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   |
|:-----|:----------------------------------------|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|:----|
| ACR  | Comm Ag Rec & Res Studies               |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   1 | A   |
| AL   | Arts and Letters                        |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   1 | H   |
| ANP  | Anthropology                            |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   1 | H   |
| BMB  | Biochem and Molecular Biology           |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   1 | S   |
| CAS  | Communication Arts and Sciences         |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   1 |   0 |   0 |   2 | C   |
| CHE  | Chemical Engineering                    |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   2 |   0 |   3 | E   |
| CHS  | Chinese                                 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   1 | L   |
| CSE  | Computer Science and Engineering        |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   1 | E   |
| CSS  | Crop and Soil Sciences                  |   0 |   0 |   0 |   0 |   3 |   0 |   0 |   2 |   0 |   0 |   5 | A   |
| EC   | Economics                               |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   1 | B   |
| ENG  | English                                 |   0 |   0 |   0 |   0 |   2 |   0 |   0 |   0 |   0 |   0 |   2 | H   |
| ENT  | Entomology                              |   0 |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   2 | S   |
| EPI  | Epidemiology                            |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   1 | S   |
| FI   | Finance                                 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   1 | B   |
| FSC  | Food Science                            |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   1 | S   |
| FW   | Fisheries and Wildlife                  |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   2 |   0 |   3 | A   |
| GSAH | Global Studies in Arts and Humanities   |   0 |   0 |   0 |   0 |   2 |   0 |   0 |   0 |   0 |   0 |   2 | H   |
| HA   | History of Art                          |   0 |   0 |   0 |   0 |   5 |   4 |   0 |   0 |   0 |   0 |   9 | H   |
| HM   | Human Medicine                          |   0 |   0 |   0 |   0 |   4 |   0 |   0 |  16 |  10 |   0 |  30 | S   |
| HST  | History                                 |   0 |   0 |   0 |   0 |   0 |   4 |   0 |   5 |  12 |   0 |  21 | H   |
| LIN  | Linguistics                             |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   2 |   0 |   2 | L   |
| LIR  | Labor and Industrial Relations          |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   1 | B   |
| MKT  | Marketing                               |   0 |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   2 | N   |
| MSE  | Materials Science and Engineering       |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   1 | E   |
| MTHE | Mathematics Education                   |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   1 |   0 |   0 |   3 | Ed  |
| NEU  | Neurology                               |   0 |   0 |   0 |   0 |   0 |   4 |   0 |   4 |   0 |   0 |   8 | S   |
| PHL  | Philosophy                              |   0 |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   2 | H   |
| PKG  | Packaging                               |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   1 |   0 |   0 |   2 | B   |
| PIM  | Program in Integrative Management       |   0 |   0 |   0 |   0 |   4 |   0 |   0 |   4 |   1 |   0 |   9 | B   |
| PPL  | Public Policy                           |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   1 | PS  |
| RCAH | Residential College in Arts and Letters |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   1 | H   |
| REL  | Religious Studies                       |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   1 |   1 |   0 |   3 | H   |
| SOC  | Sociology                               |   0 |   0 |   0 |   0 |   2 |   2 |   0 |   3 |   2 |   0 |   9 | SS  |
| SPN  | Spanish                                 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   1 |   0 |   2 | L   |
| TC   | Telecommunication                       |   0 |   0 |   0 |   0 |   4 |   3 |   0 |   0 |   0 |   0 |   7 | C   |
| TE   | Teacher Education                       |   0 |   0 |   0 |   0 |   5 |   3 |   0 |   6 |   0 |   0 |  14 | Ed  |
| WRA  | Writing, Rhetoric, and American Culture |   0 |   0 |   0 |   0 |   2 |   2 |   0 |   1 |   7 |   0 |  12 | H   |
| WS   | Women's Studies                         |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   1 | H   |
| ZOL  | Zoology                                 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   2 |   0 |   0 |   2 | S   |



labeled_formulas: D=C*M
E=C*G
E=C*H
E=C*J
E=C*K
E=C*M
C=G*I
C=I*K
D=E*G
E=D*H
E=D*I
E=D*J
E=D*K
E=D*M
F=D*M
L=D*G
L=D*M
F=E*G
F=E*M
L=E*G
L=E*H
L=E*J
L=E*K
L=E*M
F=G*I
F=I*J
F=I*K
L=G*I
L=I*K
E=(C*G)*H
E=(C*G)*J
E=(C*G)*K
E=(C*G)*M
E=(C*H)*J
C=(H-K)*E
E=(C*H)*M
E=(J-K)*C
E=(C*J)*M
E=(C*K)*M
C=(G*H)*I
C=(G*I)*J
C=(G*I)*K
C=(G*I)*M
C=(H*I)*J
C=(H*I)*K
C=(I*J)*K
E=(D*G)*H
E=(D*G)*J
E=(D*G)*K
D=(E*G)*M
E=(D*H)*I
E=(H-J)*D
E=(D*H)*K
E=(D*H)*M
E=(D*I)*J
E=(D*I)*K
E=(D*I)*M
E=(D*J)*K
E=(D*J)*M
E=(D*K)*M
D=(G*H)*I
D=(G*I)*J
D=(G*I)*K
L=(D*G)*M
F=(E*G)*M
F=(E*H)*M
L=(E*G)*H
E=(G*I)*J
E=(G*I)*K
L=(E*G)*M
E=(H*I)*K
L=(E*H)*J
L=(E*H)*M
L=(E*J)*M
L=(E*K)*M
F=(G*H)*I
F=(G*I)*J
F=(G*I)*K
F=(G*I)*M
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_607253___xlsx_13fd2df0f86c3971b59370bf67af49f513c27bd9.xlsx___line_177