DeepSeek-Prover-V2-ultra
DeepSeek Prover V2 is a named formal-proof profile for Lean 4 tasks. Give it the theorem, imports and assumptions and request a proof plan with formal code, then use the Lean environment to check the returned proposal.
- Ailoot Ultra · OpenAI Chat
POST /v1/chat/completionsDeepSeek-Prover-V2-ultra - Ailoot Ultra · Anthropic Messages
POST /v1/messagesDeepSeek-Prover-V2-ultra
About the model
This description covers the model’s capabilities. Available in Ailoot inputs, outputs and options are listed for the selected method below.
DeepSeek Prover V2 is a named hosted profile for the DeepSeek formal-theorem-proving family. The maker describes Prover V2 as connecting informal mathematical reasoning with formal proofs in Lean 4. The supplied theorem and its environment define the result the model should establish.
Provide a complete formal task
Include the Lean statement, relevant imports, assumptions and definitions. Ask for the proof plan and the formal code needed to complete the proposition. Intermediate lemmas can make the relationship between the mathematical idea and formal proof structure easier to inspect.
Preserve the statement when revising a proposal. If Lean rejects a step, provide the diagnostic and the surrounding code and ask for a correction at that location. The generated text is a proof proposal; acceptance comes from the formal environment that checks it.
Retain the profile and verification evidence
The published hosted profile lists a 128,000-token context and a 128,000-token completion allowance. Use the active interface’s working budget for the actual statement, conversation and response, with appropriate space for each.
The maker releases the family in more than one model size, while this hosted profile’s name does not identify a size. Keep that identity distinction when saving results rather than assigning it the architecture or limits of a specific 7B or 671B release. Retain the original theorem, generated proof and verifier output together.
Practical task
Complete a Lean inequality proof
Technical example in English
Complete a Lean inequality proof
Complete this Lean 4 proof without changing its statement or using sorry. Include a short proof plan and the complete proposed code.
import Mathlib
theorem add_preserves_order (a b c : ℕ) (h : a ≤ b) : a + c ≤ b + c := by
-- proof here
The result will be checked in a Mathlib-enabled Lean environment.Expected result
A brief proof plan followed by a complete Lean code block preserving the imports, theorem name, parameters and conclusion.Check the result
Compile the proposal in the stated Lean environment and confirm there are no sorry placeholders or added assumptions.Ailoot Ultra · OpenAI Chat POST /v1/chat/completions DeepSeek-Prover-V2-ultra
DeepSeek-Prover-V2-ultraOverview
DeepSeek Prover V2 is a named formal-proof profile for Lean 4 tasks. Give it the theorem, imports and assumptions and request a proof plan with formal code, then use the Lean environment to check the returned proposal.
- Accepted inputs
- Text
- Results
- Text
Available in Ailoot · inputs & methods
Ailoot Ultra · OpenAI Chat POST /v1/chat/completions
- Input types
text- Output types
text- Output format
- json or SSE
| Field | Type | Requirement | Values & limits | Default |
|---|---|---|---|---|
Fieldmodel | Typestring | RequirementRequired | Values & limits DeepSeek-Prover-V2-ultra | Default— |
Fieldmessages | Typemessage[] | RequirementRequired | Values & limits Minimum items: 1 | Default— |
Fieldmessages[].role | Typestring | RequirementRequired | Values & limits Examples: system, user, assistant, tool, function Conditions: These roles are explicitly represented by Source compatibility types; the exact model role set remains model-specific. Model-specific | Default— |
Fieldmessages[].content | Typestring|content_part[]|null | RequirementOptional | Values & limits | Default— |
Fieldmessages[].tool_calls | Typetool_call[] | RequirementOptional | Values & limits | Default— |
Fieldmessages[].tool_call_id | Typestring | RequirementOptional | Values & limits Applies when: role=tool; use actual returned ID | Default— |
