % i) for i in range(X1_len)]
for i in range(X1_len):
solver.Add(X1Abs[i] == abs(X1[i]))
solver.Add(solver.Sum(X1Abs) > 0)