Oops. What I got in the email works but what you posted here doesn't work.

list1third=Union[Map[#[[3]]&,list1]];
list2third=Union[Map[#[[3]]&,list2]];

I guess you did an edit after the email notification was sent. But those two lines work. Thanks again.

Thank you for your patience. Now I think I understand. Try this

list1={
  {{0.955469,-0.295092,0},1,1},{{-0.999148,-0.0412787,0},-1,3},{{0.905129,0.425137,0},1,4},
  {{0.517574,0.855638,0},-1,6},{{-0.985269,-0.171011,0},1,8},{{-0.550035,0.835141,0},-1,9},
  {{-0.615241,-0.788339,0},-1,10},{{0.345384,0.938461,0},-1,11},{{0.973115,0.230318,0},1,12},
  {{-0.799272,0.600969,0},1,14},{{-0.690606,0.723231,0},-1,16},{{0.0841899,-0.99645,0},1,17},
  {{0.609325,0.792921,0},1,19},{{-0.274095,0.961703,0},1,20}};
list2={
  {{0.71463,-0.699502,0},-1,1},{{0.888074,-0.459701,0},-1,4},{{0.69891,-0.715209,0},-1,6},
  {{0.780179,0.625557,0},-1,7},{{0.715609,0.698501,0},-1,8},{{0.280162,0.959953,0},-1,10},
  {{0.176816,0.984244,0},-1,13},{{0.112615,0.993639,0},-1,15},{{0.922023,0.387135,0},-1,16},
  {{0.986248,-0.165273,0},-1,17},{{0.974008,-0.226515,0},-1,19}};
list1third=list1[[All,3]];
list2third=list2[[All,3]];
list1del=Select[list1,Intersection[{#[[3]]},list2third]=={#[[3]]}&]
list2del=Select[list2,Intersection[{#[[3]]},list1third]=={#[[3]]}&]

which should give you

{{{0.955469,-0.295092,0},1,1},{{0.905129,0.425137,0},1,4},{{0.517574,0.855638,0},-1,6},
 {{-0.985269,-0.171011,0},1,8},{{-0.615241,-0.788339,0},-1,10},{{-0.690606,0.723231,0},-1,16},
 {{0.0841899,-0.99645,0},1,17},{{0.609325,0.792921,0},1,19}}

and

{{{0.71463,-0.699502,0},-1,1},{{0.888074,-0.459701,0},-1,4},{{0.69891,-0.715209,0},-1,6},
 {{0.715609,0.698501,0},-1,8},{{0.280162,0.959953,0},-1,10},{{0.922023,0.387135,0},-1,16},
{{0.986248,-0.165273,0},-1,17},{{0.974008,-0.226515,0},-1,19}}

Does that do exactly what you want on this sample data? And does it do exactly what you want on your real data?

Please check this carefully Thanks

Thank you.

Am I correct in thinking that the last two lists you just showed are the input to the final step that you don't know how to do and that you want to do another two DeleteCases, or perhaps something else, to get the final result?

If that is correct then can you show what the result should be after those two DeleteCases?

Perhaps from that someone can see how to reverse engineer the operation needed to automate that final step for you.

Thanks

Would you be able to make up some fake data, perhaps 10 rows for your first list and 12 rows for your second list, that have the same properties that your real data has after your first DeleteCases has finished? And then show and explain what the result of performing your last step on those two example tables would be? With that someone might be able to show a few lines of code that would do what you want.