Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
|   A | B                                         |       C |   D | E     |     F |   G |     H |   I |     J |   K |    L |   M |   N |
|----:|:------------------------------------------|--------:|----:|:------|------:|----:|------:|----:|------:|----:|-----:|----:|----:|
|   1 | Air Freshner,spray,320ml, lemon           |   260   |   4 | btls  |  1040 |   1 |   260 |   1 |   260 |   1 |  260 |   1 | 260 |
|   3 | Battery,AA, 1.5V (Energizer)              |    35   |  16 | pcs   |   560 |  16 |   560 |   0 |     0 |   0 |    0 |   0 |   0 |
|   4 | Battery,C, 1.5V (Energizer)               |    40   |  16 | pcs   |   640 |   8 |   320 |   8 |   320 |   0 |    0 |   0 |   0 |
|   5 | Binder Clip ,3/4 (small)                  |    45   |   4 | bxs   |   180 |   2 |    90 |   2 |    90 |   0 |    0 |   0 |   0 |
|   6 | Book Paper,long,70g/m2                    |   280   |  10 | reams |  2800 |   0 |     0 |   5 |  1400 |   5 | 1400 |   0 |   0 |
|   7 | Book Paper,short,70g/m2                   |   250   |   5 | reams |  1250 |   0 |     0 |   0 |     0 |   5 | 1250 |   0 |   0 |
|   8 | Certificate Holder,short                  |    70   |  30 | pcs   |  2100 |  30 |  2100 |   0 |     0 |   0 |    0 |   0 |   0 |
|  10 | Dishwashing Liquid                        |   105   |   4 | btls  |   420 |   1 |   105 |   1 |   105 |   1 |  105 |   1 | 105 |
|  11 | Door Mat                                  |    60   |   4 | pcs   |   240 |   1 |    60 |   1 |    60 |   1 |   60 |   1 |  60 |
|  12 | Envelop, Brown, Long                      |     7   |  40 | pcs   |   280 |  20 |   140 |  20 |   140 |   0 |    0 |   0 |   0 |
|  13 | Envelope, Expanding w/ garter, blue, long |    35   |  40 | pcs   |  1400 |  40 |  1400 |   0 |     0 |   0 |    0 |   0 |   0 |
|  14 | Eraser, White B50 (Steadler)              |    62   |   1 | pcs   |    62 |   1 |    62 |   0 |     0 |   0 |    0 |   0 |   0 |
|  15 | Extension wire,10m, 4 outlets             |  1200   |   2 | pcs   |  2400 |   0 |     0 |   1 |  1200 |   1 | 1200 |   0 |   0 |
|  16 | Fastener Plastic Coated                   |    55   |   4 | bxs   |   220 |   2 |   110 |   0 |     0 |   2 |  110 |   0 |   0 |
|  17 | Feather Duster                            |   105   |   1 | pcs   |   105 |   0 |     0 |   1 |   105 |   0 |    0 |   0 |   0 |
|  18 | Filling Cabinet, locker style             | 16000   |   1 | pc    | 16000 |   0 |     0 |   1 | 16000 |   0 |    0 |   0 |   0 |
|  19 | Folder,Ivory, Long                        |     7   |  40 | pcs   |   280 |  20 |   140 |   0 |     0 |  20 |  140 |   0 |   0 |
|  20 | Folding Divider                           | 10000   |   1 | pc    | 10000 |   1 | 10000 |   0 |     0 |   0 |    0 |   0 |   0 |
|  21 | Frixion Pen, Black                        |   900   |   1 | bxs   |   900 |   0 |     0 |   1 |   900 |   0 |    0 |   0 |   0 |
|  22 | Frixion Pen, Blue                         |   900   |   1 | bxs   |   900 |   0 |     0 |   0 |     0 |   1 |  900 |   0 |   0 |
|  24 | Glass Cleaner, 500ml.w/ spray             |   260   |   2 | btls  |   520 |   1 |   260 |   0 |     0 |   1 |  260 |   0 |   0 |
|  25 | Gun Tacker -T 50, Heavy duty              |  3700   |   1 | pc    |  3700 |   0 |     0 |   0 |     0 |   1 | 3700 |   0 |   0 |
|  26 | Hand Santizer                             |   170   |   2 | btls  |   340 |   1 |   170 |   0 |     0 |   1 |  170 |   0 |   0 |
|  27 | In and Out Tray, 3 Layer                  |   850   |   1 | pcs   |   850 |   0 |     0 |   1 |   850 |   0 |    0 |   0 |   0 |
|  28 | Ink refill for Parker pen, black          |   205   |   4 | pcs   |   820 |   1 |   205 |   1 |   205 |   1 |  205 |   1 | 205 |
|  29 | Mono Block Chair w/o arm                  |   605   |  14 | pcs   |  8470 |   0 |     0 |   0 |     0 |  14 | 8470 |   0 |   0 |
|  30 | Office Table, ordinary                    |  3500   |   1 | pcs   |  3500 |   1 |  3500 |   0 |     0 |   0 |    0 |   0 |   0 |
|  31 | Paper Clip Plastic Coated, Big            |    45   |   4 | bxs   |   180 |   4 |   180 |   0 |     0 |   0 |    0 |   0 |   0 |
