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 |
|----:|----:|----:|----:|----:|----:|----:|
|   1 |   0 |   0 |   0 |   0 |   1 |   1 |
|   2 |   0 |   0 |   1 |   1 |   1 |   2 |
|   3 |   0 |   1 |   1 |   2 |   1 |   3 |
|   4 |   1 |   1 |   1 |   3 |   1 |   4 |
|   5 |   1 |   1 |   2 |   4 |   1 |   5 |
|   6 |   1 |   2 |   2 |   5 |   1 |   6 |
|   7 |   1 |   2 |   3 |   6 |   1 |   7 |
|   8 |   1 |   2 |   3 |   6 |   2 |   8 |
|   9 |   1 |   2 |   4 |   7 |   2 |   9 |
|  10 |   2 |   2 |   4 |   8 |   2 |  10 |
|  11 |   2 |   3 |   4 |   9 |   2 |  11 |
|  12 |   2 |   3 |   5 |  10 |   2 |  12 |
|  13 |   2 |   3 |   5 |  10 |   3 |  13 |
|  14 |   2 |   4 |   5 |  11 |   3 |  14 |
|  15 |   2 |   4 |   6 |  12 |   3 |  15 |
|  16 |   2 |   4 |   7 |  13 |   3 |  16 |
|  17 |   3 |   4 |   7 |  14 |   3 |  17 |
|  18 |   3 |   5 |   7 |  15 |   3 |  18 |
|  19 |   3 |   5 |   8 |  16 |   3 |  19 |
|  20 |   3 |   5 |   8 |  16 |   4 |  20 |
|  21 |   3 |   5 |   9 |  17 |   4 |  21 |
|  22 |   3 |   6 |   9 |  18 |   4 |  22 |
|  23 |   3 |   6 |   9 |  18 |   5 |  23 |
|  24 |   4 |   6 |   9 |  19 |   5 |  24 |
|  25 |   4 |   6 |  10 |  20 |   5 |  25 |
|  26 |   4 |   7 |  11 |  22 |   5 |  27 |
|  27 |   4 |   7 |  11 |  22 |   5 |  27 |
|  28 |   4 |   7 |  11 |  22 |   6 |  28 |
|  29 |   4 |   7 |  12 |  23 |   6 |  29 |
|  30 |   5 |   7 |  12 |  24 |   6 |  30 |
|  31 |   5 |   8 |  12 |  25 |   6 |  31 |
|  32 |   5 |   8 |  13 |  26 |   6 |  32 |
|  33 |   5 |   8 |  13 |  26 |   7 |  33 |
|  34 |   5 |   9 |  13 |  27 |   7 |  34 |
|  35 |   5 |   9 |  14 |  28 |   7 |  35 |
|  36 |   5 |   9 |  15 |  29 |   7 |  36 |
|  37 |   6 |   9 |  15 |  30 |   7 |  37 |
|  38 |   6 |  10 |  15 |  31 |   7 |  38 |
|  39 |   6 |  10 |  16 |  32 |   7 |  39 |
|  40 |   6 |  10 |  16 |  32 |   8 |  40 |
|  41 |   6 |  10 |  17 |  33 |   8 |  41 |
|  42 |   6 |  11 |  17 |  34 |   8 |  42 |
|  43 |   6 |  11 |  17 |  34 |   9 |  43 |
|  44 |   7 |  11 |  17 |  35 |   9 |  44 |
|  45 |   7 |  11 |  18 |  36 |   9 |  45 |
|  46 |   7 |  12 |  18 |  37 |   9 |  46 |
|  47 |   7 |  12 |  19 |  38 |   9 |  47 |
|  48 |   7 |  12 |  19 |  38 |  10 |  48 |
|  49 |   7 |  12 |  20 |  39 |  10 |  49 |
|  50 |   8 |  12 |  20 |  40 |  10 |  50 |
|  51 |   8 |  13 |  20 |  41 |  10 |  51 |
|  52 |   8 |  13 |  21 |  42 |  10 |  52 |
