They are all correct and amazing!

Uw2 Fw 3Uw2 3Rw' 3Uw' 3Fw Uw2 3Uw2 3Fw' 3Uw 3Rw 3Uw2 Fw' Uw2 =

[Uw2 Fw D2 R' B' L: u2](13 btm, 17 ltm, 14 ftm, 20 qtm)

R U' Fw2 3Fw U2 Fw2 R Fw2 U2 Fw2 R 3Fw' U R' =

R U' B Fw2 L2 Fw2 U Fw2 L2 Fw2 U B' U R' (14 btm, 18 ltm, 14 ftm, 20 qtm)

F2 Rw2 U R2 U' R2 3Rw2 U R2 U' R2 Rw2 3Rw2 F2 =

F2 Rw2 U R2 U' M2 U R2 U' R2 l2 F2 (12 btm, 14 ltm, 14 ftm, 24 qtm)

F2 Rw2 U' F2 U F2 3Fw2 U' F2 U F2 3Fw2 Rw2 F2 =

F2 Rw2 U' F2 U S2 U' F2 U S2 Rw2 F2 (12 btm, 16 ltm, 14 ftm, 24 qtm)

Yes there is a position I would like you to find the optimal OBTM (ftm) solution for.

I'm not sure if 18 OBTM is out of reach for your solver, but 18 OBTM is the briefest I have found (and currently exists) for this case (which I have studied extensively).

(Rw2 Uw U S Lw2 u2) r (u2 Lw2 S' U' Uw' Rw2)

(Rw2 Uw' U' S Lw2 u2) r (u2 Lw2 S' U Uw Rw2)

I forgot to post your solved scrambles.

