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 |
|:--------------------------------------------------|-----:|----:|-----:|----:|----:|----:|----:|
| AKRON, UNIVERSITY OF                              |  274 | 170 |  444 |   6 |   4 |   2 |   0 |
| ALBANY LAW SCHOOL OF UNION UNIVERSITY             |  420 |  46 |  466 |   9 |   0 |   9 |   0 |
| AMERICAN UNIVERSITY                               | 1117 | 250 | 1367 | 199 | 175 |  24 |   0 |
| APPALACHIAN SCHOOL OF LAW                         |  153 |   2 |  155 |   5 |   0 |   5 |   0 |
| ARIZONA SUMMIT LAW SCHOOL                         |  476 | 313 |  789 |   0 |   0 |   0 |   0 |
| ARIZONA, UNIVERSITY OF                            |  379 |   0 |  379 |  58 |  38 |  20 |   0 |
| ARKANSAS, LITTLE ROCK, UNIVERSITY OF              |  306 | 118 |  424 |   0 |   0 |   0 |   0 |
| AVE MARIA SCHOOL OF LAW                           |  267 |   2 |  269 |   0 |   0 |   0 |   0 |
| BALTIMORE, UNIVERSITY OF                          |  567 | 297 |  864 |  70 |  70 |   0 |   0 |
| BARRY UNIVERSITY                                  |  517 | 265 |  782 |   0 |   0 |   0 |   0 |
| BAYLOR UNIVERSITY                                 |  376 |   6 |  382 |   0 |   0 |   0 |   0 |
| BELMONT UNIVERSITY                                |  252 |   0 |  252 |   0 |   0 |   0 |   0 |
| BOSTON COLLEGE                                    |  698 |   0 |  698 |  19 |  19 |   0 |   0 |
| BRIGHAM YOUNG UNIVERSITY                          |  394 |  12 |  406 |   0 |   0 |   0 |   0 |
| BROOKLYN LAW SCHOOL                               |  881 | 238 | 1119 |  22 |  22 |   0 |   0 |
| BUFFALO-SUNY, UNIVERSITY OF                       |  552 | 142 |  694 |   9 |   9 |   0 |   0 |
| CALIFORNIA WESTERN SCHOOL OF LAW                  |  525 |   4 |  529 |  74 |  66 |   8 |   0 |
| CALIFORNIA-BERKELEY, UNIVERSITY OF                |  890 |   0 |  890 | 289 | 243 |  46 |   0 |
| CALIFORNIA-DAVIS, UNIVERSITY OF                   |  513 |   2 |  515 |  55 |  55 |   0 |   0 |
| CALIFORNIA-HASTINGS, UNIVERSITY OF                |  931 |   0 |  931 |  70 |  36 |  34 |   0 |
| CALIFORNIA-IRVINE, UNIVERSITY OF                  |  326 |   0 |  326 |   0 |   0 |   0 |   0 |
| CALIFORNIA-LOS ANGELES, UNIVERSITY OF             |  992 |  21 | 1013 | 179 | 165 |  14 |   0 |
| CAMPBELL UNIVERSITY                               |  421 | 184 |  605 |   2 |   0 |   2 |   0 |
| CAPITAL UNIVERSITY                                |  291 |  75 |  366 |  13 |   7 |   6 |   0 |
| CARDOZO SCHOOL OF LAW, YESHIVA UNIVERSITY         |  947 |   1 |  948 |  89 |  55 |  34 |   0 |
| CASE WESTERN RESERVE UNIVERSITY                   |  397 | 164 |  561 | 115 |  96 |  19 |   0 |
| CATHOLIC UNIVERSITY OF AMERICA                    |  291 |  29 |  320 |   9 |   4 |   5 |   0 |
| CHAPMAN UNIVERSITY                                |  444 |  92 |  536 |  53 |  53 |   0 |   0 |
| CHARLESTON SCHOOL OF LAW                          |  362 | 310 |  672 |   0 |   0 |   0 |   0 |
| CHARLOTTE SCHOOL OF LAW                           |  957 |   0 |  957 |   9 |   9 |   0 |   0 |
| CHICAGO, UNIVERSITY OF                            |  604 | 107 |  711 |  92 |  92 |   0 |   0 |
| CHICAGO-KENT COLLEGE OF LAW-IIT                   |  692 |   0 |  692 | 124 | 124 |   0 |   0 |
| CINCINNATI, UNIVERSITY OF                         |  293 |   5 |  298 |  11 |  11 |   0 |   0 |
