SAT
(True, None) stars: [] alpha: 3
   {01234}:01234
   {0123}:03|12  {0124}:02|14  {0134}:01|34  {0234}:04|23  {1234}:13|24
   {012}:0|1|2  {013}:0|1|3  {023}:0|2|3  {123}:1|2|3  {014}:0|1|4  {024}:0|2|4  {124}:1|2|4  {034}:0|3|4  {134}:1|3|4  {234}:2|3|4
   {01}:0|1  {02}:0|2  {12}:1|2  {03}:0|3  {13}:1|3  {23}:2|3  {04}:0|4  {14}:1|4  {24}:2|4  {34}:3|4
