i forgot my appleid now i cant activate my iphone

hello i have an iphone 4s and i had to update and restore it from itunes but the last owner of it says she cant remember the appleid we have been trying to find out what it is for almost half a year but we cant find out i cant call apple support either because i have no proof of purchase is there any way to get around the appleid activation or not

my serial number if that helps: ****

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