Code:

```
Solutions To Scramble = F2 U' l' r' U F' L U' F l r F' U L' F'
TOP FRONT RIGHT
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|####|OOOO| |XXXX|####|XXXX|XXXX|
--------------------- --------------------- ---------------------
|^^^^|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|^^^^|####|####|OOOO| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|XXXX|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
BOTTOM BACK LEFT
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|####|####|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
Solution [001] = d2 f D F2 U' F2 r2 F2 [inside 5-TFS] ---> U F2 D' f' d2 @ 0128707314012 nodes with 1010604690894 5-TFS probes
Solutions To Scramble = r2 U' B2 U' F L F' r2 F L' F' U B2 U r2
TOP FRONT RIGHT
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|####|####|OOOO| |XXXX|XXXX|&&&&|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|OOOO|OOOO|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
BOTTOM BACK LEFT
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|XXXX|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
Solution [001] = u2 b' U' b' l D2 f2 D2 [inside 5-TFS] ---> l' b U b u2 @ 0090736443045 nodes with 0750247004859 5-TFS probes
Solution [002] = u2 b' U' b' l' D2 f2 D2 [inside 5-TFS] ---> l b U b u2 @ 0090736464321 nodes with 0750247150267 5-TFS probes
Solution [003] = d' r2 d B2 D2 F' R2 D2 [inside 5-TFS] ---> L2 B l2 r' u' @ 0110414034303 nodes with 0885175449290 5-TFS probes
Solution [004] = d2 r' U' B2 D' r' f2 r [inside 5-TFS] ---> D B2 U r d2 @ 0123089215000 nodes with 0972086306647 5-TFS probes
Solution [005] = d2 b' U' b' l D2 f2 D2 [inside 5-TFS] ---> l' b U b d2 @ 0130611366693 nodes with 1023666280309 5-TFS probes
Solution [006] = d2 b' U' b' l' D2 f2 D2 [inside 5-TFS] ---> l b U b d2 @ 0130611387969 nodes with 1023666424889 5-TFS probes
Solution [007] = r2 b U r D l' b2 l [inside 5-TFS] ---> D' r' U' b' r2 @ 0259062671872 nodes with 1904439161555 5-TFS probes
Solutions To Scramble = l2 U' B2 U' F L F' l2 F L' F' U B2 U l2
TOP FRONT RIGHT
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|####|####|OOOO| |XXXX|&&&&|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|OOOO|OOOO|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
BOTTOM BACK LEFT
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|XXXX|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
Solution [001] = u2 f U' f r D2 b2 D2 [inside 5-TFS] ---> r' f' U f' u2 @ 0088691387205 nodes with 0736229771312 5-TFS probes
Solution [002] = u2 f U' f r' D2 b2 D2 [inside 5-TFS] ---> r f' U f' u2 @ 0088691410749 nodes with 0736229934429 5-TFS probes
Solution [003] = d2 l U' B2 D' l b2 l' [inside 5-TFS] ---> D B2 U l' d2 @ 0124135640777 nodes with 0979264921448 5-TFS probes
Solution [004] = d2 f U' f r D2 b2 D2 [inside 5-TFS] ---> r' f' U f' d2 @ 0128566310853 nodes with 1009645389864 5-TFS probes
Solution [005] = d2 f U' f r' D2 b2 D2 [inside 5-TFS] ---> r f' U f' d2 @ 0128566334397 nodes with 1009645555635 5-TFS probes
Solutions To Scramble = r2 U l r U' F R' U F' l' r' F U' R F' r2
TOP FRONT RIGHT
--------------------- --------------------- ---------------------
|####|####|^^^^|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|####|####|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|XXXX| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|&&&&|####|####|XXXX| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
BOTTOM BACK LEFT
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|####|&&&&|&&&&| |^^^^|^^^^|####|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
Solution [001] = u2 f' D B2 U' B2 r2 B2 [inside 5-TFS] ---> U B2 D' f u2 @ 0089361202383 nodes with 0740808355065 5-TFS probes
Solution [002] = d2 f' D B2 U' B2 r2 B2 [inside 5-TFS] ---> U B2 D' f d2 @ 0129236126031 nodes with 1014223718305 5-TFS probes
Solution [003] = l2 f' U R2 U' L2 b2 L2 [inside 5-TFS] ---> U R2 U' f l2 @ 0297890262609 nodes with 2170654243169 5-TFS probes
Solution [004] = l2 f' U R2 D' B2 r2 B2 [inside 5-TFS] ---> D R2 U' f l2 @ 0297890471079 nodes with 2170655663948 5-TFS probes
Solution [005] = l2 f' U' b2 D' B2 r2 B2 [inside 5-TFS] ---> D b2 U f l2 @ 0297922559391 nodes with 2170875725249 5-TFS probes
Solution [006] = l2 f' L2 U R2 U' b2 U [inside 5-TFS] ---> R2 U' L2 f l2 @ 0298295606800 nodes with 2173433925721 5-TFS probes
Solution [007] = l2 f' L2 D B2 U' l2 U [inside 5-TFS] ---> B2 D' L2 f l2 @ 0298301859982 nodes with 2173476807387 5-TFS probes
