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 | P9K40A         | HPE 42U 600x1200 Ent G2 Shock Rack                                                           |   1 |   0 |   0 |
|   2 | P9K40A#001     | HPE Factory Express Base Racking Service                                                     |   1 |   0 |   0 |
|   3 | 797740-B21     | HPE Synergy12000 CTO Frame 1xFLM 10x Fan                                                     |   1 |   0 |   0 |
|   4 | 797740-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|   5 | 871940-B21     | HPE SY 480 Gen10 CTO Cmpt Mdl                                                                |  12 |   0 |   0 |
|   6 | 871940-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|   7 | P07345-L21     | HPE SY 480/660 Gen10 Xeon-G 6240 FIO Kit                                                     |  12 |   0 |   0 |
|   8 | P07345-B21     | HPE SY 480/660 Gen10 Xeon-G 6240 Kit                                                         |  12 |   0 |   0 |
|   9 | P07345-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  10 | P00928-B21     | HPE 128GB 8Rx4 PC4-2933Y-L 3DS Smart Kit                                                     | 192 |   0 |   0 |
|  11 | P00928-B21#0D1 | Factory integrated                                                                           | 192 |   0 |   0 |
|  12 | P18432-B21     | HPE 480GB SATA 6G Mixed Use SFF (2.5in) SC 3yr Wty Multi Vendor SSD                          |  24 |   0 |   0 |
|  13 | P18432-B21#0D1 | Factory integrated                                                                           |  24 |   0 |   0 |
|  14 | P01367-B21     | HPE 96W Smart Storage Battery 260mm Cbl                                                      |  12 |   0 |   0 |
|  15 | P01367-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  16 | 804424-B21     | HPE Smart Array P204i-c SR Gen10 Ctrlr                                                       |  12 |   0 |   0 |
|  17 | 804424-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  18 | 777430-B21     | HPE Synergy 3820C 10/20Gb CNA                                                                |  12 |   0 |   0 |
|  19 | 777430-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  20 | 339778-B21     | HPE Raid 1 Drive 1 FIO Setting                                                               |  12 |   0 |   0 |
|  21 | 779218-B21     | HPE Synergy 20Gb Interconnect Link Mod                                                       |   1 |   0 |   0 |
|  22 | 779218-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  23 | 794502-B23     | HPE VC SE 40Gb F8 Module                                                                     |   1 |   0 |   0 |
|  24 | 794502-B23#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  25 | 817040-B21     | HPE Synergy 40/4x10GbE/4x8GbFC QSFP XCVR                                                     |   4 |   0 |   0 |
|  26 | 817040-B21#0D1 | Factory integrated                                                                           |   4 |   0 |   0 |
|  27 | N3R43A         | HPE Synergy 8Gb FC License Upgrade                                                           |   1 |   0 |   0 |
|  28 | N3R43A#0D1     | Factory integrated                                                                           |   1 |   0 |   0 |
|  29 | 798096-B21     | HPE Synergy 12000F 6x 2650W AC Ti FIO PS                                                     |   1 |   0 |   0 |
|  30 | 804938-B21     | HPE Synergy 12000 Frame Rack Rail Option                                                     |   1 |   0 |   0 |
|  31 | 804938-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  32 | 804353-B21     | HPE Synergy Composer                                                                         |   1 |   0 |   0 |
|  33 | 804353-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  34 | 804942-B21     | HPE Synergy Frame Link Module                                                                |   1 |   0 |   0 |
|  35 | 804942-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  36 | 804943-B21     | HPE Synergy 12000 Frame 4x Lift Handle                                                       |   1 |   0 |   0 |
|  37 | 804943-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  38 | 859493-B21     | Synergy Multi Frame Master1 FIO                                                              |   1 |   0 |   0 |
|  39 | 804101-B21     | HPE Synergy Interconnect Link 3m AOC                                                         |   8 |   0 |   0 |
|  40 | 804101-B21#0D1 | Factory integrated                                                                           |   8 |   0 |   0 |
|  41 | 720199-B21     | HPE BLc 40G QSFP+ QSFP+ 3m DAC Cable                                                         |   2 |   0 |   0 |
|  42 | 720199-B21#0D1 | Factory integrated                                                                           |   2 |   0 |   0 |
|  43 | 861412-B21     | HPE CAT6A 4ft Cbl                                                                            |   2 |   0 |   0 |
