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 |
|:-----------------------|----:|:------|-----:|:---------------------|-------:|------:|----------:|----:|------:|------:|----:|
| Spacetime Technologies |   2 | A0111 | 6489 | O-Ring               |   3    |   900 |   2700    |  25 | 41192 | 41200 |   8 |
| Steelpin Inc.          |   6 | A0115 | 5319 | Shielded Cable/ft.   |   1.1  | 17500 |  19250    |  30 | 41141 | 41152 |  11 |
| Steelpin Inc.          |   6 | A0123 | 4312 | Bolt-nut package     |   3.75 |  4250 |  15937.5  |  30 | 41146 | 41153 |   7 |
| Steelpin Inc.          |   6 | A0204 | 5319 | Shielded Cable/ft.   |   1.1  | 16500 |  18150    |  30 | 41167 | 41187 |  20 |
| Steelpin Inc.          |   6 | A0205 | 5677 | Side Panel           | 195    |   120 |  23400    |  30 | 41215 | 41226 |  11 |
| Steelpin Inc.          |   6 | A0207 | 4312 | Bolt-nut package     |   3.75 |  4200 |  15750    |  30 | 41153 | 41162 |   9 |
| Alum Sheeting          |   5 | A0223 | 4224 | Bolt-nut package     |   3.95 |  4500 |  17775    |  30 | 41197 | 41202 |   5 |
| Alum Sheeting          |   5 | A0433 | 5417 | Control Panel        | 255    |   500 | 127500    |  30 | 41202 | 41209 |   7 |
| Alum Sheeting          |   5 | A0443 | 1243 | Airframe fasteners   |   4.25 | 10000 |  42500    |  30 | 41129 | 41135 |   6 |
| Alum Sheeting          |   5 | A0446 | 5417 | Control Panel        | 255    |   406 | 103530    |  30 | 41153 | 41162 |   9 |
| Spacetime Technologies |   2 | A0533 | 9752 | Gasket               |   4.05 |  1500 |   6075    |  25 | 41172 | 41177 |   5 |
| Spacetime Technologies |   2 | A0555 | 6489 | O-Ring               |   3    |  1100 |   3300    |  25 | 41187 | 41192 |   5 |
| Spacetime Technologies |   2 | A0622 | 9752 | Gasket               |   4.05 |  1550 |   6277.5  |  25 | 41177 | 41187 |  10 |
| Spacetime Technologies |   2 | A0666 | 5125 | Shielded Cable/ft.   |   1.15 | 15000 |  17250    |  25 | 41183 | 41197 |  14 |
| Spacetime Technologies |   2 | A0777 | 6489 | O-Ring               |   3    |  1050 |   3150    |  25 | 41211 | 41223 |  12 |
| Spacetime Technologies |   2 | A1222 | 4111 | Bolt-nut package     |   3.55 |  4200 |  14910    |  25 | 41167 | 41197 |  30 |
| Durrable Products      |   3 | A1234 | 9399 | Gasket               |   3.65 |  1250 |   4562.5  |  45 | 41183 | 41188 |   5 |
| Durrable Products      |   3 | A1235 | 9399 | Gasket               |   3.65 |  1450 |   5292.5  |  45 | 41185 | 41190 |   5 |
| Durrable Products      |   3 | A1344 | 5454 | Control Panel        | 220    |   550 | 121000    |  45 | 41191 | 41196 |   5 |
| Durrable Products      |   3 | A1345 | 9399 | Gasket               |   3.65 |  1470 |   5365.5  |  45 | 41189 | 41194 |   5 |
| Durrable Products      |   3 | A1346 | 9399 | Gasket               |   3.65 |  1985 |   7245.25 |  45 | 41187 | 41193 |   6 |
| Spacetime Technologies |   2 | A1444 | 4111 | Bolt-nut package     |   3.55 |  4250 |  15087.5  |  25 | 41172 | 41192 |  20 |
| Spacetime Technologies |   2 | A1445 | 4111 | Bolt-nut package     |   3.55 |  4200 |  14910    |  25 | 41177 | 41207 |  30 |