|  53 |   8 |  13 |  21 |  42 |  11 |  53 |
|  54 |   8 |  14 |  21 |  43 |  11 |  54 |
|  55 |   8 |  14 |  22 |  44 |  11 |  55 |
|  56 |   8 |  14 |  23 |  45 |  11 |  56 |
|  57 |   9 |  14 |  23 |  46 |  11 |  57 |
|  58 |   9 |  15 |  23 |  47 |  11 |  58 |
|  59 |   9 |  15 |  24 |  48 |  11 |  59 |
|  60 |   9 |  15 |  24 |  48 |  12 |  60 |
|  61 |   9 |  15 |  25 |  49 |  12 |  61 |
|  62 |   9 |  16 |  25 |  50 |  12 |  62 |
|  63 |   9 |  16 |  25 |  50 |  13 |  63 |
|  64 |  10 |  16 |  25 |  51 |  13 |  64 |
|  65 |  10 |  16 |  26 |  52 |  13 |  65 |
|  66 |  10 |  17 |  26 |  53 |  13 |  66 |
|  67 |  10 |  17 |  27 |  54 |  13 |  67 |
|  68 |  10 |  17 |  27 |  54 |  14 |  68 |
|  69 |  10 |  17 |  28 |  55 |  14 |  69 |
|  70 |  11 |  17 |  28 |  56 |  14 |  70 |
|  71 |  11 |  18 |  28 |  57 |  14 |  71 |
|  72 |  11 |  18 |  29 |  58 |  14 |  72 |
|  73 |  11 |  18 |  29 |  58 |  15 |  73 |
|  74 |  11 |  19 |  29 |  59 |  15 |  74 |
|  75 |  11 |  19 |  30 |  60 |  15 |  75 |
|  76 |  11 |  19 |  31 |  61 |  15 |  76 |
|  77 |  12 |  19 |  31 |  62 |  15 |  77 |
|  78 |  12 |  20 |  31 |  63 |  15 |  78 |
|  79 |  12 |  20 |  32 |  64 |  15 |  79 |
|  80 |  12 |  20 |  32 |  64 |  16 |  80 |
|  81 |  12 |  20 |  33 |  65 |  16 |  81 |
|  82 |  12 |  21 |  33 |  66 |  16 |  82 |
|  83 |  12 |  21 |  33 |  66 |  17 |  83 |
|  84 |  13 |  21 |  33 |  67 |  17 |  84 |
|  85 |  13 |  21 |  34 |  68 |  17 |  85 |
|  86 |  13 |  22 |  34 |  69 |  17 |  86 |
|  87 |  13 |  22 |  35 |  70 |  17 |  87 |
|  88 |  13 |  22 |  35 |  70 |  18 |  88 |
|  89 |  13 |  22 |  36 |  71 |  18 |  89 |
|  90 |  14 |  22 |  36 |  72 |  18 |  90 |
|  91 |  14 |  23 |  36 |  73 |  18 |  91 |
|  92 |  14 |  23 |  37 |  74 |  18 |  92 |
|  93 |  14 |  23 |  37 |  74 |  19 |  93 |
|  94 |  14 |  24 |  37 |  75 |  19 |  94 |
|  95 |  14 |  24 |  38 |  76 |  19 |  95 |
|  96 |  14 |  24 |  39 |  77 |  19 |  96 |
|  97 |  15 |  24 |  39 |  78 |  19 |  97 |
|  98 |  15 |  25 |  39 |  79 |  19 |  98 |
|  99 |  15 |  25 |  40 |  80 |  19 |  99 |
| 100 |  15 |  25 |  40 |  80 |  20 | 100 |
| 101 |  15 |  25 |  41 |  81 |  20 | 101 |
| 102 |  15 |  26 |  41 |  82 |  20 | 102 |
| 103 |  15 |  26 |  41 |  82 |  21 | 103 |
| 104 |  16 |  26 |  41 |  83 |  21 | 104 |
| 105 |  16 |  26 |  42 |  84 |  21 | 105 |
| 106 |  16 |  27 |  42 |  85 |  21 | 106 |
| 107 |  16 |  27 |  43 |  86 |  21 | 107 |