| CITY UNIVERSITY OF NEW YORK                       |  322 |  91 |  413 |   0 |   0 |   0 |   0 |
| CLEVELAND STATE UNIVERSITY                        |  314 |   0 |  314 |  38 |  12 |  26 |   0 |
| COLORADO, UNIVERSITY OF                           |  509 |   0 |  509 |   0 |   0 |   0 |   0 |
| COLUMBIA UNIVERSITY                               | 1170 | 115 | 1285 | 284 | 284 |   0 |   0 |
| CORNELL UNIVERSITY                                |  595 |   7 |  602 |  92 |  92 |   0 |   0 |
| CREIGHTON UNIVERSITY                              |  354 |   0 |  354 |   0 |   0 |   0 |   0 |
| DAYTON, UNIVERSITY OF                             |  276 | 138 |  414 |  16 |  16 |   0 |   0 |
| DENVER, UNIVERSITY OF                             |  725 | 120 |  845 | 237 |  68 | 169 |   0 |
| DEPAUL UNIVERSITY                                 |  642 |  92 |  734 |  38 |  34 |   4 |   0 |
| DETROIT MERCY, UNIVERSITY OF                      |  431 | 144 |  575 |   0 |   0 |   0 |   0 |
| DISTRICT OF COLUMBIA, UNIVERSITY OF               |  162 |   8 |  170 |   6 |   6 |   0 |   0 |
| DRAKE UNIVERSITY                                  |  325 |  10 |  335 |   7 |   5 |   2 |   0 |
| DUKE UNIVERSITY                                   |  646 | 114 |  760 | 162 | 135 |  27 |   0 |
| DUQUESNE UNIVERSITY                               |  310 |   0 |  310 |   6 |   6 |   0 |   0 |
| ELON UNIVERSITY                                   |  281 |   0 |  281 |   0 |   0 |   0 |   0 |
| EMORY UNIVERSITY                                  |  819 |  10 |  829 | 168 |  92 |  76 |   0 |
| FAULKNER UNIVERSITY                               |  273 | 143 |  416 |   0 |   0 |   0 |   0 |
| FLORIDA A&M UNIVERSITY                            |  321 | 191 |  512 |   0 |   0 |   0 |   0 |
| FLORIDA COASTAL SCHOOL OF LAW                     |  924 | 131 | 1055 |  98 |  98 |   0 |   0 |
| FLORIDA INTERNATIONAL UNIVERSITY                  |  356 |  30 |  386 |  17 |  17 |   0 |   0 |
| FLORIDA STATE UNIVERSITY                          |  614 |   0 |  614 |  22 |  20 |   2 |   0 |
| FLORIDA, UNIVERSITY OF                            |  944 | 203 | 1147 | 113 | 108 |   5 |   0 |
| FORDHAM UNIVERSITY                                | 1006 | 150 | 1156 | 195 | 195 |   0 |   0 |
| GEORGE MASON UNIVERSITY                           |  340 | 270 |  610 |   8 |   8 |   0 |   0 |
| GEORGE WASHINGTON UNIVERSITY                      | 1376 | 247 | 1623 | 242 | 242 |   0 |   0 |
| GEORGETOWN UNIVERSITY                             | 1719 | 192 | 1911 | 618 | 618 |   0 |   0 |
| GEORGIA STATE UNIVERSITY                          |  435 |   0 |  435 |   0 |   0 |   0 |   0 |
| GEORGIA, UNIVERSITY OF                            |  583 | 148 |  731 |  21 |  18 |   3 |   0 |
| GOLDEN GATE UNIVERSITY                            |  301 |   0 |  301 | 130 | 130 |   0 |   0 |
| GONZAGA UNIVERSITY                                |  339 | 102 |  441 |   0 |   0 |   0 |   0 |
| HARVARD UNIVERSITY                                | 1752 |  68 | 1820 | 255 | 255 |   0 |   0 |
| HAWAII, UNIVERSITY OF                             |  257 |  24 |  281 |   6 |   6 |   0 |   0 |
| HOFSTRA UNIVERSITY                                |  769 | 117 |  886 |  21 |  21 |   0 |   0 |
| HOUSTON, UNIVERSITY OF                            |  615 |   4 |  619 | 126 | 126 |   0 |   0 |
| HOWARD UNIVERSITY                                 |  408 |   2 |  410 |   5 |   5 |   0 |   0 |
