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Other Intangible Assets, net and Goodwill - Narrative (Details) - USD ($) $ in Millions | 3 Months Ended | 9 Months Ended
--- | --- | ---
Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2022 | Sep. 30, 2021
Goodwill [Line Items] |  |  |  |
Amortization of intangible assets | $ 161.1 | $ 128.1 | $ 492.7 | $ 383.4
Goodwill impairment charge | 4,407.9 |  | 4,407.9 |
Academia & Government |  |  |  |
Goodwill [Line Items] |  |  |  |
Goodwill impairment charge | 1,745.8 |  | 1,745.8 |
IP Segment |  |  |  |
Goodwill [Line Items] |  |  |  |
Goodwill impairment charge |  |  | $ 2,662.1 |
IP Segment | IP Management |  |  |  |
Goodwill [Line Items] |  |  |  |
Goodwill impairment charge | 2,569.1 |  |  |
IP Segment | Patent |  |  |  |
Goodwill [Line Items] |  |  |  |
Goodwill impairment charge | $ 93.0 |  |  |

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