| 108 |  16 |  27 |  43 |  86 |  22 | 108 |
| 109 |  16 |  27 |  44 |  87 |  22 | 109 |
| 110 |  17 |  27 |  44 |  88 |  22 | 110 |
| 111 |  17 |  28 |  44 |  89 |  22 | 111 |
| 112 |  17 |  28 |  45 |  90 |  22 | 112 |
| 113 |  17 |  28 |  45 |  90 |  23 | 113 |
| 114 |  17 |  29 |  45 |  91 |  23 | 114 |
| 115 |  17 |  29 |  46 |  92 |  23 | 115 |
| 116 |  17 |  29 |  47 |  93 |  23 | 116 |
| 117 |  18 |  29 |  47 |  94 |  23 | 117 |
| 118 |  18 |  30 |  47 |  95 |  23 | 118 |
| 119 |  18 |  30 |  48 |  96 |  23 | 119 |
| 120 |  18 |  30 |  48 |  96 |  24 | 120 |
| 121 |  18 |  30 |  49 |  97 |  24 | 121 |
| 122 |  18 |  31 |  49 |  98 |  24 | 122 |
| 123 |  18 |  31 |  49 |  98 |  25 | 123 |
| 124 |  19 |  31 |  49 |  99 |  25 | 124 |
| 125 |  19 |  31 |  50 | 100 |  25 | 125 |
| 126 |  19 |  32 |  50 | 101 |  25 | 126 |
| 127 |  19 |  32 |  51 | 102 |  25 | 127 |
| 128 |  19 |  32 |  51 | 102 |  26 | 128 |
| 129 |  19 |  32 |  52 | 103 |  26 | 129 |
| 130 |  20 |  32 |  52 | 104 |  26 | 130 |
| 131 |  20 |  33 |  52 | 105 |  26 | 131 |
| 132 |  20 |  33 |  53 | 106 |  26 | 132 |
| 133 |  20 |  33 |  53 | 106 |  27 | 133 |
| 134 |  20 |  34 |  53 | 107 |  27 | 134 |
| 135 |  20 |  34 |  54 | 108 |  27 | 135 |
| 136 |  20 |  34 |  55 | 109 |  27 | 136 |
| 137 |  21 |  34 |  55 | 110 |  27 | 137 |
| 138 |  21 |  35 |  55 | 111 |  27 | 138 |
| 139 |  21 |  35 |  56 | 112 |  27 | 139 |
| 140 |  21 |  35 |  56 | 112 |  28 | 140 |
| 141 |  21 |  35 |  57 | 113 |  28 | 141 |
| 142 |  21 |  36 |  57 | 114 |  28 | 142 |
| 143 |  21 |  36 |  57 | 114 |  29 | 143 |
| 144 |  22 |  36 |  57 | 115 |  29 | 144 |
| 145 |  22 |  36 |  58 | 116 |  29 | 145 |
| 146 |  22 |  37 |  58 | 117 |  29 | 146 |
| 147 |  22 |  37 |  59 | 118 |  29 | 147 |
| 148 |  22 |  37 |  59 | 118 |  30 | 148 |
| 149 |  22 |  37 |  60 | 119 |  30 | 149 |
| 150 |  23 |  37 |  60 | 120 |  30 | 150 |
| 151 |  23 |  38 |  60 | 121 |  30 | 151 |
| 152 |  23 |  38 |  61 | 122 |  30 | 152 |
| 153 |  23 |  38 |  61 | 122 |  31 | 153 |
| 154 |  23 |  39 |  61 | 123 |  31 | 154 |
| 155 |  23 |  39 |  62 | 124 |  31 | 155 |
| 156 |  23 |  39 |  63 | 125 |  31 | 156 |
| 157 |  24 |  39 |  63 | 126 |  31 | 157 |
| 158 |  24 |  40 |  63 | 127 |  31 | 158 |
| 159 |  24 |  40 |  64 | 128 |  31 | 159 |
| 160 |  24 |  40 |  64 | 128 |  32 | 160 |
| 161 |  24 |  40 |  65 | 129 |  32 | 161 |
