Hi Agnes,
If it stood up to jif (or cif as its now known in the uk) then i guess it has a relatively stable dye and construction.
I would use something like fabric restorer and extract with fine fabric detergent/fibre rinse depending on how manky it is. If its really manky and defiantely synthetic, you could use a traffic lane cleaner on it and rinse with fibre rinse. If its not synthetic or there is any doubt, use a milder detergent with a solvent booster like citra boost.
It sounds like the kind of job that you will try loads of stuff on and not be completely satisfied.
You could allways use a stair-tool to rinse with much more water than an upholstery tool allows. yeeehaa cowgirl

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I have no idea what dentists make thier chairs from, but if it was PP then you could just bleach it with something like oxibrite.....man i have my spurs on today. Seriously though, dont try this unless you know its PP for sure and have tested it.
Others will say splitter or magic water.. i guess you could try them too.
Graeme
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