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 |
|----:|----:|----:|----:|----:|----:|
|   1 |   0 |   1 |   0 |   1 |   0 |
|   1 |   1 |   1 |   0 |   1 |   0 |
|   1 |   2 |   1 |   0 |   1 |   0 |
|   1 |   3 |   1 |   0 |   1 |   0 |
|   1 |   4 |   1 |   0 |   1 |   0 |
|   1 |   5 |   1 |   0 |   1 |   0 |
|   1 |   6 |   0 |   1 |   1 |   0 |
|   1 |   7 |   0 |   1 |   1 |   0 |
|   1 |   8 |   0 |   1 |   1 |   0 |
|   1 |   9 |   0 |   1 |   1 |   0 |
|   1 |  10 |   0 |   1 |   1 |   0 |
|   1 |  11 |   0 |   1 |   1 |   0 |
|   1 |  12 |   0 |   1 |   1 |   0 |
|   1 |  13 |   0 |   1 |   1 |   0 |
|   1 |  14 |   0 |   1 |   1 |   0 |
|   1 |  15 |   0 |   1 |   1 |   0 |
|   1 |  16 |   0 |   1 |   1 |   0 |
|   1 |  17 |   0 |   1 |   1 |   0 |
|   1 |  18 |   0 |   1 |   1 |   0 |
|   1 |  19 |   0 |   1 |   1 |   0 |
|   1 |  20 |   0 |   1 |   1 |   0 |
|   1 |  21 |   0 |   1 |   1 |   0 |
|   1 |  22 |   1 |   0 |   1 |   0 |
|   2 |   0 |   1 |   0 |   1 |   0 |
|   2 |   1 |   1 |   0 |   1 |   0 |
|   2 |   2 |   1 |   0 |   1 |   0 |
|   2 |   3 |   1 |   0 |   1 |   0 |
|   2 |   4 |   1 |   0 |   1 |   0 |
|   2 |   5 |   1 |   0 |   1 |   0 |
|   2 |   6 |   0 |   1 |   1 |   0 |
|   2 |   7 |   0 |   1 |   1 |   0 |
|   2 |   8 |   0 |   1 |   1 |   0 |
|   2 |   9 |   0 |   1 |   1 |   0 |
|   2 |  10 |   0 |   1 |   1 |   0 |
|   2 |  11 |   0 |   1 |   1 |   0 |
|   2 |  12 |   0 |   1 |   1 |   0 |
|   2 |  13 |   0 |   1 |   1 |   0 |
|   2 |  14 |   0 |   1 |   1 |   0 |
|   2 |  15 |   0 |   1 |   1 |   0 |
|   2 |  16 |   0 |   1 |   1 |   0 |
|   2 |  17 |   0 |   1 |   1 |   0 |
|   2 |  18 |   0 |   1 |   1 |   0 |
|   2 |  19 |   0 |   1 |   1 |   0 |
|   2 |  20 |   0 |   1 |   1 |   0 |
|   2 |  21 |   0 |   1 |   1 |   0 |
|   2 |  22 |   1 |   0 |   1 |   0 |
|   2 |  23 |   1 |   0 |   1 |   0 |
|   3 |   0 |   1 |   0 |   1 |   0 |
|   3 |   1 |   1 |   0 |   1 |   0 |
|   3 |   2 |   1 |   0 |   1 |   0 |
|   3 |   3 |   1 |   0 |   1 |   0 |
|   3 |   4 |   1 |   0 |   1 |   0 |
|   3 |   5 |   1 |   0 |   1 |   0 |
|   3 |   6 |   0 |   1 |   1 |   0 |
|   3 |   7 |   0 |   1 |   1 |   0 |
|   3 |   8 |   0 |   1 |   1 |   0 |
|   3 |   9 |   0 |   1 |   1 |   0 |
|   3 |  10 |   0 |   1 |   1 |   0 |
|   3 |  11 |   0 |   1 |   1 |   0 |
|   3 |  12 |   0 |   1 |   1 |   0 |
|   3 |  13 |   0 |   1 |   1 |   0 |
|   3 |  14 |   0 |   1 |   1 |   0 |
|   3 |  15 |   0 |   1 |   1 |   0 |
|   3 |  16 |   0 |   1 |   1 |   0 |
|   3 |  17 |   0 |   1 |   1 |   0 |
|   3 |  18 |   0 |   1 |   1 |   0 |
|   3 |  19 |   0 |   1 |   1 |   0 |
|   3 |  20 |   0 |   1 |   1 |   0 |
|   3 |  21 |   0 |   1 |   1 |   0 |
|   3 |  22 |   1 |   0 |   1 |   0 |
|   3 |  23 |   1 |   0 |   1 |   0 |
|   4 |   6 |   0 |   1 |   1 |   0 |
|   4 |   7 |   0 |   1 |   1 |   0 |
|   4 |   8 |   0 |   1 |   1 |   0 |
|   4 |   9 |   0 |   1 |   1 |   0 |
|   4 |  10 |   0 |   1 |   1 |   0 |