| 162 |  24 |  41 |  65 | 130 |  32 | 162 |
| 163 |  24 |  41 |  65 | 130 |  33 | 163 |
| 164 |  25 |  41 |  65 | 131 |  33 | 164 |
| 165 |  25 |  41 |  66 | 132 |  33 | 165 |
| 166 |  25 |  42 |  66 | 133 |  33 | 166 |
| 167 |  25 |  42 |  67 | 134 |  33 | 167 |
| 168 |  25 |  42 |  67 | 134 |  34 | 168 |
| 169 |  25 |  42 |  68 | 135 |  34 | 169 |
| 170 |  26 |  42 |  68 | 136 |  34 | 170 |
| 171 |  26 |  43 |  68 | 137 |  34 | 171 |
| 172 |  26 |  43 |  69 | 138 |  34 | 172 |
| 173 |  26 |  43 |  69 | 138 |  35 | 173 |
| 174 |  26 |  44 |  69 | 139 |  35 | 174 |
| 175 |  26 |  44 |  70 | 140 |  35 | 175 |
| 176 |  26 |  44 |  71 | 141 |  35 | 176 |
| 177 |  27 |  44 |  71 | 142 |  35 | 177 |
| 178 |  27 |  45 |  71 | 143 |  35 | 178 |
| 179 |  27 |  45 |  72 | 144 |  35 | 179 |
| 180 |  27 |  45 |  72 | 144 |  36 | 180 |
| 181 |  27 |  45 |  73 | 145 |  36 | 181 |
| 182 |  27 |  46 |  73 | 146 |  36 | 182 |
| 183 |  27 |  46 |  73 | 146 |  37 | 183 |
| 184 |  28 |  46 |  73 | 147 |  37 | 184 |
| 185 |  28 |  46 |  74 | 148 |  37 | 185 |
| 186 |  28 |  47 |  74 | 149 |  37 | 186 |
| 187 |  28 |  47 |  75 | 150 |  37 | 187 |
| 188 |  28 |  47 |  75 | 150 |  38 | 188 |
| 189 |  28 |  47 |  76 | 151 |  38 | 189 |
| 190 |  29 |  47 |  76 | 152 |  38 | 190 |
| 191 |  29 |  48 |  76 | 153 |  38 | 191 |
| 192 |  29 |  48 |  77 | 154 |  38 | 192 |
| 193 |  29 |  48 |  77 | 154 |  39 | 193 |
| 194 |  29 |  49 |  77 | 155 |  39 | 194 |
| 195 |  29 |  49 |  78 | 156 |  39 | 195 |
| 196 |  29 |  49 |  79 | 157 |  39 | 196 |
| 197 |  30 |  49 |  79 | 158 |  39 | 197 |
| 198 |  30 |  50 |  79 | 159 |  39 | 198 |
| 199 |  30 |  50 |  80 | 160 |  39 | 199 |
| 200 |  30 |  50 |  80 | 160 |  40 | 200 |
| 201 |  30 |  50 |  81 | 161 |  40 | 201 |
| 202 |  30 |  51 |  81 | 162 |  40 | 202 |
| 203 |  30 |  51 |  81 | 162 |  41 | 203 |
| 204 |  31 |  51 |  81 | 163 |  41 | 204 |
| 205 |  31 |  51 |  82 | 164 |  41 | 205 |
| 206 |  31 |  52 |  82 | 165 |  42 | 207 |
| 207 |  31 |  52 |  83 | 166 |  41 | 207 |
| 208 |  31 |  52 |  83 | 166 |  42 | 208 |
| 209 |  31 |  52 |  84 | 167 |  42 | 209 |
| 210 |  32 |  52 |  84 | 168 |  42 | 210 |
| 211 |  32 |  53 |  84 | 169 |  42 | 211 |
| 212 |  32 |  53 |  85 | 170 |  42 | 212 |
| 213 |  32 |  53 |  85 | 170 |  43 | 213 |
| 214 |  32 |  54 |  85 | 171 |  43 | 214 |
| 215 |  32 |  54 |  86 | 172 |  43 | 215 |
| 216 |  32 |  54 |  87 | 173 |  43 | 216 |
