models

DeepSeek Prover v2 671B

Markdown · JSON

DeepSeek Prover v2 671B

DeepSeek Prover V2 671B generates formal mathematical proofs in Lean 4, combining a written proof plan with formal code. The maker’s workflow decomposes a theorem into subgoals and uses verification feedback to develop complete proofs.

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 671B is DeepSeek’s large formal-theorem-proving model for Lean 4. It connects informal mathematical reasoning with formal proof construction. The maker describes training material built by decomposing challenging theorems into subgoals, solving them and composing the formal proofs into a complete result.

Supply the formal statement and environment

Give the Lean 4 theorem to complete, including its imports, assumptions and surrounding definitions. The maker’s example supplies a theorem containing a proof placeholder and asks for a proof plan before the Lean code. That arrangement makes the intended mathematical steps visible alongside the formal artifact.

Keep the statement unchanged when requesting a proof. If a lemma or definition is available in the project, supply its exact name and relevant form. The proof must establish the given proposition in that environment; an explanation of a similar proposition is a different result.

Plan the proof through useful subgoals

Ask the model to outline the main ideas, intermediate lemmas and proof structure before producing code. For a longer theorem, these subgoals help connect the mathematical argument with the formal steps needed by Lean. A clear plan also gives the user a way to examine whether the argument addresses every assumption.

The model’s output is a proof proposal and formal code. The application or user runs the code through the Lean environment to determine whether it is accepted. Preserve the original statement, generated code and verifier output together when checking the result.

Use verification feedback for a focused revision

If Lean rejects part of a proposal, supply the diagnostic and the code at the relevant location. Ask for a correction that preserves the theorem statement and resolves that error. A revised proof can then be checked in the same environment, so the observed failure and changed step remain connected.

The maker’s training uses binary correctness feedback to improve formal proof construction. In a practical workflow, the formal verifier provides the decisive evidence about the returned proof. A persuasive written explanation alone does not establish that the Lean code has been accepted.

Preserve the 671B edition

The maker releases Prover V2 in 7B and 671B sizes. The 671B edition is trained on DeepSeek V3 Base; the smaller edition has a different base. This entry retains the large edition and does not borrow the smaller model’s context specification. Prepare the request and generation budget according to the exact hosted profile and Lean task being used.

Practical task

Complete a Lean distributivity proof

Technical example in English

Complete a Lean distributivity proof

Complete this Lean 4 theorem without changing its statement: import Mathlib; theorem pair_sum (a b : ℤ) : (a + b) * 2 = a * 2 + b * 2 := by sorry. Give a brief proof plan, then the replacement proof. Use only the imported environment and distinguish a proposed proof from a compiler-checked result.

Expected result

A short plan followed by Lean code replacing sorry while retaining the theorem statement.

Check the result

Run the unchanged statement and proposed proof in the stated Lean environment; only acceptance establishes success.
Ailoot Ultra · OpenAI Chat POST /v1/chat/completions deepseek/deepseek-prover-v2-671b

deepseek/deepseek-prover-v2-671b

DeepSeek /deepseek/deepseek-prover-v2-671b

Overview

DeepSeek Prover V2 671B generates formal mathematical proofs in Lean 4, combining a written proof plan with formal code. The maker’s workflow decomposes a theorem into subgoals and uses verification feedback to develop complete proofs.

