A pairwise factor graph that has strange behavior in ad3 branch and bound

graph.ad3

28
105
0.232269334
0.767730666
0.30221087
0.69778913
0.260731565
0.739268435
0.461288309
0.538711691
0.827495934
0.172504066
0.179560965
0.820439035
0.134009647
0.865990353
0.118120145
0.881879855
0.119712972
0.880287028
0.128078402
0.871921598
0.123289667
0.876710333
0.873494427
0.126505573
0.877575304
0.122424696
0.129883622
0.870116378
DENSE 4 1 2 3 4 2 2 2 0.128322914 -0.0733141141 -0.0873260879 0.032317288
DENSE 4 1 2 5 6 2 2 2 -0.0667600713 0.121768871 0.0980049224 -0.153013722
DENSE 4 1 2 7 8 2 2 2 0.0606852796 -0.00567647968 -0.017014407 -0.0379943929
DENSE 4 1 2 9 10 2 2 2 0.0238374001 0.0311713998 0.0363403025 -0.0913491024
DENSE 4 1 2 11 12 2 2 2 0.0640009288 -0.00899212892 -0.00576099998 -0.0492477999
DENSE 4 1 2 13 14 2 2 2 0.0531758413 0.00183295859 0.00880780424 -0.0638166041
DENSE 4 1 2 15 16 2 2 2 0.0572778674 -0.00226906746 0.00220154398 -0.0572103439
DENSE 4 1 2 17 18 2 2 2 0.0582913439 -0.00328254396 0.000905808225 -0.0559146081
DENSE 4 1 2 19 20 2 2 2 0.0509209505 0.0040878494 0.00845413165 -0.0634629316
DENSE 4 1 2 21 22 2 2 2 0.056981439 -0.00197263913 0.00282313879 -0.0578319387
DENSE 4 1 2 23 24 2 2 2 -0.0048875097 0.0598963096 -0.0545985957 -0.000410204167
DENSE 4 1 2 25 26 2 2 2 0.00102712568 0.0539816742 -0.0593517356 0.0043429357
DENSE 4 1 2 27 28 2 2 2 0.0598150821 -0.00480628219 0.00136483856 -0.0563736385
DENSE 4 3 4 5 6 2 2 2 0.135653524 -0.0946566975 -0.104408672 0.0634118463
DENSE 4 3 4 7 8 2 2 2 -0.0567763923 0.0977732184 0.100447265 -0.141444091
DENSE 4 3 4 9 10 2 2 2 0.0548737261 -0.0138769 0.00530397661 -0.0463008027
DENSE 4 3 4 11 12 2 2 2 0.044038382 -0.00304155591 0.0142015468 -0.0551983729
DENSE 4 3 4 13 14 2 2 2 0.0499595246 -0.00896269847 0.012024121 -0.0530209471
DENSE 4 3 4 15 16 2 2 2 0.0507342189 -0.00973739283 0.00874519242 -0.0497420185
DENSE 4 3 4 17 18 2 2 2 0.0535398121 -0.012542986 0.00565734001 -0.0466541661
DENSE 4 3 4 19 20 2 2 2 0.051224677 -0.0102278509 0.00815040519 -0.0491472313
DENSE 4 3 4 21 22 2 2 2 0.0507104618 -0.00971363574 0.00909411599 -0.0500909421
DENSE 4 3 4 23 24 2 2 2 -0.0134455977 0.0544424238 -0.0460405078 0.00504368167
DENSE 4 3 4 25 26 2 2 2 -0.00852862485 0.0495254509 -0.0497959851 0.00879915898
DENSE 4 3 4 27 28 2 2 2 0.0369978839 0.00399894215 0.0241820367 -0.0651788628
DENSE 4 5 6 7 8 2 2 2 0.139222513 -0.107977662 -0.0955516408 0.0643067896
DENSE 4 5 6 9 10 2 2 2 0.00586183825 0.0253830129 0.0543158644 -0.0855607156
DENSE 4 5 6 11 12 2 2 2 0.0579463091 -0.0267014579 0.00029361975 -0.0315384709