| Spacetime Technologies |   2 | A1449 | 4111 | Bolt-nut package     |   3.55 |  4600 |  16330    |  25 | 41187 | 41201 |  14 |
| Durrable Products      |   3 | A1456 | 5454 | Control Panel        | 220    |   500 | 110000    |  45 | 41197 | 41202 |   5 |
| Durrable Products      |   3 | A1457 | 4569 | Bolt-nut package     |   3.5  |  3900 |  13650    |  45 | 41187 | 41192 |   5 |
| Durrable Products      |   3 | A1567 | 1369 | Airframe fasteners   |   4.2  | 15000 |  63000    |  45 | 41177 | 41182 |   5 |
| Manley Valve           |   7 | A2345 | 6431 | O-Ring               |   2.85 |  1250 |   3562.5  |  30 | 41187 | 41192 |   5 |
| Manley Valve           |   7 | A2356 | 7258 | Pressure Gauge       | 100.5  |    95 |   9547.5  |  30 | 41202 | 41211 |   9 |
| Manley Valve           |   7 | A2367 | 9977 | Panel Decal          |   1    |   525 |    525    |  30 | 41214 | 41220 |   6 |
| Manley Valve           |   7 | A2378 | 6431 | O-Ring               |   2.85 |  1350 |   3847.5  |  30 | 41183 | 41189 |   6 |
| Spacetime Technologies |   2 | A3467 | 4111 | Bolt-nut package     |   3.55 |  4800 |  17040    |  25 | 41157 | 41172 |  15 |
| Spacetime Technologies |   2 | A5689 | 4111 | Bolt-nut package     |   3.55 |  4585 |  16276.8  |  25 | 41162 | 41182 |  20 |
| Manley Valve           |   7 | A9821 | 6431 | O-Ring               |   2.85 |  1300 |   3705    |  30 | 41177 | 41183 |   6 |
| Manley Valve           |   7 | A9842 | 7258 | Pressure Gauge       | 100.5  |   100 |  10050    |  30 | 41197 | 41206 |   9 |
| Manley Valve           |   7 | A9865 | 9967 | Hatch Decal          |   0.85 |   550 |    467.5  |  30 | 41218 | 41224 |   6 |
| Manley Valve           |   7 | A9876 | 9955 | Door Decal           |   0.55 |   150 |     82.5  |  30 | 41214 | 41219 |   5 |
| Pylon Accessories      |   8 | A9999 | 6433 | O-Ring               |   2.95 |  1500 |   4425    |  15 | 41183 | 41192 |   9 |
| Alum Sheeting          |   5 | B0247 | 1243 | Airframe fasteners   |   4.25 |  9000 |  38250    |  30 | 41157 | 41164 |   7 |
| Steelpin Inc.          |   6 | B0445 | 4312 | Bolt-nut package     |   3.75 |  4150 |  15562.5  |  30 | 41155 | 41163 |   8 |
| Alum Sheeting          |   5 | B0447 | 5634 | Side Panel           | 185    |   150 |  27750    |  30 | 41207 | 41216 |   9 |
| Alum Sheeting          |   5 | B0479 | 5634 | Side Panel           | 185    |   140 |  25900    |  30 | 41211 | 41217 |   6 |
| Alum Sheeting          |   5 | B0567 | 1243 | Airframe fasteners   |   4.25 | 10500 |  44625    |  30 | 41192 | 41199 |   7 |
| Pylon Accessories      |   8 | B1111 | 9764 | Gasket               |   3.75 |  1980 |   7425    |  15 | 41172 | 41181 |   9 |
| Durrable Products      |   3 | B1234 | 7258 | Pressure Gauge       |  90    |   100 |   9000    |  45 | 41146 | 41149 |   3 |
| Durrable Products      |   3 | B1345 | 7258 | Pressure Gauge       |  90    |   120 |  10800    |  45 | 41157 | 41161 |   4 |
| Durrable Products      |   3 | B1468 | 1369 | Airframe fasteners   |   4.2  | 14000 |  58800    |  45 | 41179 | 41185 |   6 |