|  44 | 861412-B21#0D1 | Factory integrated                                                                           |   2 |   0 |   0 |
|  45 | 797740-B21     | HPE Synergy12000 CTO Frame 1xFLM 10x Fan                                                     |   1 |   0 |   0 |
|  46 | 797740-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  47 | 871940-B21     | HPE SY 480 Gen10 CTO Cmpt Mdl                                                                |  12 |   0 |   0 |
|  48 | 871940-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  49 | P07345-L21     | HPE SY 480/660 Gen10 Xeon-G 6240 FIO Kit                                                     |  12 |   0 |   0 |
|  50 | P07345-B21     | HPE SY 480/660 Gen10 Xeon-G 6240 Kit                                                         |  12 |   0 |   0 |
|  51 | P07345-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  52 | P00928-B21     | HPE 128GB 8Rx4 PC4-2933Y-L 3DS Smart Kit                                                     | 192 |   0 |   0 |
|  53 | P00928-B21#0D1 | Factory integrated                                                                           | 192 |   0 |   0 |
|  54 | P18432-B21     | HPE 480GB SATA 6G Mixed Use SFF (2.5in) SC 3yr Wty Multi Vendor SSD                          |  24 |   0 |   0 |
|  55 | P18432-B21#0D1 | Factory integrated                                                                           |  24 |   0 |   0 |
|  56 | P01367-B21     | HPE 96W Smart Storage Battery 260mm Cbl                                                      |  12 |   0 |   0 |
|  57 | P01367-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  58 | 804424-B21     | HPE Smart Array P204i-c SR Gen10 Ctrlr                                                       |  12 |   0 |   0 |
|  59 | 804424-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  60 | 777430-B21     | HPE Synergy 3820C 10/20Gb CNA                                                                |  12 |   0 |   0 |
|  61 | 777430-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  62 | 339778-B21     | HPE Raid 1 Drive 1 FIO Setting                                                               |  12 |   0 |   0 |
|  63 | 779218-B21     | HPE Synergy 20Gb Interconnect Link Mod                                                       |   1 |   0 |   0 |
|  64 | 779218-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  65 | 794502-B23     | HPE VC SE 40Gb F8 Module                                                                     |   1 |   0 |   0 |
|  66 | 794502-B23#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  67 | 817040-B21     | HPE Synergy 40/4x10GbE/4x8GbFC QSFP XCVR                                                     |   4 |   0 |   0 |
|  68 | 817040-B21#0D1 | Factory integrated                                                                           |   4 |   0 |   0 |
|  69 | N3R43A         | HPE Synergy 8Gb FC License Upgrade                                                           |   1 |   0 |   0 |
|  70 | N3R43A#0D1     | Factory integrated                                                                           |   1 |   0 |   0 |
|  71 | 798096-B21     | HPE Synergy 12000F 6x 2650W AC Ti FIO PS                                                     |   1 |   0 |   0 |
|  72 | 804938-B21     | HPE Synergy 12000 Frame Rack Rail Option                                                     |   1 |   0 |   0 |
|  73 | 804938-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  74 | 804353-B21     | HPE Synergy Composer                                                                         |   1 |   0 |   0 |
|  75 | 804353-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  76 | 804942-B21     | HPE Synergy Frame Link Module                                                                |   1 |   0 |   0 |
|  77 | 804942-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  78 | 859494-B22     | Synergy Multi Frame Master2 FIO                                                              |   1 |   0 |   0 |
|  79 | 797740-B21     | HPE Synergy12000 CTO Frame 1xFLM 10x Fan                                                     |   1 |   0 |   0 |
|  80 | 797740-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
|  81 | 871940-B21     | HPE SY 480 Gen10 CTO Cmpt Mdl                                                                |  12 |   0 |   0 |
|  82 | 871940-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  83 | P07345-L21     | HPE SY 480/660 Gen10 Xeon-G 6240 FIO Kit                                                     |  12 |   0 |   0 |
|  84 | P07345-B21     | HPE SY 480/660 Gen10 Xeon-G 6240 Kit                                                         |  12 |   0 |   0 |
|  85 | P07345-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  86 | P00928-B21     | HPE 128GB 8Rx4 PC4-2933Y-L 3DS Smart Kit                                                     |  96 |   0 |   0 |
|  87 | P00928-B21#0D1 | Factory integrated                                                                           |  96 |   0 |   0 |
|  88 | P18432-B21     | HPE 480GB SATA 6G Mixed Use SFF (2.5in) SC 3yr Wty Multi Vendor SSD                          |  24 |   0 |   0 |
