Your example isn't the traxler after 4 d3. Also Castling is the move after 5 Ng5.
The traxler is 1 e4 e5 2 Nf3 Nc6 3 Bc4 Nf6 4 Ng5 Bc5 after which indeed Bxf7 is the best response by white, as mentioned before
The traxler is refuted after 5. d4. Here is some analysis:
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 Bc5 5. d4 {First white attacks the c5
bishop, and second the c1 bishop is open, so the ...Bxf2+ tricks do not work
anymore.} 5... Bxd4? {Not best, by a long shot.} 6. Nxf7 (6. c3 {first is also
mighty strong.} 6... Bxf2+ 7. Kxf2 O-O 8. Re1 {With two pawns for the piece, and
no serious attacking chances, Black is almost lost.}) 6... Bxf2+ 7. Kxf2 Nxe4+
8. Kg1 Qh4 9. g3 {The differencxe is now apparent: The f4 square is not
accesssible to the Black queen.} 9... Nxg3 10. Nxh8! (10. hxg3 {Also good, but
not best.} 10... Qxg3+ 11. Kf1 Rf8 12. Qd3 ±) 10... Nxh1 11. Qd5! {and white has
a killing attack, while Black's counterplay is limited to a couple of checks.} *
I have a lot of experience against Traxler, if any one here needs it I can play a few casual games with them.
> Black wins, so is there any way to refute it?
Just play the position against Stockfish and youl'll find out. :-)
And take back as many moves as you want.
A few people are saying that Bxf7 is a refutation... As someone who plays the Traxler (as black) very often, I can say that while Bxf7 lines are (probably) safer than Nxf7, don't expect to just play simple moves and escape. I've won games against Bxf7 in the past, even in rapid (where the opponent has some time to actually think about their moves).
Another thing to note is that the Traxler isn't necessarily just about objectively good moves. I win a fairly large percentage of my games with it (higher than with other openings, anyway), for the following reasons:
1. I'm very prepared for all of the different variations, while my opponents usually only know a few moves. Plus, most lines in the Traxler have very long sequences of "only moves" for both sides, so one bad move can lose you the game on the spot.
2. The tactics are so bizarre and complicated that even computer assistance starts to struggle. You can see this for yourself by taking Stockfish through the mainline of the Traxler and leaving it to analyse for a while (a few minutes). In most positions, after about depth 20-30 of analysis the evaluation will start to change dramatically as Stockfish discovers some of black's hidden resources that start off beyond its search horizon.
Another added bonus of playing the Traxler is that I've found it's very useful for training tactics...
ng5?! d6?? it's not traxler
Can anyone explain me why didn't White take the Bishop on f2 right away?
As white the best response to Traxler is bishop takes pawn check then castle probs
@sheldonleecooper515 I've no idea, it seems to be a blunder. I think OP and his opponent thought this was a Traxler counter-attack, in which its better to decline the bishop on f2, and although it bears resemblences, its not the Traxler as there are pawns on d3 and d6.
@william_chen this isn't a Traxler.