| Durrable Products      |   3 | B1589 | 5275 | Shielded Cable/ft.   |   1    | 25000 |  25000    |  45 | 41207 | 41212 |   5 |
| Durrable Products      |   3 | B1666 | 1369 | Airframe fasteners   |   4.2  | 10000 |  42000    |  45 | 41181 | 41186 |   5 |
| Fast-Tie Aerospace     |   4 | B2333 | 6321 | O-Ring               |   2.45 |  1300 |   3185    |  30 | 41146 | 41156 |  10 |
| Fast-Tie Aerospace     |   4 | B2345 | 6321 | O-Ring               |   2.45 |  1200 |   2940    |  30 | 41164 | 41175 |  11 |
| Fast-Tie Aerospace     |   4 | B2356 | 6321 | O-Ring               |   2.45 |  2500 |   6125    |  30 | 41177 | 41186 |   9 |
| Fast-Tie Aerospace     |   4 | B2367 | 6321 | O-Ring               |   2.45 |  1250 |   3062.5  |  30 | 41194 | 41203 |   9 |
| Fast-Tie Aerospace     |   4 | B2378 | 6321 | O-Ring               |   2.45 |  1500 |   3675    |  30 | 41207 | 41215 |   8 |
| Fast-Tie Aerospace     |   4 | B2498 | 5689 | Side Panel           | 175    |   150 |  26250    |  30 | 41214 | 41222 |   8 |
| Fast-Tie Aerospace     |   4 | B2499 | 7268 | Pressure Gauge       |  95    |   110 |  10450    |  30 | 41214 | 41225 |  11 |
| Fast-Tie Aerospace     |   4 | B2511 | 7268 | Pressure Gauge       |  95    |   105 |   9975    |  30 | 41218 | 41229 |  11 |
| Fast-Tie Aerospace     |   4 | B2519 | 5462 | Shielded Cable/ft.   |   1.05 | 22500 |  23625    |  30 | 41141 | 41147 |   6 |
| Fast-Tie Aerospace     |   4 | B2528 | 5689 | Side Panel           | 175    |   175 |  30625    |  30 | 41218 | 41228 |  10 |
| Fast-Tie Aerospace     |   4 | B2537 | 5462 | Shielded Cable/ft.   |   1.05 | 21500 |  22575    |  30 | 41136 | 41143 |   7 |
| Fast-Tie Aerospace     |   4 | B2566 | 5462 | Shielded Cable/ft.   |   1.05 | 23000 |  24150    |  30 | 41131 | 41136 |   5 |
| Steelpin Inc.          |   6 | B3022 | 5677 | Side Panel           | 195    |   110 |  21450    |  30 | 41218 | 41230 |  12 |
| Steelpin Inc.          |   6 | B3041 | 5234 | Electrical Connector |   1.65 |  4500 |   7425    |  30 | 41149 | 41157 |   8 |
| Steelpin Inc.          |   6 | B3042 | 5234 | Electrical Connector |   1.65 |  4750 |   7837.5  |  30 | 41157 | 41165 |   8 |
| Steelpin Inc.          |   6 | B3111 | 5234 | Electrical Connector |   1.65 |  4850 |   8002.5  |  30 | 41154 | 41163 |   9 |
| Steelpin Inc.          |   6 | B3222 | 8008 | Machined Valve       | 645    |   150 |  96750    |  30 | 41197 | 41208 |  11 |
| Steelpin Inc.          |   6 | B3333 | 8008 | Machined Valve       | 645    |   100 |  64500    |  30 | 41192 | 41203 |  11 |
| Fast-Tie Aerospace     |   4 | C0234 | 5166 | Electrical Connector |   1.25 |  5650 |   7062.5  |  30 | 41183 | 41188 |   5 |
| Fast-Tie Aerospace     |   4 | C0423 | 5689 | Side Panel           | 175    |   155 |  27125    |  30 | 41207 | 41216 |   9 |
| Fast-Tie Aerospace     |   4 | C0433 | 5462 | Shielded Cable/ft.   |   1.05 | 22500 |  23625    |  30 | 41146 | 41154 |   8 |
| Steelpin Inc.          |   6 | C0456 | 5677 | Side Panel           | 195    |   130 |  25350    |  30 | 41210 | 41220 |  10 |