|  89 | P18432-B21#0D1 | Factory integrated                                                                           |  24 |   0 |   0 |
|  90 | P01367-B21     | HPE 96W Smart Storage Battery 260mm Cbl                                                      |  12 |   0 |   0 |
|  91 | P01367-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  92 | 804424-B21     | HPE Smart Array P204i-c SR Gen10 Ctrlr                                                       |  12 |   0 |   0 |
|  93 | 804424-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  94 | 777430-B21     | HPE Synergy 3820C 10/20Gb CNA                                                                |  12 |   0 |   0 |
|  95 | 777430-B21#0D1 | Factory integrated                                                                           |  12 |   0 |   0 |
|  96 | 339778-B21     | HPE Raid 1 Drive 1 FIO Setting                                                               |  12 |   0 |   0 |
|  97 | 779218-B21     | HPE Synergy 20Gb Interconnect Link Mod                                                       |   2 |   0 |   0 |
|  98 | 779218-B21#0D1 | Factory integrated                                                                           |   2 |   0 |   0 |
|  99 | 798096-B21     | HPE Synergy 12000F 6x 2650W AC Ti FIO PS                                                     |   1 |   0 |   0 |
| 100 | 804938-B21     | HPE Synergy 12000 Frame Rack Rail Option                                                     |   1 |   0 |   0 |
| 101 | 804938-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
| 102 | 804942-B21     | HPE Synergy Frame Link Module                                                                |   1 |   0 |   0 |
| 103 | 804942-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
| 104 | 861413-B21     | HPE CAT6 10Ft Cbl                                                                            |   1 |   0 |   0 |
| 105 | 861413-B21#0D1 | Factory integrated                                                                           |   1 |   0 |   0 |
| 106 | H6J85A         | HPE Rack Hardware Kit                                                                        |   1 |   0 |   0 |
| 107 | H6J85A#0D1     | Factory integrated                                                                           |   1 |   0 |   0 |
| 108 | P9S21A         | HPE G2 Mtrd/Swtd 3P 14.4kVA/C13 NA/J PDU                                                     |   4 |   0 |   0 |
| 109 | P9S21A#0D1     | Factory integrated                                                                           |   4 |   0 |   0 |
| 110 | BW932A         | HPE 600mm Rack Stabilizer Kit                                                                |   1 |   0 |   0 |
| 111 | BW932A#B01     | Include with complete system                                                                 |   1 |   0 |   0 |
| 112 | K2Q47A         | HPE MPO to 4 x LC 15m Cable                                                                  |   8 |   0 |   0 |
| 113 | BW928A         | HPE 1U Blck Universal 10-pk Filler Panel                                                     |   2 |   0 |   0 |
| 114 | U4VT2AS        | HPE PCA Proactive Credits Per Year SVC                                                       |  30 |   0 |   0 |
| 115 | H8B36A3        | HPE 3Y Proactive Care Adv 24x7 wDMR SVC                                                      |   1 |   0 |   0 |
| 116 | H8B36A3#WJP    | HPE Synergy Composer Supp                                                                    |   2 |   0 |   0 |
| 117 | H8B36A3#W4A    | HPE SY480 Gen10 Support                                                                      |  36 |   0 |   0 |
| 118 | H8B36A3#WJN    | HPE Synergy 1200 Frame Supp                                                                  |   3 |   0 |   0 |
| 119 | H8B36A3#WJR    | HPE Synergy VC SE 40Gb F8 Module Supp                                                        |   2 |   0 |   0 |
| 120 | H8B36A3#WJT    | HPE Synergy Interconnect LinkModule Supp                                                     |   4 |   0 |   0 |
| 121 | HA124A1        | HPE Technical Installation Startup SVC                                                       |   1 |   0 |   0 |
| 122 | HA124A1#5ZQ    | HPE Synergy Additional Frame Startup SVC                                                     |   2 |   0 |   0 |
| 123 | HA124A1#5ZM    | HPE Synergy First Frame Startup SVC                                                          |   1 |   0 |   0 |
| 124 | HF385A1        | HPE Training Credits for Serv and CS SVC                                                     |  12 |   0 |   0 |
| 125 | MZ-76P4T0E     | Smsg 4TB 860 PRO SATA III 2.5” Internal SSD                                                  |  60 |   0 |   0 |
| 126 | 9EA-00267      | WinSvrDCCore SNGL LicSAPk MVL 2Lic CoreLic - From Microsoft Select Plus Agreement # 9B6ABDDA | 648 |   0 |   0 |



label: F=D*E
labeled_formulas: F=D*E
output: {"Arithmetic-Relationship": ["F=D*E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_89931___xlsx_b848d75b08b4457834c09e859264ed9d55231185.xlsx___line_474