Fieldmessages[].name | Typestring | RequirementOptional | Values & limits | Default— |
Fieldmessages[].reasoning_content | Typestring | RequirementOptional | Values & limits Applies when: Round-trip actual returned reasoning where this model uses it | Default— |
Fieldmessages[].reasoning_details | Typeobject|array | RequirementOptional | Values & limits Model-specific | Default— |
Fieldmax_tokens | Typeinteger | RequirementOptional | Values & limits Minimum: 1 Model-specific | Default— |
Fieldmax_completion_tokens | Typeinteger | RequirementOptional | Values & limits Minimum: 1 Model-specific | Default— |
Fieldstream | Typeboolean | RequirementOptional | Values & limits | Defaultfalse |
Fieldstream_options.include_usage | Typeboolean | RequirementOptional | Values & limits Model-specific | Default— |
Fieldtemperature | Typenumber | RequirementOptional | Values & limits Model-specific | Default— |
Fieldtop_p | Typenumber | RequirementOptional | Values & limits Model-specific | Default— |
Fieldstop | Typestring|string[] | RequirementOptional | Values & limits Model-specific | Default— |
Fieldtools | Typefunction_tool[] | RequirementOptional | Values & limits Model-specific | Default— |
Fieldtools[].type | Typestring | RequirementOptional | Values & limits function Model-specific | Default— |
Fieldtools[].function.name | Typestring | RequirementRequired | Values & limits Applies when: function tool supplied | Default— |
Fieldtools[].function.description | Typestring | RequirementOptional | Values & limits | Default— |
Fieldtools[].function.parameters | TypeJSON_schema | RequirementOptional | Values & limits | Default— |
Fieldtool_choice | Typestring|object | RequirementOptional | Values & limits Model-specific | Default— |
Fieldparallel_tool_calls | Typeboolean | RequirementOptional | Values & limits Model-specific | Default— |
Fieldresponse_format | Typeobject | RequirementOptional | Values & limits Model-specific | Default— |
Fieldreasoning_effort | Typestring | RequirementOptional | Values & limits Model-specific | Default— |
Fieldreasoning | Typeobject | RequirementOptional | Values & limits Model-specific | Default— |
Fieldservice_tier | Typestring | RequirementOptional | Values & limits Model-specific | Default— |
Fieldinstructions | Typestring | RequirementOptional | Values & limits Compatibility field | Default— |
Fieldfunctions | Typefunction[] | RequirementOptional | Values & limits Model-specific | Default— |
Fieldfunction_call | Typestring|object | RequirementOptional | Values & limits Model-specific | Default— |
Fieldprompt_cache_options | Typeobject | RequirementOptional | Values & limits Model-specific | Default— |
Fieldmodalities | Typestring[] | RequirementOptional | Values & limits text | Default— |
Fieldprovider | Typeobject | RequirementOptional | Values & limits Conditions: provider.options is rejected on this Ultra text route | Default— |
Fieldcache_control.ttl | Typestring | RequirementOptional | Values & limits Conditions: 1h is rejected in actual prompt-cache locations | Default— |
Input material combinations
Text · UTF8 text
messages[].content
Method parameters and lifecycle
| Parameter | Contract |
|---|---|
Parametercontent_type | Contractapplication/json |
Parameterrequired | Contractmodel, messages |
Parametermaterial_types | Contracttext |
Parametermessages | Contractmessage array with role/content shape |
Parameterfile_material | Contractactual UTF-8 document inserted as literal text; no file ID inferred |
Parameteroptional_controls | Contractstream, temperature, top_p, stop, max_tokens, max_completion_tokens, reasoning, response_format, tools, tool_choice |
Parametercontrol_scope | Contractmodel-specific; user function tools differ from hosted tools |
Parameteroutput_modalities | Contracttext |
Parameterhosted_operations | Contractfalse |
Parametermultimodal_input_binding | Contractnull |
Lifecycle: synchronous_or_streamed
Send exact model ID with messages.
Context length is not an output cap.
A text file may supply literal text; image/audio/file-object inputs need exact binding.
Pricing
Tariff references do not add request options. Supported parameters are listed for the selected method.