| Steelpin Inc.          |   6 | C0467 | 8008 | Machined Valve       | 645    |   120 |  77400    |  30 | 41210 | 41217 |   7 |
| Steelpin Inc.          |   6 | C0589 | 5319 | Shielded Cable/ft.   |   1.1  | 18100 |  19910    |  30 | 41146 | 41157 |  11 |
| Manley Valve           |   7 | C1111 | 9955 | Door Decal           |   0.55 |   125 |     68.75 |  30 | 41218 | 41223 |   5 |
| Hulkey Fasteners       |   1 | C1212 | 1122 | Airframe fasteners   |   4.25 | 19500 |  82875    |  30 | 41126 | 41134 |   8 |
| Hulkey Fasteners       |   1 | C1313 | 3166 | Electrical Connector |   1.25 |  5600 |   7000    |  30 | 41146 | 41150 |   4 |
| Pylon Accessories      |   8 | C2211 | 9764 | Gasket               |   3.75 |  1850 |   6937.5  |  15 | 41177 | 41187 |  10 |
| Manley Valve           |   7 | C2222 | 7258 | Pressure Gauge       | 100.5  |    90 |   9045    |  30 | 41192 | 41199 |   7 |
| Hulkey Fasteners       |   1 | C2323 | 1122 | Airframe fasteners   |   4.25 | 15500 |  65875    |  30 | 41156 | 41164 |   8 |
| Hulkey Fasteners       |   1 | C2929 | 3166 | Electrical Connector |   1.25 |  5500 |   6875    |  30 | 41153 | 41158 |   5 |
| Hulkey Fasteners       |   1 | C3232 | 1122 | Airframe fasteners   |   4.25 | 18000 |  76500    |  30 | 41183 | 41190 |   7 |
| Manley Valve           |   7 | C3333 | 8148 | Machined Valve       | 655.5  |   125 |  81937.5  |  30 | 41192 | 41199 |   7 |
| Hulkey Fasteners       |   1 | C3434 | 1122 | Airframe fasteners   |   4.25 | 12500 |  53125    |  30 | 41157 | 41163 |   6 |
| Hulkey Fasteners       |   1 | C4545 | 1122 | Airframe fasteners   |   4.25 | 15000 |  63750    |  30 | 41160 | 41167 |   7 |
| Hulkey Fasteners       |   1 | C5656 | 1122 | Airframe fasteners   |   4.25 | 14500 |  61625    |  30 | 41180 | 41185 |   5 |
| Hulkey Fasteners       |   1 | C6765 | 5066 | Shielded Cable/ft.   |   0.95 | 25000 |  23750    |  30 | 41157 | 41164 |   7 |
| Hulkey Fasteners       |   1 | C7875 | 3166 | Electrical Connector |   1.25 |  5650 |   7062.5  |  30 | 41157 | 41162 |   5 |
| Hulkey Fasteners       |   1 | C8854 | 3166 | Electrical Connector |   1.25 |  5425 |   6781.25 |  30 | 41162 | 41167 |   5 |
| Hulkey Fasteners       |   1 | C8989 | 9966 | Hatch Decal          |   0.75 |   500 |    375    |  30 | 41146 | 41152 |   6 |
| Pylon Accessories      |   8 | D1111 | 9764 | Gasket               |   3.75 |  1800 |   6750    |  15 | 41180 | 41187 |   7 |
| Hulkey Fasteners       |   1 | D1212 | 5066 | Shielded Cable/ft.   |   0.95 | 17500 |  16625    |  30 | 41167 | 41174 |   7 |
| Hulkey Fasteners       |   1 | D2121 | 1122 | Airframe fasteners   |   4.25 | 17500 |  74375    |  30 | 41207 | 41216 |   9 |
| Hulkey Fasteners       |   1 | D3232 | 1122 | Airframe fasteners   |   4.25 | 17000 |  72250    |  30 | 41193 | 41201 |   8 |
| Pylon Accessories      |   8 | D3333 | 9764 | Gasket               |   3.75 |  1750 |   6562.5  |  15 | 41172 | 41177 |   5 |



label: H=F*G
L=K-J
labeled_formulas: H=F*G
L=K-J
output: {"Arithmetic-Relationship": ["H=F*G", "L=K-J"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_463348___xlsx_ea5050eb10c3f0eb0861d8121ae679ff67ee3647.xlsx___line_632