DENSE 4 5 6 13 14 2 2 2 0.0366023395 -0.00535748833 0.0253813061 -0.0566261572
DENSE 4 5 6 15 16 2 2 2 0.0467371338 -0.0154922826 0.0127422776 -0.0439871287
DENSE 4 5 6 17 18 2 2 2 0.0458725602 -0.014627709 0.0133245919 -0.0445694431
DENSE 4 5 6 19 20 2 2 2 0.048839061 -0.0175942098 0.0105360212 -0.0417808723
DENSE 4 5 6 21 22 2 2 2 0.0403998549 -0.00915500371 0.0194047229 -0.0506495741
DENSE 4 5 6 23 24 2 2 2 -0.0133191139 0.0445639651 -0.0461669915 0.0149221403
DENSE 4 5 6 25 26 2 2 2 -0.0130549274 0.0442997785 -0.0452696826 0.0140248314
DENSE 4 5 6 27 28 2 2 2 0.0531520848 -0.0219072337 0.00802783583 -0.039272687
DENSE 4 7 8 9 10 2 2 2 0.0918250301 -0.0481541575 -0.0316473274 -0.0120235452
DENSE 4 7 8 11 12 2 2 2 0.0125871423 0.0310837303 0.0456527865 -0.0893236591
DENSE 4 7 8 13 14 2 2 2 0.0490380843 -0.00536721164 0.0129455613 -0.0566164339
DENSE 4 7 8 15 16 2 2 2 0.0489152018 -0.00524432915 0.0105642096 -0.0542350822
DENSE 4 7 8 17 18 2 2 2 0.0510814839 -0.00741061131 0.00811566816 -0.0517865408
DENSE 4 7 8 19 20 2 2 2 0.048971714 -0.00530084143 0.0104033681 -0.0540742407
DENSE 4 7 8 21 22 2 2 2 0.0515176677 -0.00784679509 0.00828691011 -0.0519577827
DENSE 4 7 8 23 24 2 2 2 -0.00675011124 0.0504209839 -0.0527359942 0.00906512158
DENSE 4 7 8 25 26 2 2 2 -0.00204753084 0.0457184035 -0.0562770791 0.0126062065
DENSE 4 7 8 27 28 2 2 2 0.0642674142 -0.0205965416 -0.00308749359 -0.040583379
DENSE 4 9 10 11 12 2 2 2 0.113289859 -0.053112156 -0.0550499299 -0.0051277728
DENSE 4 9 10 13 14 2 2 2 0.039444042 0.0207336607 0.0225396036 -0.0827173062
DENSE 4 9 10 15 16 2 2 2 0.0557214047 0.00445629796 0.00375800664 -0.0639357093
DENSE 4 9 10 17 18 2 2 2 0.0601936104 -1.59077715e-05 -0.000996458344 -0.0591812443
DENSE 4 9 10 19 20 2 2 2 0.0658580047 -0.00568030202 -0.00648292252 -0.0536947801
DENSE 4 9 10 21 22 2 2 2 0.0533966028 0.00678109981 0.00640797497 -0.0665856776
DENSE 4 9 10 23 24 2 2 2 -0.00553336139 0.065711064 -0.053952744 -0.00622495861
DENSE 4 9 10 25 26 2 2 2 0.00367060687 0.0565070958 -0.0619952168 0.00181751413
DENSE 4 9 10 27 28 2 2 2 0.0639205654 -0.00374286277 -0.00274064478 -0.0574370579
DENSE 4 11 12 13 14 2 2 2 0.0825740512 -0.0243341224 -0.0205904057 -0.0376495232
DENSE 4 11 12 15 16 2 2 2 0.0558124308 0.00242749802 0.00366698052 -0.0619069094
DENSE 4 11 12 17 18 2 2 2 0.0582078434 3.20854365e-05 0.000989308688 -0.0592292375
DENSE 4 11 12 19 20 2 2 2 0.0539575983 0.00428233053 0.00541748384 -0.0636574127
DENSE 4 11 12 21 22 2 2 2 0.0646232968 -0.00638336797 -0.00481871899 -0.0534212098
DENSE 4 11 12 23 24 2 2 2 0.00235281487 0.055887114 -0.0618389203 0.00359899147