| IDAHO, UNIVERSITY OF                              |  351 |   0 |  351 |   0 |   0 |   0 |   0 |
| ILLINOIS, UNIVERSITY OF                           |  510 |   0 |  510 |  65 |   0 |  65 |   0 |
| INDIANA UNIVERSITY - BLOOMINGTON                  |  586 | 326 |  912 | 100 |  88 |  12 |   0 |
| INDIANA UNIVERSITY - INDIANAPOLIS                 |  531 | 408 |  939 |  54 |  44 |  10 |   0 |
| INTER AMERICAN UNIVERSITY OF PUERTO RICO          |  372 |   2 |  374 |  69 |  69 |   0 |   0 |
| IOWA, UNIVERSITY OF                               |  388 | 303 |  691 |  15 |  15 |   0 |   0 |
| KANSAS, UNIVERSITY OF                             |  376 |   0 |  376 |  19 |  19 |   0 |   0 |
| KENTUCKY, UNIVERSITY OF                           |  388 |  43 |  431 |   0 |   0 |   0 |   0 |
| LA VERNE, UNIVERSITY OF                           |  106 | 188 |  294 |   0 |   0 |   0 |   0 |
| LEWIS AND CLARK COLLEGE                           |  437 |   0 |  437 |  27 |  23 |   4 |   0 |
| LIBERTY UNIVERSITY                                |  205 |  29 |  234 |   0 |   0 |   0 |   0 |
| LOUISIANA STATE UNIVERSITY                        |  551 |  15 |  566 |  13 |   5 |   8 |   0 |
| LOUISVILLE, UNIVERSITY OF                         |  336 | 194 |  530 |   3 |   0 |   3 |   0 |
| LOYOLA MARYMOUNT UNIVERSITY-LOS ANGELES           |  901 |  68 |  969 |  43 |  43 |   0 |   0 |
| LOYOLA UNIVERSITY-NEW ORLEANS                     |  503 |  11 |  514 |   7 |   6 |   1 |   0 |
| MAINE, UNIVERSITY OF                              |  241 |  93 |  334 |   4 |   4 |   0 |   0 |
| MARQUETTE UNIVERSITY                              |  572 | 152 |  724 |   4 |   0 |   4 |   0 |
| MARYLAND, UNIVERSITY OF                           |  558 |  88 |  646 |  10 |   7 |   3 |   0 |
| MASSACHUSETTS DARTMOUTH, UNIVERSITY OF            |  126 | 137 |  263 |   0 |   0 |   0 |   0 |
| MCGEORGE SCHOOL OF LAW, UNIVERSITY OF THE PACIFIC |  416 |  22 |  438 |  54 |  28 |  26 |   0 |
| MEMPHIS, UNIVERSITY OF                            |  312 |   1 |  313 |   0 |   0 |   0 |   0 |
| MERCER UNIVERSITY                                 |  426 |  39 |  465 |   5 |   5 |   0 |   0 |
| MIAMI, UNIVERSITY OF                              |  972 | 130 | 1102 | 135 | 135 |   0 |   0 |
| MICHIGAN, UNIVERSITY OF                           | 1000 |  17 | 1017 |  46 |  46 |   0 |   0 |
| MINNESOTA, UNIVERSITY OF                          |  681 |  23 |  704 | 139 |  55 |  84 |   0 |
| MISSISSIPPI COLLEGE                               |  409 |   0 |  409 |   6 |   6 |   0 |   0 |
| MISSISSIPPI, UNIVERSITY OF                        |  386 |  17 |  403 |   9 |   9 |   0 |   0 |
| MISSOURI, UNIVERSITY OF                           |  351 |  69 |  420 |  14 |  14 |   0 |   0 |
| MISSOURI-KANSAS CITY, UNIVERSITY OF               |  399 |   0 |  399 |  41 |  14 |  27 |   0 |
| MONTANA, UNIVERSITY OF                            |  247 |   1 |  248 |   0 |   0 |   0 |   0 |
| NEVADA - LAS VEGAS, UNIVERSITY OF                 |  288 | 247 |  535 |   0 |   0 |   0 |   0 |
| NEW ENGLAND LAW | BOSTON                          |  624 |   1 |  625 |   0 |   0 |   0 |   0 |
| NEW MEXICO, UNIVERSITY OF                         |  344 | 308 |  652 |   0 |   0 |   0 |   0 |
| NORTH CAROLINA CENTRAL UNIVERSITY                 |  495 |   0 |  495 |   0 |   0 |   0 |   0 |
| NORTH CAROLINA, UNIVERSITY OF                     |  667 |   0 |  667 |  15 |   7 |   8 |   0 |
