Thanks for your question.
A person cannot petition themselves under grounds of adultery, only your spouse can do this.
Separation requires separation for either a period of 2 years (with spouse consent) or 5 years (without).
At the present time the only option if she will not petition you is to divorce on the grounds of her unreasonable behaviour. If you ask a solicitor to draft particulars of unreasonable behaviour and send them to her contained in a letter then it might bring home to her that you wish to divorce and precipitate either her agreeing to acknowledge a petition based on UB or deciding to petition you.
You should consider mediation though in the meantime:-
It sounds as if the root of the issue is for her to come to the realisation that the marriage is over. This can take time. Once she has reconciled herself to this then it will be an easier issue to manage.
I will answer your follow up questions you may have.
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