DENSE 4 11 12 25 26 2 2 2 -0.00282148588 0.0610614147 -0.055503124 -0.0027368048
DENSE 4 11 12 27 28 2 2 2 0.0610549718 -0.00281504298 0.000124948841 -0.0583648777
DENSE 4 13 14 15 16 2 2 2 0.0766623669 -0.0146787213 -0.0171829556 -0.04480069
DENSE 4 13 14 17 18 2 2 2 0.0514167992 0.0105668464 0.00778035293 -0.0697639985
DENSE 4 13 14 19 20 2 2 2 0.0614257408 0.000557904779 -0.00205065862 -0.0599329869
DENSE 4 13 14 21 22 2 2 2 0.0565720386 0.00541160694 0.00323253921 -0.0652161848
DENSE 4 13 14 23 24 2 2 2 0.00443716959 0.057546476 -0.063923275 0.00193962948
DENSE 4 13 14 25 26 2 2 2 0.003155409 0.0588282365 -0.0614800189 -0.000503626629
DENSE 4 13 14 27 28 2 2 2 0.0695194396 -0.007535794 -0.0083395189 -0.0536441267
DENSE 4 15 16 17 18 2 2 2 0.0723542394 -0.012874828 -0.0131570873 -0.0463223241
DENSE 4 15 16 19 20 2 2 2 0.0518533545 0.00762605682 0.00752172763 -0.067001139
DENSE 4 15 16 21 22 2 2 2 0.0611043551 -0.00162494373 -0.00129977726 -0.0581796341
DENSE 4 15 16 23 24 2 2 2 -0.00389984756 0.0633792589 -0.0555862579 -0.00389315347
DENSE 4 15 16 25 26 2 2 2 0.00470309187 0.0547763195 -0.0630277018 0.00354829045
DENSE 4 15 16 27 28 2 2 2 0.0579115479 0.00156786349 0.0032683728 -0.0627477841
DENSE 4 17 18 19 20 2 2 2 0.0715224236 -0.0123252715 -0.0121473415 -0.0470498106
DENSE 4 17 18 21 22 2 2 2 0.0541355875 0.00506156462 0.00566899035 -0.0648661424
DENSE 4 17 18 23 24 2 2 2 -0.00161266033 0.0608098124 -0.0578734451 -0.00132370699
DENSE 4 17 18 25 26 2 2 2 -0.000434111085 0.0596312632 -0.0578904988 -0.00130665326
DENSE 4 17 18 27 28 2 2 2 0.0639863123 -0.00478916018 -0.00280639162 -0.0563907605
DENSE 4 19 20 21 22 2 2 2 0.0713088546 -0.0119337725 -0.0115042768 -0.0478708053
DENSE 4 19 20 23 24 2 2 2 -0.000173748716 0.0595488309 -0.0593123567 -6.27254354e-05
DENSE 4 19 20 25 26 2 2 2 0.00326179613 0.056113286 -0.0615864061 0.0022113239
DENSE 4 19 20 27 28 2 2 2 0.0601836334 -0.000808551203 0.000996287295 -0.0603713695
DENSE 4 21 22 23 24 2 2 2 0.00185335389 0.0579512239 -0.0613394593 0.0015348815
DENSE 4 21 22 25 26 2 2 2 -0.00522750016 0.065032078 -0.0530971098 -0.00670746806
DENSE 4 21 22 27 28 2 2 2 0.0616036715 -0.00179909364 -0.000423750806 -0.059380827
DENSE 4 23 24 25 26 2 2 2 -0.0458172593 -0.0136688462 -0.0125073507 0.0719934561
DENSE 4 23 24 27 28 2 2 2 2.92656818e-05 -0.0595153711 0.061150655 -0.00166454954
DENSE 4 25 26 27 28 2 2 2 0.000558168083 -0.058882778 0.0606217526 -0.00229714265
XOR 2 1 2
XOR 2 3 4
XOR 2 5 6
XOR 2 7 8
XOR 2 9 10
XOR 2 11 12
XOR 2 13 14
XOR 2 15 16
XOR 2 17 18
XOR 2 19 20
XOR 2 21 22
XOR 2 23 24
XOR 2 25 26
XOR 2 27 28