Solutions To Scramble = R2 r' F' L R F r' F' R' F r2 F' L' F R2
TOP FRONT RIGHT
--------------------- --------------------- ---------------------
|####|####|OOOO|####| |OOOO|OOOO|####|OOOO| |XXXX|XXXX|####|XXXX|
--------------------- --------------------- ---------------------
|XXXX|####|####|^^^^| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|&&&&|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
BOTTOM BACK LEFT
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|####|&&&&|&&&&| |^^^^|####|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
Solution [001] = r F2 r U b' L B' L' [inside 5-TFS] ---> l B' U2 f l2 @ 0227762813531 nodes with 1689809785046 5-TFS probes
Solution [002] = r B' R L' B r B' L [inside 5-TFS] ---> B r2 B' R' B @ 0231706464436 nodes with 1716850086155 5-TFS probes
Solution [003] = r' u2 r u2 b' l U F2 [inside 5-TFS] ---> F r B L2 R2 @ 0235278692736 nodes with 1741344225356 5-TFS probes
Solution [004] = r' F' R' L F r' F' R [inside 5-TFS] ---> F r2 F' L' F @ 0241864066531 nodes with 1786499735871 5-TFS probes
Solution [005] = L F' L' b2 L B L' b' [inside 5-TFS] ---> L B' F L' b' @ 0308623479380 nodes with 2244260809189 5-TFS probes
Solutions To Scramble = r2 U F2 U B' R B r2 B' R' B U' F2 U' r2
TOP FRONT RIGHT
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|&&&&|OOOO| |XXXX|####|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|XXXX|####|####|^^^^| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
BOTTOM BACK LEFT
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|OOOO|&&&&| |^^^^|^^^^|####|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
Solution [001] = R2 f' D F2 f' u2 l2 u2 [inside 5-TFS] ---> f F2 D' f R2 @ 0214056276801 nodes with 1595827407974 5-TFS probes
Solution [002] = R2 f' D F2 f' d2 l2 d2 [inside 5-TFS] ---> f F2 D' f R2 @ 0214056279072 nodes with 1595827423505 5-TFS probes
Solution [003] = R2 f' D b' B2 u2 r2 u2 [inside 5-TFS] ---> B2 b D' f R2 @ 0214059607653 nodes with 1595850227820 5-TFS probes
Solution [004] = R2 f' D b' B2 d2 r2 d2 [inside 5-TFS] ---> B2 b D' f R2 @ 0214059609924 nodes with 1595850243100 5-TFS probes
Solution [005] = R2 f' D B2 d2 b' r2 b [inside 5-TFS] ---> d2 B2 D' f R2 @ 0214061510578 nodes with 1595863321622 5-TFS probes
Solution [006] = R2 f' D' F2 u2 b' l2 b [inside 5-TFS] ---> u2 F2 D f R2 @ 0214071048247 nodes with 1595928696941 5-TFS probes
Solution [007] = R2 f' D' F2 b' u2 l2 u2 [inside 5-TFS] ---> b F2 D f R2 @ 0214071539037 nodes with 1595932069181 5-TFS probes
Solution [008] = R2 f' D' F2 b' d2 l2 d2 [inside 5-TFS] ---> b F2 D f R2 @ 0214071541308 nodes with 1595932084901 5-TFS probes
Solution [009] = R2 f' D' f' B2 u2 r2 u2 [inside 5-TFS] ---> B2 f D f R2 @ 0214072943817 nodes with 1595941686238 5-TFS probes
Solution [010] = R2 f' D' f' B2 d2 r2 d2 [inside 5-TFS] ---> B2 f D f R2 @ 0214072946088 nodes with 1595941701785 5-TFS probes
Solution [011] = R2 f' D' B2 u2 f' r2 f [inside 5-TFS] ---> u2 B2 D f R2 @ 0214076638621 nodes with 1595967056929 5-TFS probes
Solution [012] = F L f2 D' B r2 d2 r2 [inside 5-TFS] ---> B' D f2 L' F' @ 0348708026223 nodes with 2519103241100 5-TFS probes
Solution [013] = F L f2 D' B l2 d2 l2 [inside 5-TFS] ---> B' D f2 L' F' @ 0348708028575 nodes with 2519103256699 5-TFS probes
Solutions To Scramble = L U F L' U' L U L F' L2 U L U L' U' L U' L'
TOP FRONT RIGHT
--------------------- --------------------- ---------------------
|####|####|####|####| |^^^^|&&&&|&&&&|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
--------------------- --------------------- ---------------------
BOTTOM BACK LEFT
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|OOOO|OOOO|^^^^| |OOOO|^^^^|^^^^|&&&&|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
--------------------- --------------------- ---------------------
Solution [001] = U B2 L2 F B2 U' F R2 B' [inside 5-TFS] ---> D F' R2 B F' @ 0001119126581 nodes with 0017853193809 5-TFS probes
Solution [002] = U' R L' B2 R D' L B2 R' [inside 5-TFS] ---> U L2 R' F2 L2 @ 0001371388154 nodes with 0019582866730 5-TFS probes
Solution [003] = U' F2 L2 F2 B' U B' R2 F [inside 5-TFS] ---> D' B R2 B F' @ 0002020120411 nodes with 0024031075167 5-TFS probes
Solution [004] = U2 F R' B U2 F' L F' B2 [inside 5-TFS] ---> D2 B2 L' B' F @ 0002951816961 nodes with 0030420382639 5-TFS probes
Solution [005] = U2 F B' R F2 D2 F2 B R' [inside 5-TFS] ---> B U2 F' L B' @ 0002982652928 nodes with 0030631752492 5-TFS probes
Solution [006] = U2 F B' R' B2 D2 F' B2 R [inside 5-TFS] ---> F' U2 B L' F @ 0002983217161 nodes with 0030635615750 5-TFS probes