|   4 |  11 |   0 |   1 |   1 |   0 |
|   4 |  12 |   0 |   1 |   1 |   0 |
|   4 |  13 |   0 |   1 |   1 |   0 |
|   4 |  14 |   0 |   1 |   1 |   0 |
|   4 |  15 |   0 |   1 |   1 |   0 |
|   4 |  16 |   0 |   1 |   1 |   0 |
|   4 |  17 |   0 |   1 |   1 |   0 |
|   4 |  18 |   0 |   1 |   1 |   0 |
|   4 |  21 |   0 |   1 |   1 |   0 |
|   5 |   0 |   1 |   0 |   1 |   0 |
|   5 |   1 |   1 |   0 |   1 |   0 |
|   5 |   2 |   1 |   0 |   1 |   0 |
|   5 |   3 |   1 |   0 |   1 |   0 |
|   5 |   4 |   1 |   0 |   1 |   0 |
|   5 |   5 |   1 |   0 |   1 |   0 |
|   5 |   6 |   0 |   1 |   1 |   0 |
|   5 |   7 |   0 |   1 |   1 |   0 |
|   5 |   8 |   0 |   1 |   1 |   0 |
|   5 |   9 |   0 |   1 |   1 |   0 |
|   5 |  10 |   0 |   1 |   1 |   0 |
|   5 |  11 |   0 |   1 |   1 |   0 |
|   5 |  12 |   0 |   1 |   1 |   0 |
|   5 |  15 |   0 |   1 |   1 |   0 |
|   5 |  16 |   0 |   1 |   1 |   0 |
|   5 |  20 |   0 |   1 |   1 |   0 |
|   5 |  21 |   0 |   1 |   1 |   0 |
|   5 |  22 |   1 |   0 |   1 |   0 |
|   5 |  23 |   1 |   0 |   1 |   0 |
|   6 |   0 |   1 |   0 |   1 |   0 |
|   6 |   1 |   1 |   0 |   1 |   0 |
|   6 |   2 |   1 |   0 |   1 |   0 |
|   6 |   3 |   1 |   0 |   1 |   0 |
|   6 |   4 |   1 |   0 |   1 |   0 |
|   6 |   5 |   1 |   0 |   1 |   0 |
|   6 |   6 |   0 |   1 |   1 |   0 |
|   6 |   7 |   0 |   1 |   1 |   0 |
|   6 |   8 |   0 |   1 |   1 |   0 |
|   6 |   9 |   0 |   1 |   1 |   0 |
|   6 |  10 |   0 |   1 |   1 |   0 |
|   6 |  13 |   0 |   1 |   1 |   0 |
|   6 |  14 |   0 |   1 |   1 |   0 |
|   6 |  15 |   0 |   1 |   1 |   0 |
|   6 |  16 |   0 |   1 |   1 |   0 |
|   6 |  17 |   0 |   1 |   1 |   0 |
|   6 |  18 |   0 |   1 |   1 |   0 |
|   6 |  19 |   0 |   1 |   1 |   0 |
|   6 |  20 |   0 |   1 |   1 |   0 |
|   6 |  21 |   0 |   1 |   1 |   0 |
|   6 |  22 |   1 |   0 |   1 |   0 |
|   6 |  23 |   1 |   0 |   1 |   0 |
|   7 |   0 |   1 |   0 |   1 |   0 |
|   7 |   1 |   1 |   0 |   1 |   0 |
|   7 |   2 |   1 |   0 |   1 |   0 |
|   7 |   3 |   1 |   0 |   1 |   0 |
|   7 |   4 |   1 |   0 |   1 |   0 |
|   7 |   5 |   1 |   0 |   1 |   0 |
|   7 |   6 |   0 |   1 |   1 |   0 |
|   7 |   7 |   0 |   1 |   1 |   0 |
|   7 |   8 |   0 |   1 |   1 |   0 |
|   7 |   9 |   0 |   1 |   1 |   0 |
|   7 |  10 |   0 |   1 |   1 |   0 |
|   7 |  11 |   0 |   1 |   1 |   0 |
|   7 |  12 |   0 |   1 |   1 |   0 |
|   7 |  13 |   0 |   1 |   1 |   0 |
|   7 |  14 |   0 |   1 |   1 |   0 |
|   7 |  15 |   0 |   1 |   1 |   0 |
|   7 |  16 |   0 |   1 |   1 |   0 |
|   7 |  17 |   0 |   1 |   1 |   0 |
|   7 |  18 |   0 |   1 |   1 |   0 |
|   7 |  19 |   0 |   1 |   1 |   0 |
|   7 |  20 |   0 |   1 |   1 |   0 |
|   7 |  22 |   1 |   0 |   1 |   0 |
|   7 |  23 |   1 |   0 |   1 |   0 |



labeled_formulas: E=C+D
F=C*D
F=(A*C)*D
F=(B*C)*D
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_87114___xlsx_c5d75f3ee0504a12941216cbc86925f831f38242.xlsx___line_580