|  32 | Paper Clip Plastic Coated, Small          |    35   |   4 | bxs   |   140 |   4 |   140 |   0 |     0 |   0 |    0 |   0 |   0 |
|  33 | Parker Pen (black)                        |   780   |   4 | pcs   |  3120 |   1 |   780 |   1 |   780 |   1 |  780 |   1 | 780 |
|  34 | Pencil (Mongol)                           |   102   |   2 | bxs   |   204 |   0 |     0 |   0 |     0 |   2 |  204 |   0 |   0 |
|  35 | Permanent Marker, Black,Blue              |    37.5 |  10 | pcs   |   375 |   0 |     0 |   0 |     0 |  10 |  375 |   0 |   0 |
|  36 | Photo Paper, High Gloss,A4, 20 Sheets     |   175   |   2 | pks   |   350 |   0 |     0 |   0 |     0 |   2 |  350 |   0 |   0 |
|  37 | Plastic Envelope, Long                    |    15   |  40 | pcs   |   600 |   0 |     0 |  40 |   600 |   0 |    0 |   0 |   0 |
|  38 | Pledge,Furniture, Polish,250ml            |   300   |   2 | btls  |   600 |   1 |   300 |   0 |     0 |   1 |  300 |   0 |   0 |
|  40 | Pressboard Folder, Long, Blue             |    30   |  40 | pcs   |  1200 |  10 |   300 |   0 |     0 |  30 |  900 |   0 |   0 |
|  41 | Pressboard Folder, Long,Green             |    30   |  40 | pcs   |  1200 |  10 |   300 |   0 |     0 |  30 |  900 |   0 |   0 |
|  43 | Record Book, Regular size, 300p           |   105   |   2 | pcs   |   210 |   0 |     0 |   2 |   210 |   0 |    0 |   0 |   0 |
|  44 | Record Book,Regular size, 150p            |    85   |   6 | pcs   |   510 |   0 |     0 |   3 |   255 |   3 |  255 |   0 |   0 |
|  45 | Ruler, 24''                               |    80   |   2 | pcs   |   160 |   0 |     0 |   2 |   160 |   0 |    0 |   0 |   0 |
|  46 | Scissors Stainless #8                     |    96   |   2 | pcs   |   192 |   0 |     0 |   0 |     0 |   2 |  192 |   0 |   0 |
|  48 | Signpen Black, 1.0 , (High-techpoint)     |  1100   |   1 | bxs   |  1100 |   1 |  1100 |   0 |     0 |   0 |    0 |   0 |   0 |
|  49 | Signpen, Gel pen, 0.5, green              |   470   |   2 | bxs   |   940 |   0 |     0 |   2 |   940 |   0 |    0 |   0 |   0 |
|  50 | Signpen,Gel pen, 0.5, blue                |   470   |   2 | bxs   |   940 |   0 |     0 |   0 |     0 |   2 |  940 |   0 |   0 |
|  51 | Specialty Paper Long,  Beige              |    79   |  10 | pks   |   790 |   0 |     0 |  10 |   790 |   0 |    0 |   0 |   0 |
|  52 | Specialty Paper Short,  Cream             |    66   |  10 | pks   |   660 |   0 |     0 |  10 |   660 |   0 |    0 |   0 |   0 |
|  53 | Sponge (Scotch bright)                    |    50   |   4 | pcs   |   200 |   1 |    50 |   1 |    50 |   1 |   50 |   1 |  50 |
|  54 | Stabilo                                   |    39   |   4 | pcs   |   156 |   0 |     0 |   0 |     0 |   4 |  156 |   0 |   0 |
|  55 | Stamp (received and date)                 |   275   |   1 | pc    |   275 |   1 |   275 |   0 |     0 |   0 |    0 |   0 |   0 |
|  56 | Staple Wire #35                           |    55   |   4 | pcs   |   220 |   1 |    55 |   1 |    55 |   1 |   55 |   1 |  55 |
|  57 | Swivel Chair                              |  5000   |   1 | pcs   |  5000 |   1 |  5000 |   0 |     0 |   0 |    0 |   0 |   0 |
|  59 | Table,Foldable, Black (6 ft)              |  7000   |   1 | pcs   |  7000 |   0 |     0 |   0 |     0 |   1 | 7000 |   0 |   0 |
|  60 | Tape, masking,  1"                        |    42   |   8 | rolls |   336 |   0 |     0 |   4 |   168 |   4 |  168 |   0 |   0 |
|  65 | Wall Clock                                |   600   |   1 | pc    |   600 |   1 |   600 |   0 |     0 |   0 |    0 |   0 |   0 |
|  66 | Zonrox Bleach                             |   260   |   1 | gal   |   260 |   1 |   260 |   0 |     0 |   0 |    0 |   0 |   0 |



label: F=D*C
H=G*C
J=I*C
L=K*C
N=M*C
labeled_formulas: F=D*C
H=G*C
J=I*C
L=K*C
N=M*C
N=H*M
N=J*M
N=L*M
N=(C*G)*M
N=(C*I)*M
N=(C*K)*M
N=(G*H)*M
M=(G*I)*K
N=(G*I)*L
N=(G*J)*K
N=(G*J)*M
N=(G*L)*M
N=(H*I)*K
N=(H*I)*M
N=(H*K)*M
N=(I*J)*M
N=(I*L)*M
N=(J*K)*M
N=(K*L)*M
output: {"Arithmetic-Relationship": ["F=D*C", "H=G*C", "J=I*C", "L=K*C", "N=M*C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_748910___xlsx_219d3299044d1fd9f61cd38a3be7b2b3bfbdc03f.xlsx___line_214