| 217 |  33 |  54 |  87 | 174 |  43 | 217 |
| 218 |  33 |  55 |  87 | 175 |  43 | 218 |
| 219 |  33 |  55 |  88 | 176 |  43 | 219 |
| 220 |  33 |  55 |  88 | 176 |  44 | 220 |
| 221 |  33 |  55 |  89 | 177 |  44 | 221 |
| 222 |  33 |  56 |  89 | 178 |  44 | 222 |
| 223 |  33 |  56 |  89 | 178 |  45 | 223 |
| 224 |  34 |  56 |  89 | 179 |  45 | 224 |
| 225 |  34 |  56 |  90 | 180 |  45 | 225 |
| 226 |  34 |  57 |  90 | 181 |  45 | 226 |
| 227 |  34 |  57 |  91 | 182 |  45 | 227 |
| 228 |  34 |  57 |  91 | 182 |  46 | 228 |
| 229 |  34 |  57 |  92 | 183 |  46 | 229 |
| 230 |  35 |  57 |  92 | 184 |  46 | 230 |
| 231 |  35 |  58 |  92 | 185 |  46 | 231 |
| 232 |  35 |  58 |  93 | 186 |  46 | 232 |
| 233 |  35 |  58 |  93 | 186 |  47 | 233 |
| 234 |  35 |  59 |  93 | 187 |  47 | 234 |
| 235 |  35 |  59 |  94 | 188 |  47 | 235 |
| 236 |  35 |  59 |  95 | 189 |  47 | 236 |
| 237 |  36 |  59 |  95 | 190 |  47 | 237 |
| 238 |  36 |  60 |  95 | 191 |  47 | 238 |
| 239 |  36 |  60 |  96 | 192 |  47 | 239 |
| 240 |  36 |  60 |  96 | 192 |  48 | 240 |
| 241 |  36 |  60 |  97 | 193 |  48 | 241 |
| 242 |  36 |  61 |  97 | 194 |  48 | 242 |
| 243 |  36 |  61 |  97 | 194 |  49 | 243 |
| 244 |  37 |  61 |  97 | 195 |  49 | 244 |
| 245 |  37 |  61 |  98 | 196 |  49 | 245 |
| 246 |  37 |  62 |  98 | 197 |  49 | 246 |
| 247 |  37 |  62 |  99 | 198 |  49 | 247 |
| 248 |  37 |  62 |  99 | 198 |  50 | 248 |
| 249 |  37 |  62 | 100 | 199 |  50 | 249 |
| 250 |  38 |  62 | 100 | 200 |  50 | 250 |
| 251 |  38 |  63 | 100 | 201 |  50 | 251 |
| 252 |  38 |  63 | 101 | 202 |  50 | 252 |
| 253 |  38 |  63 | 101 | 202 |  51 | 253 |
| 254 |  38 |  64 | 101 | 203 |  51 | 254 |
| 255 |  38 |  64 | 102 | 204 |  51 | 255 |
| 256 |  38 |  64 | 103 | 205 |  51 | 256 |
| 257 |  39 |  64 | 103 | 206 |  51 | 257 |
| 258 |  39 |  65 | 103 | 207 |  51 | 258 |
| 259 |  39 |  65 | 104 | 208 |  51 | 259 |
| 260 |  39 |  65 | 104 | 208 |  52 | 260 |
| 261 |  39 |  65 | 105 | 209 |  52 | 261 |
| 262 |  39 |  66 | 105 | 210 |  52 | 262 |
| 263 |  39 |  66 | 105 | 210 |  53 | 263 |
| 264 |  40 |  66 | 105 | 211 |  53 | 264 |
| 265 |  40 |  66 | 106 | 212 |  53 | 265 |



label: G=E+F
E=B+C+D
labeled_formulas: G=E+F
E=B+C+D
output: {"Arithmetic-Relationship": ["G=E+F", "E=B+C+D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_577830___xlsx_9871ade003459f2ff845fd05b95b962466666d31.xlsx___line_414