If the output is on the rail with the non-inverting output @ the ~5V of the zener, then something must be setup wrong on your breadboard or whatever construction you have to test the output. If what you say about X1-1 and X1-2 is true why would one put Vcc (12V) to the output of an op amp? It would appear that certain assumptions made are faulty, else why place any device expected to produce a signal across zero potential as shown between 1X-1 and 1X-2? Ensure you have the correct connections made to the correct pins. It would be more likely that the potential between 1X-1 & 1X-2 is the difference between the two of ~7V across the unknown sensor rather than 0V.
After many, many years of breadboarding, solderballing, etc, I still have brain cramps from lack of attention to detail. Good luck!