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Identifiable Intangible Assets Schedule of Intangible Assets and Goodwill (Details) - USD ($) | 12 Months Ended |
--- | --- | ---
Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020
Indefinite-lived intangible assets: |  |  |
Goodwill | $ 98,600,000 | $ 115,100,000 | $ 99,800,000
Intangible Assets, Gross, (Including Goodwill) | 764,200,000 | 770,300,000 |
Accumulated amortization: |  |  |
Intangible Assets, Net (Excluding Goodwill) | 361,200,000 | 392,500,000 |
Goodwill, Acquired During Period | 12 |  |
Indefinite-lived Intangible Assets, Foreign Currency Translation Gain (Loss) | (9,700,000) | 3,200,000 |
i2O |  |  |
Accumulated amortization: |  |  |
Goodwill, Acquired During Period |  | 12,100,000 |
Business Combination-Related Identifiable Intangible [Member] |  |  |
Accumulated amortization: |  |  |
Accumulated Amortization | 411,700,000 | 387,800,000 |
Net book value | 352,500,000 | 382,500,000 |
Trademarks and Trade Names [Member] |  |  |
Indefinite-lived intangible assets: |  |  |
Trade names and trademarks | 272,700,000 | 273,800,000 |
Software and Software Development Costs [Member] |  |  |
Capitalized external-use software: |  |  |
Capitalized Computer Software, Gross | 35,500,000 | 34,100,000 |
Accumulated amortization | 26,800,000 | 24,100,000 |
Net book value | 8,700,000 | 10,000,000.0 |
Technology-Based Intangible Assets [Member] |  |  |
Finite-lived intangible assets: |  |  |
Technology | 119,900,000 | 123,500,000 |
Accumulated amortization: |  |  |
Accumulated Amortization | 89,500,000 | 85,800,000 |
Customer Relationships [Member] |  |  |
Finite-lived intangible assets: |  |  |
Customer relationships and other | 371,600,000 | 373,000,000.0 |
Accumulated amortization: |  |  |
Accumulated Amortization | $ 322,200,000 | $ 302,000,000.0 |

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