- Fast mode
- Not specified When fast mode is selected
- Flex mode
- Not specified When flex mode is selected
- Maximum reasoning effort
- Not specified When maximum reasoning effort uses the default adjustment
Ailoot rates
Prices by configuration
| Configuration | Rate schedule | Charge |
|---|---|---|
| ConfigurationBase token rates | Rate scheduleBase rate | Charge Input · Input tokens $0.00114 / 1K tokens Output · Output tokens $0.00458 / 1K tokens Input · Cache read $0 / 1K tokens Input · Cache write $0 / 1K tokens Input · Cache write, 1 hour — / 1K tokens |
Ailoot reserves an estimated amount before a request. After the result, it settles the final charge from measured usage. Streaming settlement uses the final usage record. How reservation and settlement work →
Example requests
Ailoot Ultra · OpenAI Chat
set -eu
: "${AILOOT_API_KEY:?Set your Ailoot API key}"
python3 - <<'PY_REQUEST'
import json,os
from pathlib import Path
p=json.loads('{"model": "DeepSeek-Prover-V2-ultra", "messages": [{"role": "user", "content": "Explain the difference between an observation and a hypothesis in three sentences."}]}')
Path("request.json").write_text(json.dumps(p,ensure_ascii=False))
PY_REQUEST
curl --fail-with-body --silent --show-error https://api.ailoot.ai/v1/chat/completions \
-H "Authorization: Bearer $AILOOT_API_KEY" -H 'Content-Type: application/json' \
--data-binary @request.json -D response-headers.txt -o result.json
python3 - <<'PY_RESULT'
import json
from pathlib import Path
r=json.loads(Path("result.json").read_text())
for x in r.get("choices",[]):
if x.get("message",{}).get("content"): print(x["message"]["content"])
PY_RESULT
from openai import OpenAI
import os
if not os.environ.get("AILOOT_API_KEY", "").strip(): raise SystemExit("Set AILOOT_API_KEY before making a request")
client=OpenAI(base_url="https://api.ailoot.ai/v1",api_key=os.environ["AILOOT_API_KEY"],max_retries=0)
result=client.chat.completions.create(model='DeepSeek-Prover-V2-ultra',messages=[{"role":"user","content":"Explain observations and hypotheses in three sentences."}])
import base64, json
from pathlib import Path
def save_result(data, stem="result"):
# Keep every field, including usage, IDs, reasoning and tool requests.
Path(stem + ".json").write_text(json.dumps(data, ensure_ascii=False, indent=2), encoding="utf-8")
print(json.dumps(data, ensure_ascii=False, indent=2))
def save_blob(encoded, suffix, label):
raw = base64.b64decode(encoded, altchars=b"-_", validate=True)
ext = "png" if raw.startswith(b"\x89PNG\r\n\x1a\n") else "jpg" if raw.startswith(b"\xff\xd8") else "webp" if raw[:4] == b"RIFF" and raw[8:12] == b"WEBP" else suffix
file = Path(stem + "-" + label + "." + ext)
file.write_bytes(raw)
print("Saved", file)
for index, block in enumerate(data.get("content") or []):
print("Content", index, json.dumps(block, ensure_ascii=False))
for choice in data.get("choices") or []:
print("Choice", choice.get("index"), json.dumps(choice.get("message", choice.get("delta", {})), ensure_ascii=False))
for index, item in enumerate(data.get("output") or []):
print("Output", index, json.dumps(item, ensure_ascii=False))
if item.get("type") == "image_generation_call" and item.get("result"):
save_blob(item["result"], item.get("output_format") or "bin", "output-" + str(index))
for ci, candidate in enumerate(data.get("candidates") or []):
for pi, part in enumerate((candidate.get("content") or {}).get("parts") or []):
print("Candidate/part", ci, pi, json.dumps(part, ensure_ascii=False))
blob = part.get("inlineData") or part.get("inline_data")
if blob and blob.get("data"):
mime = blob.get("mimeType") or blob.get("mime_type")
suffix = {"image/png":"png", "image/jpeg":"jpg", "image/webp":"webp", "audio/wav":"wav", "audio/mpeg":"mp3", "video/mp4":"mp4"}.get(mime, "bin")
save_blob(blob["data"], suffix, "candidate-" + str(ci) + "-part-" + str(pi))
save_result(result.to_dict(mode="json"))
from openai import OpenAI
import os
from pathlib import Path
if not os.environ.get("AILOOT_API_KEY", "").strip(): raise SystemExit("Set AILOOT_API_KEY before making a request")
client=OpenAI(base_url="https://api.ailoot.ai/v1",api_key=os.environ["AILOOT_API_KEY"],max_retries=0)
import base64, json
from pathlib import Path
def save_result(data, stem="result"):