| NORTH DAKOTA, UNIVERSITY OF                       |  229 |   4 |  233 |   0 |   0 |   0 |   0 |
| NORTHEASTERN UNIVERSITY                           |  469 |  12 |  481 |  36 |  36 |   0 |   0 |
| NORTHERN ILLINOIS UNIVERSITY                      |  265 | 136 |  401 |   0 |   0 |   0 |   0 |
| NORTHERN KENTUCKY UNIVERSITY                      |  287 |   0 |  287 |   0 |   0 |   0 |   0 |
| NORTHWESTERN UNIVERSITY                           |  737 |   0 |  737 | 231 | 200 |  31 |   0 |
| NOTRE DAME, UNIVERSITY OF                         |  549 | 191 |  740 |  32 |  28 |   4 |   0 |
| OHIO NORTHERN UNIVERSITY                          |  206 |   0 |  206 |   0 |   0 |   0 |   0 |
| OHIO STATE UNIVERSITY                             |  532 |  54 |  586 |  38 |  30 |   8 |   0 |
| OKLAHOMA CITY UNIVERSITY                          |  399 |   0 |  399 |   0 |   0 |   0 |   0 |
| OREGON, UNIVERSITY OF                             |  365 |  64 |  429 |  73 |   8 |  65 |   0 |
| PACE UNIVERSITY                                   |  443 |   0 |  443 |  41 |  41 |   0 |   0 |
| PENNSYLVANIA STATE UNIVERSITY                     |  479 |   0 |  479 | 105 | 105 |   0 |   0 |
| PENNSYLVANIA, UNIVERSITY OF                       |  756 |   0 |  756 | 144 | 139 |   5 |   0 |
| PEPPERDINE UNIVERSITY                             |  605 |   3 |  608 |  99 |  33 |  66 |   0 |
| PITTSBURGH, UNIVERSITY OF                         |  526 | 181 |  707 |  31 |  18 |  13 |   0 |
| PONTIFICAL CATHOLIC UNIVERSITY OF P.R.            |  404 | 244 |  648 |   0 |   0 |   0 |   0 |
| PUERTO RICO, UNIVERSITY OF                        |  433 |  57 |  490 |   2 |   2 |   0 |   0 |
| QUINNIPIAC UNIVERSITY                             |  230 |  25 |  255 |   2 |   0 |   2 |   0 |
| RICHMOND, UNIVERSITY OF                           |  455 |   0 |  455 |   2 |   0 |   2 |   0 |
| ROGER WILLIAMS UNIVERSITY                         |  370 |  85 |  455 |   0 |   0 |   0 |   0 |
| RUTGERS UNIVERSITY-CAMDEN                         |  415 | 171 |  586 |   1 |   0 |   1 |   0 |
| RUTGERS UNIVERSITY-NEWARK                         |  501 |  72 |  573 |   6 |   6 |   0 |   0 |
| SAINT LOUIS UNIVERSITY                            |  461 |  25 |  486 |   6 |   6 |   0 |   0 |
| SAMFORD UNIVERSITY                                |  401 | 108 |  509 |   0 |   0 |   0 |   0 |
| SAN DIEGO, UNIVERSITY OF                          |  632 |  98 |  730 |  84 |  75 |   9 |   0 |
| SAN FRANCISCO, UNIVERSITY OF                      |  424 | 165 |  589 |  42 |  36 |   6 |   0 |
| SANTA CLARA UNIVERSITY                            |  478 | 163 |  641 |  53 |  53 |   0 |   0 |
| SEATTLE UNIVERSITY                                |  630 | 190 |  820 |   0 |   0 |   0 |   0 |
| SETON HALL UNIVERSITY                             |  381 |   2 |  383 |  83 |   2 |  81 |   0 |
| SOUTH CAROLINA, UNIVERSITY OF                     |  619 |   4 |  623 |   0 |   0 |   0 |   0 |
| SOUTH DAKOTA, UNIVERSITY OF                       |  194 | 266 |  460 |   0 |   0 |   0 |   0 |
| SOUTH TEXAS COLLEGE OF LAW                        |  850 |   2 |  852 |   0 |   0 |   0 |   0 |
| SOUTHERN METHODIST UNIVERSITY                     |  537 | 135 |  672 | 112 | 112 |   0 |   0 |
| SOUTHERN UNIVERSITY                               |  509 | 364 |  873 |   0 |   0 |   0 |   0 |
| ST. JOHN'S UNIVERSITY                             |  620 | 171 |  791 |  71 |  68 |   3 |   0 |
