The sentence you originally presented is not only perfectly grammatical, it is perfectly natural and extremely common in all forms of English written and spoken alike, properties notably lacking in several of the four sentences you offered as possible alternatives. (However, we do not do proofreading here, and the errors in your alternatives are too elementary for our site.)
This is not even a traditional if-then condition in reverse order, since it means something other than:
- If we paid in cash, then a shop offered us a reduction (in price).
Rather, it means something more like these, ordered from least to most natural-sounding:
- One shop was willing to give us a discount if only we would pay in cash.
- One shop was willing to give us a discount if we paid in cash.
- One shop was willing to give us a discount if we paid cash.
- One shop was willing to give us a discount in return for paying in cash.
- One shop was willing to give us a discount for paying in cash.
- One shop was willing to give us a discount for paying cash.
- One shop offered a discount for a cash payment.
- One shop offered a cash discount.
So that original sentence does not really offer the traditional protasis and apodosis found in conditional constructions.
“More things in heaven and earth...”
As Hamlet wryly observed:
There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.
And this is the crux of your entire problem here. That “as far as I know” part of your question is based on a disastrously erroneous premise, for the world is filled with infinitely many more undreamt things than have ever troubled your restless dreams. And for thing, here read grammatical English conditional construction.
Addressing this central matter in a comment, John Lawler wrote:
This is a set of construction blueprints called the "first conditional", etc. in many non-Anglophone schools in the world. Somebody somewhere published a book that said there were these four constructions with very complicated rules for use, and it was so authoritatively stated that every non-native English teacher has used it since (to judge by the questions here). It's nonsense, of course; but students who got it in their English classes believe it implicitly. Like future tense, subjunctive mood, and unsplit infinitives.
And in my answer to the ELL question Difference between “if + present, will + infinitive” and “if + present, would + infinitive”, I observe:
But it does learners a disservice to pretend that these few possibilities are the only the ones that exist or the only ones which are grammatical.³ They do not even reflect actual usage by native speakers, as Christian Jones and Daniel Waller observe in their journal entry from the English Language Teaching Journal titled “If only it were true: the problem with the four conditionals”¹ when they write:
It is clear that a division of conditionals into the zero, first, second, and third categories does not adequately reflect actual usage.
If you actually look at corpus occurrences, as they have done, you find that many of the modal combinations frequently found in speech and writing by native speakers are simply not explained to beginners. By attempting to deflect learners from common errors, these errors of omission lead to even more confusion. And this can do genuine harm, as explained below.
Professor Lawler has also elsewhere in a comment written, with bold emphasis my own:
They're just mostly-safe combinations of if..then clause types; they're not tenses and they don't cover every possibility. Linguists don't have names for the Zero-thru-N types you mentioned, and not for any others that some textbook writer might dream up, either. Generally there is a hypothetical clause of some sort and a conclusion clause of some sort; but there are hundreds of possible combinations, and they rarely have to do with tense -- too much depends on the type of condition and its results, which can vary all over the lot.
Finally, if perchance you fancy something else to count than sheep while you lie in bed sleepless from undreamt nightmares of numberless infinities of English conditional constructions,
you might find diversion in studying my enumeratively enlightening answer to How many conditional types are possible? — preferably with tongue lodged firmly in whichever cheek it is that most ails you.
- ELT Journal 65:1 pp 24–32 (2011), Oxford University Press, doi: 10.1093/elt/ccp101.