# Keep every field, including usage, IDs, reasoning and tool requests.
Path(stem + ".json").write_text(json.dumps(data, ensure_ascii=False, indent=2), encoding="utf-8")
print(json.dumps(data, ensure_ascii=False, indent=2))
def save_blob(encoded, suffix, label):
raw = base64.b64decode(encoded, altchars=b"-_", validate=True)
ext = "png" if raw.startswith(b"\x89PNG\r\n\x1a\n") else "jpg" if raw.startswith(b"\xff\xd8") else "webp" if raw[:4] == b"RIFF" and raw[8:12] == b"WEBP" else suffix
file = Path(stem + "-" + label + "." + ext)
file.write_bytes(raw)
print("Saved", file)
for index, block in enumerate(data.get("content") or []):
print("Content", index, json.dumps(block, ensure_ascii=False))
for choice in data.get("choices") or []:
print("Choice", choice.get("index"), json.dumps(choice.get("message", choice.get("delta", {})), ensure_ascii=False))
for index, item in enumerate(data.get("output") or []):
print("Output", index, json.dumps(item, ensure_ascii=False))
if item.get("type") == "image_generation_call" and item.get("result"):
save_blob(item["result"], item.get("output_format") or "bin", "output-" + str(index))
for ci, candidate in enumerate(data.get("candidates") or []):
for pi, part in enumerate((candidate.get("content") or {}).get("parts") or []):
print("Candidate/part", ci, pi, json.dumps(part, ensure_ascii=False))
blob = part.get("inlineData") or part.get("inline_data")
if blob and blob.get("data"):
mime = blob.get("mimeType") or blob.get("mime_type")
suffix = {"image/png":"png", "image/jpeg":"jpg", "image/webp":"webp", "audio/wav":"wav", "audio/mpeg":"mp3", "video/mp4":"mp4"}.get(mime, "bin")
save_blob(blob["data"], suffix, "candidate-" + str(ci) + "-part-" + str(pi))
with client.chat.completions.stream(model='DeepSeek-Prover-V2-ultra',messages=[{"role":"user","content":"Explain observations and hypotheses in three sentences."}]) as stream:
with Path("stream-events.jsonl").open("w",encoding="utf-8") as log:
for event in stream:
payload=event.to_dict(mode="json")
log.write(json.dumps(payload,ensure_ascii=False)+"\n"); log.flush()
print(json.dumps(payload,ensure_ascii=False))
final=stream.get_final_completion()
save_result(final.to_dict(mode="json"),"stream-result")
Receive and save results
Ailoot Ultra · OpenAI Chat
json or SSE
Keep all completed results
Keep every complete returned response, file and content part.
Keep every choice and its content/tool calls/reasoning. In SSE assemble deltas by choice/tool index, retain the final finish reason and usage.
If the original response needs checking
Keep request/response IDs and headers. No generic text job retrieval URL is supplied.
Response fields
| Field | Type |
|---|---|
Fieldchoices[].index | Typeinteger |
Fieldchoices[].message.content | Typestring|null |
Fieldchoices[].message.tool_calls | Typetool_call[] |
Fieldchoices[].message.reasoning_content | Typestring |
Fieldchoices[].message.reasoning_details | Typeobject|array |
Fieldchoices[].finish_reason | Typestring|null |
Fieldusage | Typeobject |
Errors and next steps
| Response | Condition | Next step |
|---|---|---|
Response400 · invalid_request_error | ConditionInvalid required fields, material representation or parameter value | Next stepCorrect the indicated fields before a new creation request. |
Aliases
Model aliases
Ailoot Ultra DeepSeek-Prover-V2-ultra
Method path aliases
Use the method paths shown above.