Solution [007] = U2 B' R F' U2 B L' F2 B [inside 5-TFS] ---> D2 F2 L B' F @ 0003265166068 nodes with 0032568908988 5-TFS probes
Solution [008] = R2 F R B' R' F' R' D2 L' [inside 5-TFS] ---> F' L D2 R' B @ 0009056298908 nodes with 0072277389472 5-TFS probes
Solution [009] = R2 F R' D2 L B' L' D2 R' [inside 5-TFS] ---> B' R' F' R B @ 0009059132519 nodes with 0072296853649 5-TFS probes
Solution [010] = R2 B' R D2 L' F L D2 R [inside 5-TFS] ---> F R B R' F' @ 0009373437574 nodes with 0074452290522 5-TFS probes
Solution [011] = R2 B' R' F R B R D2 L [inside 5-TFS] ---> B L' D2 R F' @ 0009381341449 nodes with 0074506439427 5-TFS probes
Solution [012] = L2 U2 D R' L F2 R D' L [inside 5-TFS] ---> B2 R' U R B2 @ 0011473651735 nodes with 0088853541481 5-TFS probes
Solution [013] = L2 U2 D' R L' B2 R' D L' [inside 5-TFS] ---> F2 R U' R' F2 @ 0011478354296 nodes with 0088885796272 5-TFS probes
Solution [014] = L2 D R U2 R' L F2 D' L [inside 5-TFS] ---> B2 R' U R B2 @ 0011558045923 nodes with 0089432096854 5-TFS probes
Solution [015] = L2 D' R' U2 R L' B2 D L' [inside 5-TFS] ---> F2 R U' R' F2 @ 0011632890326 nodes with 0089945242796 5-TFS probes
Solution [016] = L2 F2 R L2 U' R B2 L' D [inside 5-TFS] ---> R' B2 L R' U @ 0011968390258 nodes with 0092245688140 5-TFS probes
Solution [017] = L2 B2 R' L2 U R' F2 L D' [inside 5-TFS] ---> R F2 L' R U' @ 0012195816719 nodes with 0093805095305 5-TFS probes
Solution [018] = F R B' R' F' R' D2 L' F' [inside 5-TFS] ---> L D2 R' B R2 @ 0012755309015 nodes with 0097641491153 5-TFS probes
Solution [019] = F R' D2 L B' L' D2 R' B' [inside 5-TFS] ---> R' F' R B R2 @ 0012793133387 nodes with 0097900948987 5-TFS probes
Solution [020] = F R' L2 D2 L B' L' D2 R2 [inside 5-TFS] ---> F' R' F L2 F' @ 0012809096856 nodes with 0098010381424 5-TFS probes
Solution [021] = F L2 F' R F R2 D2 L B [inside 5-TFS] ---> L' D2 L2 R F' @ 0013110831019 nodes with 0100079073946 5-TFS probes
Solution [022] = F B' R2 F D' B R2 F' U [inside 5-TFS] ---> B2 F' L2 B2 U' @ 0013255306225 nodes with 0101069575163 5-TFS probes
Solution [023] = F B' R2 B' D F' R2 B U' [inside 5-TFS] ---> B F2 L2 F2 U @ 0013257071300 nodes with 0101081687503 5-TFS probes
Solution [024] = F' U D2 R2 D' F D R2 U2 [inside 5-TFS] ---> B U B' D2 F @ 0013353083421 nodes with 0101740007997 5-TFS probes
Solution [025] = F' D2 B U' B' U2 R2 D' F' [inside 5-TFS] ---> D R2 D2 U' F @ 0013784940047 nodes with 0104701441777 5-TFS probes
Solution [026] = F' L B' U2 F R' F B2 D2 [inside 5-TFS] ---> B2 R B F' U2 @ 0014111006466 nodes with 0106937420192 5-TFS probes
Solution [027] = F' B L B2 D2 F B2 L' F [inside 5-TFS] ---> U2 B' R F' U2 @ 0014315314555 nodes with 0108338340723 5-TFS probes
Solution [028] = F' B L' F2 D2 F2 B' L B' [inside 5-TFS] ---> U2 F R' B U2 @ 0014319216425 nodes with 0108365054083 5-TFS probes
Solution [029] = F2 R U R' F2 L D' R B2 [inside 5-TFS] ---> L R' D U2 L2 @ 0014922710151 nodes with 0112502821614 5-TFS probes
Solution [030] = F2 R U R' F2 L D' B2 R' [inside 5-TFS] ---> L U2 R D L2 @ 0014922710294 nodes with 0112502822550 5-TFS probes
Solution [031] = F2 R U R' F2 L D' B2 L [inside 5-TFS] ---> R' U2 R D L2 @ 0014922710296 nodes with 0112502822551 5-TFS probes
Solution [032] = B U' D2 R2 D B' D' R2 U2 [inside 5-TFS] ---> F' U' F D2 B' @ 0015679560453 nodes with 0117692608142 5-TFS probes
Solution [033] = B D2 F' U F U2 R2 D B [inside 5-TFS] ---> D' R2 D2 U B' @ 0016014245689 nodes with 0119987577690 5-TFS probes
Solution [034] = B L' F U2 B' R F2 B' D2 [inside 5-TFS] ---> F2 R' B F' U2 @ 0016398204444 nodes with 0122620173492 5-TFS probes
Solution [035] = B' R D2 L' F L D2 R F [inside 5-TFS] ---> R B R' F' R2 @ 0016988624704 nodes with 0126668356753 5-TFS probes
Solution [036] = B' R L2 D2 L' F L D2 R2 [inside 5-TFS] ---> B R B' L2 B @ 0017004358800 nodes with 0126776299331 5-TFS probes
Solution [037] = B' R' F R B R D2 L B [inside 5-TFS] ---> L' D2 R F' R2 @ 0017094129355 nodes with 0127392092332 5-TFS probes
Solution [038] = B' L2 B R' B' R2 D2 L' F' [inside 5-TFS] ---> L D2 L2 R' B @ 0017403264353 nodes with 0129512031676 5-TFS probes
Solution [039] = B2 R' U' R B2 L' D R' F2 [inside 5-TFS] ---> L' R D' U2 L2 @ 0017964864801 nodes with 0133362816543 5-TFS probes
Solution [040] = B2 R' U' R B2 L' D F2 R [inside 5-TFS] ---> L' U2 R' D' L2 @ 0017964864892 nodes with 0133362817287 5-TFS probes
Solution [041] = B2 R' U' R B2 L' D F2 L' [inside 5-TFS] ---> R U2 R' D' L2 @ 0017964864896 nodes with 0133362817359 5-TFS probes
```

