The structure and timing of those signals are NEC1 protocol (with device 134.107) but the modulation frequency is impossibly low.

I'm not sure what the real modulation frequency should be. I assume it is not the standard NEC frequency of 38000 or most IR learning systems would learn it without problems. On the other hand, I don't expect that the frequency encoded in the signals above is correct.

You can try various frequencies using the MakeHex program and the NEC1.irp file. First edit the .irp file to change to Device=134.107
Edit the frequency and try the results.

MakeHex will generate 256 different signals labeled with function numbers 0 through 255. The three input functions you want are 2, 6 and 8. The power function is 30.

The device might not care about modulation frequency (despite its remote sending some strange frequency). Here are those four signals at the standard NEC frequency of 38000.

Device Code: 134.107 Function: 2
0000 006D 0022 0002 0157 00AC 0015 0016 0015 0041 0015 0041 0015 0016 0015 0016 0015 0016 0015 0016 0015 0041 0015 0041 0015 0041 0015 0016 0015 0041 0015 0016 0015 0041 0015 0041 0015 0016 0015 0016 0015 0041 0015 0016 0015 0016 0015 0016 0015 0016 0015 0016 0015 0016 0015 0041 0015 0016 0015 0041 0015 0041 0015 0041 0015 0041 0015 0041 0015 0041 0015 0689 0157 0056 0015 0E94

Device Code: 134.107 Function: 6
0000 006D 0022 0002 0157 00AC 0015 0016 0015 0041 0015 0041 0015 0016 0015 0016 0015 0016 0015 0016 0015 0041 0015 0041 0015 0041 0015 0016 0015 0041 0015 0016 0015 0041 0015 0041 0015 0016 0015 0016 0015 0041 0015 0041 0015 0016 0015 0016 0015 0016 0015 0016 0015 0016 0015 0041 0015 0016 0015 0016 0015 0041 0015 0041 0015 0041 0015 0041 0015 0041 0015 0689 0157 0056 0015 0E94

Device Code: 134.107 Function: 8
0000 006D 0022 0002 0157 00AC 0015 0016 0015 0041 0015 0041 0015 0016 0015 0016 0015 0016 0015 0016 0015 0041 0015 0041 0015 0041 0015 0016 0015 0041 0015 0016 0015 0041 0015 0041 0015 0016 0015 0016 0015 0016 0015 0016 0015 0041 0015 0016 0015 0016 0015 0016 0015 0016 0015 0041 0015 0041 0015 0041 0015 0016 0015 0041 0015 0041 0015 0041 0015 0041 0015 0689 0157 0056 0015 0E94

Device Code: 134.107 Function: 30
0000 006D 0022 0002 0157 00AC 0015 0016 0015 0041 0015 0041 0015 0016 0015 0016 0015 0016 0015 0016 0015 0041 0015 0041 0015 0041 0015 0016 0015 0041 0015 0016 0015 0041 0015 0041 0015 0016 0015 0016 0015 0041 0015 0041 0015 0041 0015 0041 0015 0016 0015 0016 0015 0016 0015 0041 0015 0016 0015 0016 0015 0016 0015 0016 0015 0041 0015 0041 0015 0041 0015 0689 0157 0056 0015 0E94

It is fairly likely that the correct modulation frequency is no modulation at all. MakeHex can generate them that way if you edit Frequency=0 in the .irp file. But some Pronto models and most other software that can import Pronto Hex fail to understand unmodulated signals in Pronto Hex. Try it and see if your software will import it.

The non working learned signals in post 9 are at 4860 hertz. Probably that is wrong (after all, they don't work). But if you set the .irp file for Frequency=4860 you'll get cleaner versions of the same signals. Maybe those will work.

Another possibility is to try a frequency around 1900. That would encode a modulated signal with only one pulse per burst, so it would be identical to an unmodulated signal. Most Pronto models can't process a frequency that low, but I think some can and maybe the devices discussed in this thread can import that (I really don't know).

IIUC (post 3 of this thread), chicagoinstaller has working signals in a file for an MX-850. I have an MX-850 and great software for examining IR signals, so if he emails the file to me I can test and see exactly what it is sending for working signals. Of course that still may be hard to import into other devices if it is outside the range in which the software for those devices understands Pronto Hex.

One more idea: I took the bad learns posted above and adjusted them just enough that they could be transmitted (the way they were learned couldn't even be transmitted). The results are:

Input 1

0000 0355 0022 0002 002a 0018 0001 0005 0001 000a 0001 000a 0001 0005 0001 0005 0001 0005 0001 0005 0001 000a 0001 000a 0001 000a 0001 0005 0001 000a 0001 0005 0001 000a 0001 000a 0001 0005 0001 0005 0001 000a 0001 0005 0001 0005 0001 0005 0001 0005 0001 0004 0001 0005 0001 000a 0001 0005 0001 000a 0001 000a 0001 000a 0001 000a 0001 000b 0001 000a 0001 00c5 002a 000d 0001 01d7

Input 2

0000 0355 0022 0002 002b 0017 0001 0005 0001 000a 0001 000a 0001 0004 0001 0005 0001 0004 0001 0005 0001 000a 0001 000a 0001 000a 0001 0004 0001 000a 0001 0005 0001 000a 0001 000a 0001 0004 0001 0005 0001 000a 0001 000a 0001 0004 0001 0005 0001 0005 0001 0005 0001 0004 0001 000a 0001 0005 0001 0005 0001 000a 0001 000a 0001 000a 0001 000a 0001 000a 0001 00c5 002a 000d 0001 01d7

Input 3

0000 0355 0022 0002 002a 0018 0001 0005 0001 000a 0001 000a 0001 0004 0001 0005 0001 0004 0001 0005 0001 000a 0001 000a 0001 000a 0001 0004 0001 000a 0001 0005 0001 000a 0001 000a 0001 0005 0001 0005 0001 0004 0001 0005 0001 000a 0001 0005 0001 0005 0001 0004 0001 0005 0001 000a 0001 000a 0001 000a 0001 0004 0001 000a 0001 000a 0001 000a 0001 000a 0001 00c5 002a 000d 0001 01d7

Power

0000 0355 0022 0002 002a 0018 0001 0005 0001 000a 0001 000a 0001 0005 0001 0005 0001 0005 0001 0005 0001 000a 0001 000a 0001 000a 0001 0004 0001 000a 0001 0005 0001 000a 0001 000a 0001 0005 0001 0005 0001 000a 0001 000a 0001 000a 0001 000a 0001 0004 0001 0005 0001 0005 0001 000a 0001 0005 0001 0004 0001 0005 0001 0005 0001 000a 0001 000a 0001 000a 0001 00c5 002a 000d 0001 01d7