| ST. MARY'S UNIVERSITY                             |  598 |  42 |  640 |  52 |  52 |   0 |   0 |
| ST. THOMAS UNIVERSITY (FLORIDA)                   |  601 |   8 |  609 |  52 |  12 |  40 |   0 |
| ST. THOMAS, UNIVERSITY OF (MINNESOTA)             |  368 |   0 |  368 |  31 |  27 |   4 |   0 |
| STANFORD UNIVERSITY                               |  577 | 198 |  775 |  75 |  75 |   0 |   0 |
| SUFFOLK UNIVERSITY                                |  953 |   1 |  954 |  30 |  30 |   0 |   0 |
| SYRACUSE UNIVERSITY                               |  539 | 160 |  699 |  18 |  18 |   0 |   0 |
| TEMPLE UNIVERSITY                                 |  563 |   0 |  563 | 288 | 288 |   0 |   0 |
| TENNESSEE, UNIVERSITY OF                          |  390 | 244 |  634 |   0 |   0 |   0 |   0 |
| TEXAS A&M UNIVERSITY                              |  458 |   6 |  464 |   0 |   0 |   0 |   0 |
| TEXAS AT AUSTIN, UNIVERSITY OF                    | 1025 |   0 | 1025 |  61 |  61 |   0 |   0 |
| TEXAS SOUTHERN UNIVERSITY                         |  466 |   0 |  466 |   0 |   0 |   0 |   0 |
| TEXAS TECH UNIVERSITY                             |  629 | 247 |  876 |  14 |   8 |   6 |   0 |
| TOLEDO, UNIVERSITY OF                             |  233 | 204 |  437 |   6 |   0 |   6 |   0 |
| TOURO COLLEGE                                     |  383 |   2 |  385 |  18 |  18 |   0 |   0 |
| UTAH, UNIVERSITY OF                               |  332 |  19 |  351 |   0 |   0 |   0 |   0 |
| VALPARAISO UNIVERSITY                             |  448 |  24 |  472 |   5 |   0 |   5 |   0 |
| VANDERBILT UNIVERSITY                             |  525 |   0 |  525 |  52 |  52 |   0 |   0 |
| VIRGINIA, UNIVERSITY OF                           | 1005 |   0 | 1005 |  54 |  54 |   0 |   0 |
| WAKE FOREST UNIVERSITY                            |  486 |  15 |  501 |  54 |  39 |  15 |   0 |
| WASHBURN UNIVERSITY                               |  314 |   9 |  323 |   1 |   1 |   0 |   0 |
| WASHINGTON AND LEE UNIVERSITY                     |  370 |   0 |  370 |   4 |   0 |   4 |   0 |
| WASHINGTON, UNIVERSITY OF                         |  516 |   0 |  516 | 179 | 179 |   0 |   0 |
| WAYNE STATE UNIVERSITY                            |  296 | 123 |  419 |  23 |  23 |   0 |   0 |
| WEST VIRGINIA UNIVERSITY                          |  344 |   3 |  347 |   9 |   9 |   0 |   0 |
| WESTERN STATE COLLEGE OF LAW                      |  220 | 133 |  353 |   0 |   0 |   0 |   0 |
| WHITTIER LAW SCHOOL                               |  409 | 132 |  541 |   0 |   0 |   0 |   0 |
| WIDENER UNIVERSITY-HARRISBURG                     |  174 |  71 |  245 |   0 |   0 |   0 |   0 |
| WILLAMETTE UNIVERSITY                             |  312 |   6 |  318 |  23 |  20 |   3 |   0 |
| WILLIAM AND MARY LAW SCHOOL                       |  631 |   0 |  631 |  37 |  37 |   0 |   0 |
| WILLIAM MITCHELL COLLEGE OF LAW                   |  455 | 210 |  665 |   3 |   3 |   0 |   0 |
| WISCONSIN, UNIVERSITY OF                          |  525 |  48 |  573 |  71 |  25 |  46 |   0 |
| WYOMING, UNIVERSITY OF                            |  228 |   0 |  228 |   0 |   0 |   0 |   0 |
| YALE UNIVERSITY                                   |  607 |   1 |  608 |  53 |  51 |   2 |   0 |



labeled_formulas: H=(B+C)-D
H=(E-F)-G
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_468924___xlsx_081de0a63ef53cb353b0d9603e7b52a3bc2017d4.xlsx___line_46