That makes sense to me. Lowercase letters denote multiple layer turns, the smallest of which is a turning of two layers. I retract my earlier statement. SiGN notation does appear to be internally consistent.

A Move Notation Proposal: Lodino = Logigcal Direction Notation

Background: In reviewing the various notations used by cubers,

and offering a fresh perspective as an outsider (I am no speed

cuber and can't even solve a 5x5x5 without constantly referencing

cmowla's numerous PDFs on the subject), I decided to start with a

tabula rasa.

A summary first for those who can't read this in its entirety

without falling asleep.

Goals for a hypothetical new system:

1. A notation system that reads in such a way that the cubies

to which a formula applies is obvious, with an intuitive

direction indicator.

2. The system should be telescoping and inclusive of all

cubes from 2x2x2 through NxNxN (with N currently at 11 max)

with no need to add terms as the size of the cube grows.

3. No dependence on the knowledge of mathematical notation

or symbology to ease the burden on the newly initiated.

4. System should resolve the present ambiguity concerning the

ambiguous rotation notation governing the middle slices for

all NxNxN cubes with odd N >= 5.

5. The system should be neither cumbersome for the human

to learn, nor difficult for the programmer to implement.

With these goals in mind, the system below accomplishes all

of the above.

========================================================

Logical Direction Notation (Lodino) has the following

good features.

