Complaint sub-issue: Card was charged for something you did not purchase with the card

In XXXX I took a trip to XXXX XXXX  XXXX and while traveling I lost my card and there was fraudulent activity that Discover is claiming is not fraud. The fraud was XXXX XXXX for {$1300.00} on XXXX and XXXX taxi charge for {$20.00} on XXXX. 
I lost my card sometime on the night of XX/XX/XXXX and last I remember using it is when I tried to make a payment to a taxi cab, but the charge would not go through. I do not know the exact time of this attempt, but it was fairly early in the evening. I called discover and they advised that they did not see anything on their end so it must be the merchants machine. I asked the cab driver and he said that there was nothing wrong with his machine and he has been driving all day. I used another card to make the payment and this was the last time I used the card. This is important because my card was fraudulently attempted at other taxi cabs that discover did not mention but used my early attempt to validate future attempts in their investigation. 
After I returned from my trip I could not locate my card so I filed the lost report with Discover. When I was getting ready to make a payment to my card is when I noticed the charge and reported it to discover. There is 2 weeks gap between when I reported the card lost and when I noticed the charge and thats another thing Discover is holding against me. Discover is claiming that since I did not report the charge when I filed the lost report they can not consider the charge as fraud. I told them they did not mention on their lost report that I could only file fraud claims at that time otherwise I would have reviewed my transactions. I know I should have reviewed them but I still reported within 2 weeks of filing lost report and within the same month as the charge. I further contested with Discover that there are no time frames listed for reporting fraud on their terms or on my statements. 
Discover is stating that they sent me an alert when the fraudulent charge was attempted, and I verified it. I advised them that I live in Virginia and was traveling is XXXX so all of my credit cards and banks were sending me alerts as I rarely travel this far away from home, so I was not paying attention to them. Just prior I had already gotten calls from XXXX XXXX that someone is using my card in XXXX and had to validate myself twice that day with them. Alert from discover was sent to my email and again it did not mention that if a charge is validated by accident then it can not be disputed as fraud. 
I have told discover right from the first call that I only attempted XXXX taxi cab once and it did not go through and it was early in the evening. If there are attempts after then its clearly not me. Infact discover called me after I filed the fraud claim to know when was the last time I remembered using my card. I told them the same exact as I mention before but discover used my early attempt to validate later charge from the same merchant. They never mentioned to me the time of the attempt until I brought it up later on and at that point they told me that later fraudulent XXXX taxi charge is 5 hours after XXXX XXXX charge. I told Discover that its clearly not by me then and I think your rep should have told me the time of it. I told Discover that XXXX XXXX XXXX has taxi cabs on literally every single street and who ever picked my card simply used it later on but discover reps would not listen to me. 
So based on the XXXX taxi charge that I have told them is not mine, the email alert and 2 weeks it took me to report the charge as fraud is what discover is using against me and have sent me a letter stating that charges are valid. I have spoken to their executive department and they would not ever let me talk. I would like my complaint to be published publicly so to other people can be warned about the practices of Discover. The reason it has taken me this long to file a CFBP complaint is because I work fulltime and I go to school fulltime plus discover took months in between my appeals between their departments. Please have discover conduct an actual investigation or make changes to their disclosures.