Related caller IDs
Ailoot Ultra · Anthropic Messages POST /v1/messages DeepSeek-Prover-V2-ultra
DeepSeek-Prover-V2-ultraOverview
DeepSeek Prover V2 is a named formal-proof profile for Lean 4 tasks. Give it the theorem, imports and assumptions and request a proof plan with formal code, then use the Lean environment to check the returned proposal.
- Accepted inputs
- Text
- Results
- json · sse
Available in Ailoot · inputs & methods
Ailoot Ultra · Anthropic Messages POST /v1/messages
- Input types
text- Output types
json,sse- Output format
- JSON or SSE
| Field | Type | Requirement | Values & limits | Default |
|---|---|---|---|---|
Fieldmodel | Typestring | RequirementRequired | Values & limits DeepSeek-Prover-V2-ultra | Default— |
Fieldmessages | Typemessage[] | RequirementRequired | Values & limits | Default— |
Fieldmessages[].role | Typestring | RequirementRequired | Values & limits user, assistant | Default— |
Fieldmessages[].content | Typestring | RequirementRequired | Values & limits | Default— |
Fieldmax_tokens | Typeinteger | RequirementRequired | Values & limits | Default— |
Fieldstream | Typeboolean | RequirementOptional | Values & limits | Defaultfalse |
Input material combinations
Text · UTF-8 text
messages[].content string
Method parameters and lifecycle
| Parameter | Contract |
|---|---|
Parametercontent_type | Contractapplication/json |
Parameterrequired | Contractmodel, messages, max_tokens |
Parameteroptional_controls | Contractstream |
Parametermaterial_types | Contracttext |
Parametertext_file_material | ContractRead the actual UTF-8 document and put its text in the indicated input or message content string. |
Lifecycle: synchronous_or_streamed
Pricing
Tariff references do not add request options. Supported parameters are listed for the selected method.
- Fast mode
- Not specified When fast mode is selected
- Flex mode
- Not specified When flex mode is selected
- Maximum reasoning effort
- Not specified When maximum reasoning effort uses the default adjustment
Ailoot rates
Prices by configuration
| Configuration | Rate schedule | Charge |
|---|---|---|
| ConfigurationBase token rates | Rate scheduleBase rate | Charge Input · Input tokens $0.00114 / 1K tokens Output · Output tokens $0.00458 / 1K tokens Input · Cache read $0 / 1K tokens Input · Cache write $0 / 1K tokens Input · Cache write, 1 hour — / 1K tokens |
Ailoot reserves an estimated amount before a request. After the result, it settles the final charge from measured usage. Streaming settlement uses the final usage record. How reservation and settlement work →
Example requests
Ailoot Ultra · Anthropic Messages
{
"model": "DeepSeek-Prover-V2-ultra",
"max_tokens": 128,
"messages": [
{
"role": "user",
"content": "Summarize the incident report."