1. Easy to understand direction notation. It eliminates

the arbitrary prime mark (') assignment altogether,

and the unitiated can understand which way to turn the

cube at once. Older systems may even have a right-handed

bias in that clockwise turns (no prime notation) are more

easily performed with a right hand on the R and U faces

than a left hand on the L and D faces.

2. Rotation notation is also "global" and not "relative."

There is a rotation indicator for every direction, not

merely the absence of one for the arbitrary unprimed move.

In this way, lodino supports positive reinforcement with

a standard number of descriptors per move of the same

cube size.

3. Moves are of the form: cubie_subset.direction

4. Lodino corrects the defect where larger cubes have

some move designations with no bearing or resemblance

to smaller cubes. All moves on larger cubes look like

those already seen before on smaller cubes.

5. Lodino corrects larger cube notations that complicate

situations where:

A. Multiple slices with or without the center slice

are involved in the move.

B. Slice turns + face turns are required for a move.

C. Moves involve only the center slice, which, by definition,

cannot have a rotation indicator that is unambiguous.

6. Lodino smooths out the 4x4x4 move description defect

where 2 slices in motion being turned at once have

opposing direction indicators. For example, ud' moves

the up and down slices in the same direction, yet the

move notation is inconsistent and not natural.

========================================================

Sample of Moves

========================================================

2X2X2 and larger

U.L = turn the top towards the left = U presently

U.R = turn the top towards the right = U' presently

U.2 = turn the top twice

F.R = F

F.L = F'

F.2 = F2

R.B = R

R.F = R'

R.2 = R2

D.R = D

D.L = D'

D.2 = D2

B.L = B

B.R = B'

B.2 = B2

L.F = L

L.B = L'

L.2 = L2

========================================================

4x4x4 single slice turns

Only time to use lower case for the direction is when

all moves are slices.

u.l = turn the top slice towards the left = u presently

u.r = turn the top slice towards the right = u' presently

u.2 = turn the top slice twice

f.r = f

f.l = f'

f.2 = f2

r.b = r

r.f = r'

r.2 = r2

d.r = d

d.l = d'

d.2 = d2

b.l = b

b.r = b'

b.2 = b2

l.f = l

l.b = l'

l.2 = l2

4x4x4 double slice turns

ud.l = ud'

ud.r = u'd

fb.r = fb'

fb.l = f'b

rl.b = rl'

rl.f = r'l

4x4x4 face and slice turns

Uu.L = U u

Uu.R = U' u'

Uu.2 = U2 u2

Ff.R = F f

Ff.L = F' f'

Rr.B = R r

Rr.F = R' r'

Dd.R = D d

Dd.L = D' d'

Bb.L = B b

Bb.R = B' b'

Ll.F = L l

Ll.B = L' l'

========================================================

5x5x5 middle slice turns

Enclose the moves in round parenthesis to demarcate a middle edge.

(uf) = turn the middle slice towards the front face from the top face.

When stand alone, it is both a cube selector and a direction selector.

(fu) = the opposite direction of (uf). Move from the front towards

the top

(uf).2 = move the slice twice.

(fu).2 = same as (uf).2

l.(fu) = adjoin the l slice to the middle slice and turn it from f to u.

lr.(uf) = turn 3 slices at once; l, the middle, and r, all from u to f.

This is essentially like moving R and L' on separate moves.

L.(uf).2 = turn the L face and the middle edge at the same time, from u to f.

d.(fr).2 = Turn the d and middle slices twice, in the direction of f to r.

u.(fr) = adjoin the middle slice to the top slice and it them from f to r.

========================================================

NxNxN very large cubes with multiple slice turns for N > 5

"Build" the moves from the perspective of looking either from UFR with the

middle edge rotating vertically or from DBL, likewise. Pad moves to the

left or right of the middle edge in the order in which they appear.

Enclose the moves in round parenthesis to demarcate a middle edge.

Add a padded 0 for any ommited slice not in a series of consecutive slices.

Repeat the same slice letter as many times as needed if it is in relative

motion. Always use all N terms when describing a move sequence.

There should never be more than N/2 terms in motion for a move sequence.

11x11x11 examples:

F00ff(u.r)00000

0000f(u.r)bb000

000ll(u.f)0r00R