No, system prompts are surrounded by [INST] [/INST]

No, every user input is surrounded by those tags. Scroll down from that link you posted and read the next two example prompts.

No this isn't the case.

Here's the example from https://www.promptingguide.ai/models/mistral-7b#chat-templat...

<s>[INST] What is your favorite condiment? [/INST] "Well, I'm quite partial to a good squeeze of fresh lemon juice. It adds just the right amount of zesty flavour to whatever I'm cooking up in the kitchen!"</s> [INST] The right amount of what? [/INST]

Note that the sentence starting "Well, I'm quite partial isn't inside the tag.

This example comes from the official system card created by MistralAI available here: https://huggingface.co/mistralai/Mistral-7B-Instruct-v0.1

You can try it:

   ollama run Mistral "<s>[INST] What is your favorite condiment? [/INST] Well, I'm quite partial to a good squeeze of fresh lemon juice. It adds just the right amount of zesty flavour to whatever I'm cooking up in the kitchen</s> [INST] The right amount of what? [/INST]"

That's the whole context with two user inputs in the INST tags, and one assistant output between/outside of the tags. They're just simulating the beginning of a conversation. You can see this very clearly in the JSON version in the next code block:

  messages = [
    {"role": "user", "content": "What is your favourite condiment?"},
    {"role": "assistant", "content": "Well, I'm quite partial to a good squeeze of fresh lemon juice. It adds just the right amount of zesty flavour to whatever I'm cooking up in the kitchen!"},
    {"role": "user", "content": "Do you have mayonnaise recipes?"}
  ]

Yes, but this whole block of text gets passed to the LLM on each call as the conversation history. The [INST] tags tell the LLM which parts were inputs (system instructions) as opposed to outputs.

Well, that's not what a system prompt is. There is a difference between system prompts and regular conversational inputs. https://platform.openai.com/docs/guides/prompt-engineering/t...

In actual fact system prompts are just the instruction tuning prompts that provide instructions formatted in the correct way (ie, with [INST]). It's just text all the way down.