}
],
"stream": false
}set -eu
: "${AILOOT_API_KEY:?Set your Ailoot API key}"
: "${AILOOT_TEXT_FILE:?Set your actual UTF-8 document}"
export AILOOT_TEXT_FILE
python3 - <<'PY_REQUEST'
import json, os
from pathlib import Path
source_file = Path(os.environ['AILOOT_TEXT_FILE'])
if not source_file.is_file():
raise SystemExit('Set AILOOT_TEXT_FILE to your actual UTF-8 document')
text = source_file.read_text(encoding='utf-8')
if not text.strip():
raise SystemExit('Choose a document containing text')
payload = {'model': 'DeepSeek-Prover-V2-ultra', 'max_tokens': 128, 'messages': [{'role': 'user', 'content': 'Summarize the incident report.'}]}
payload['messages'][0]['content'] = 'Summarize this material and quote supporting source passages.\n\n' + text
Path('request.json').write_text(json.dumps(payload, ensure_ascii=False), encoding='utf-8')
PY_REQUEST
curl --fail-with-body --silent --show-error https://api.ailoot.ai/v1/messages \
-H "x-api-key: $AILOOT_API_KEY" -H 'anthropic-version: 2023-06-01' -H 'Content-Type: application/json' \
--data-binary @request.json -D response-headers.txt -o result.json
python3 - <<'PY_RESULT'
import json
from pathlib import Path
result = json.loads(Path('result.json').read_text(encoding='utf-8'))
print(json.dumps(result, ensure_ascii=False, indent=2))
PY_RESULT
import json, os
from pathlib import Path
source_file = Path(os.environ['AILOOT_TEXT_FILE'])
if not source_file.is_file():
raise SystemExit('Set AILOOT_TEXT_FILE to your actual UTF-8 document')
text = source_file.read_text(encoding='utf-8')
if not text.strip():
raise SystemExit('Choose a document containing text')
payload = {'model': 'DeepSeek-Prover-V2-ultra', 'max_tokens': 128, 'messages': [{'role': 'user', 'content': 'Summarize the incident report.'}]}
payload['messages'][0]['content'] = 'Summarize this material and quote supporting source passages.\n\n' + text
from urllib.request import Request, urlopen
from urllib.error import HTTPError
api_key = os.environ['AILOOT_API_KEY']
if not api_key.strip():
raise SystemExit('Set AILOOT_API_KEY before making a request')
headers = {'x-api-key': 'PLACEHOLDER_KEY', 'anthropic-version': '2023-06-01', 'Content-Type': 'application/json'}
headers['x-api-key'] = api_key
request = Request('https://api.ailoot.ai/v1/messages', data=json.dumps(payload, ensure_ascii=False).encode('utf-8'), headers=headers, method='POST')
try:
with urlopen(request, timeout=120) as response:
raw = response.read()
Path('response-headers.txt').write_text(str(response.headers), encoding='utf-8')
except HTTPError as error:
Path('result.json').write_bytes(error.read())
Path('response-headers.txt').write_text(str(error.headers), encoding='utf-8')
raise
Path('result.json').write_bytes(raw)
import json
from pathlib import Path
result = json.loads(Path('result.json').read_text(encoding='utf-8'))
print(json.dumps(result, ensure_ascii=False, indent=2))
Receive and save results
Ailoot Ultra · Anthropic Messages
JSON or SSE
Keep all completed results
Keep every complete returned response, file and content part.
Keep all content blocks, thinking signatures and actual tool-use IDs. Assemble all SSE block deltas; a first text block is not the complete output.
If the original response needs checking
Keep request/response IDs and headers. No generic text job retrieval URL is supplied.
Response fields
| Field | Type |
|---|---|
Fieldid | Typestring |
Fieldmodel | Typestring |
Fieldcontent[] | Typetext|thinking|tool_use|other content block |
Fieldstop_reason | Typestring|null |
Fieldusage | Typeobject |
Errors and next steps
| Response | Condition | Next step |
|---|---|---|
Response400 · invalid_request_error | ConditionInvalid required fields, material representation or parameter value | Next stepCorrect the indicated fields before a new creation request. |
Aliases
Model aliases
Ailoot Ultra DeepSeek-Prover-V2-ultra
Method path aliases
Use the method paths shown above.
Related caller IDs
FAQ · DeepSeek-Prover-V2-ultra
- What inputs and results are available?
POST /v1/chat/completions·DeepSeek-Prover-V2-ultra:text→textPOST /v1/messages·DeepSeek-Prover-V2-ultra:text→json,sse- Which fields does the request use?
POST /v1/chat/completions·DeepSeek-Prover-V2-ultra:model,messages,stream,modalities,providerPOST /v1/messages·DeepSeek-Prover-V2-ultra:model,messages,max_tokens,stream- What limits apply?
POST /v1/chat/completions·DeepSeek-Prover-V2-ultra:messages.min_items:1