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from docplex.mp.model import Model

def solve_test_case_selection(lines_covered_by_tests):
    num_lines = max(max(test) for test in lines_covered_by_tests)  # assuming lines are 1-indexed
    num_tests = len(lines_covered_by_tests)
    
    # Create an ILP model instance
    mdl = Model('test_case_selection')
    
    # Decision variables: x[j] == 1 if test j is selected
    x = mdl.binary_var_list(num_tests, name='x')
    
    # Objective: Minimize the number of test cases used
    mdl.minimize(mdl.sum(x))
    
    # Constraints: Each line must be covered by at least one test case
    for i in range(1, num_lines + 1):
        mdl.add_constraint(mdl.sum(x[j] for j, test in enumerate(lines_covered_by_tests) if i in test) >= 1, f'cover_line_{i}')
    
    # Solve the model
    solution = mdl.solve()
    
    # Output selected test cases
    if solution:
        selected_tests = [j+1 for j, var in enumerate(x) if var.solution_value > 0.5]
        print("Selected Test Cases:", selected_tests)
    else:
        print("No solution found.")

# Example usage
lines_covered_by_tests = [
    [3, 4, 6, 8],
    [1, 2, 4, 9, 10],
    [5, 6, 8, 10],
    [2, 5, 8, 9],
    [1, 4, 6, 7, 9, 10],
    [1, 2, 3, 5, 8]
]
solve_test_case_selection(lines_covered_by_tests)