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
FieldTypeRequirementValues & limitsDefault
FieldmodelTypestringRequirementRequiredValues & limits
deepseek/deepseek-prover-v2-671b
Default—
FieldmessagesTypemessage[]RequirementRequiredValues & limits
Minimum items: 1
Default—
Fieldmessages[].roleTypestringRequirementRequiredValues & 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[].contentTypestring|content_part[]|nullRequirementOptionalValues & limitsDefault—
Fieldmessages[].tool_callsTypetool_call[]RequirementOptionalValues & limitsDefault—
Fieldmessages[].tool_call_idTypestringRequirementOptionalValues & limits
Applies when: role=tool; use actual returned ID
Default—
Fieldmessages[].nameTypestringRequirementOptionalValues & limitsDefault—
Fieldmessages[].reasoning_contentTypestringRequirementOptionalValues & limits
Applies when: Round-trip actual returned reasoning where this model uses it
Default—
Fieldmessages[].reasoning_detailsTypeobject|arrayRequirementOptionalValues & limits
Model-specific
Default—
Fieldmax_tokensTypeintegerRequirementOptionalValues & limits
Minimum: 1
Model-specific
Default—
Fieldmax_completion_tokensTypeintegerRequirementOptionalValues & limits
Minimum: 1
Model-specific
Default—
FieldstreamTypebooleanRequirementOptionalValues & limitsDefaultfalse
Fieldstream_options.include_usageTypebooleanRequirementOptionalValues & limits
Model-specific
Default—
FieldtemperatureTypenumberRequirementOptionalValues & limits
Model-specific
Default—
Fieldtop_pTypenumberRequirementOptionalValues & limits
Model-specific
Default—
FieldstopTypestring|string[]RequirementOptionalValues & limits
Model-specific
Default—
FieldtoolsTypefunction_tool[]RequirementOptionalValues & limits
Model-specific
Default—
Fieldtools[].typeTypestringRequirementOptionalValues & limits
function
Model-specific
Default—
Fieldtools[].function.nameTypestringRequirementRequiredValues & limits
Applies when: function tool supplied
Default—
Fieldtools[].function.descriptionTypestringRequirementOptionalValues & limitsDefault—
Fieldtools[].function.parametersTypeJSON_schemaRequirementOptionalValues & limitsDefault—
Fieldtool_choiceTypestring|objectRequirementOptionalValues & limits
Model-specific
Default—
Fieldparallel_tool_callsTypebooleanRequirementOptionalValues & limits
Model-specific
Default—
Fieldresponse_formatTypeobjectRequirementOptionalValues & limits
Model-specific
Default—
Fieldreasoning_effortTypestringRequirementOptionalValues & limits
Model-specific
Default—
FieldreasoningTypeobjectRequirementOptionalValues & limits
Model-specific
Default—
Fieldservice_tierTypestringRequirementOptionalValues & limits
Model-specific
Default—
FieldinstructionsTypestringRequirementOptionalValues & limits
Compatibility field
Default—
FieldfunctionsTypefunction[]RequirementOptionalValues & limits
Model-specific
Default—
Fieldfunction_callTypestring|objectRequirementOptionalValues & limits
Model-specific
Default—
Fieldprompt_cache_optionsTypeobjectRequirementOptionalValues & limits
Model-specific
Default—
FieldmodalitiesTypestring[]RequirementOptionalValues & limits
text
Default—
FieldproviderTypeobjectRequirementOptionalValues & limits
Conditions: provider.options is rejected on this Ultra text route
Default—
Fieldcache_control.ttlTypestringRequirementOptionalValues & limits
Conditions: 1h is rejected in actual prompt-cache locations
Default—
Input material combinations

Text · UTF8 text

messages[].content

Method parameters and lifecycle
ParameterContract
Parametercontent_typeContractapplication/json
ParameterrequiredContractmodel, messages
Parametermaterial_typesContracttext
ParametermessagesContractmessage array with role/content shape
Parameterfile_materialContractactual UTF-8 document inserted as literal text; no file ID inferred
Parameteroptional_controlsContractstream, temperature, top_p, stop, max_tokens, max_completion_tokens, reasoning, response_format, tools, tool_choice
Parametercontrol_scopeContractmodel-specific; user function tools differ from hosted tools
Parameteroutput_modalitiesContracttext
Parameterhosted_operationsContractfalse
Parametermultimodal_input_bindingContractnull

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

ConfigurationRate scheduleCharge
ConfigurationBase token ratesRate scheduleBase rateCharge
Input · Input tokens $0.0012 / 1K tokens
Output · Output tokens $0.0046 / 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

curlPython SDKPython stream
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/deepseek-prover-v2-671b", "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/deepseek-prover-v2-671b',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/deepseek-prover-v2-671b',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
FieldType
Fieldchoices[].indexTypeinteger
Fieldchoices[].message.contentTypestring|null
Fieldchoices[].message.tool_callsTypetool_call[]
Fieldchoices[].message.reasoning_contentTypestring
Fieldchoices[].message.reasoning_detailsTypeobject|array
Fieldchoices[].finish_reasonTypestring|null
FieldusageTypeobject
Errors and next steps
ResponseConditionNext step
Response400 · invalid_request_errorConditionInvalid required fields, material representation or parameter valueNext stepCorrect the indicated fields before a new creation request.

Aliases

Model aliases

Ailoot Ultra deepseek/deepseek-prover-v2-671b

Method path aliases

Use the method paths shown above.

Related caller IDs

deepseek/deepseek-prover-v2-671b

Ailoot Ultra · Anthropic Messages POST /v1/messages deepseek/deepseek-prover-v2-671b

deepseek/deepseek-prover-v2-671b

DeepSeek /deepseek/deepseek-prover-v2-671b

Overview

DeepSeek Prover V2 671B generates formal mathematical proofs in Lean 4, combining a written proof plan with formal code. The maker’s workflow decomposes a theorem into subgoals and uses verification feedback to develop complete proofs.

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
FieldTypeRequirementValues & limitsDefault
FieldmodelTypestringRequirementRequiredValues & limits
deepseek/deepseek-prover-v2-671b
Default—
FieldmessagesTypemessage[]RequirementRequiredValues & limitsDefault—
Fieldmessages[].roleTypestringRequirementRequiredValues & limits
user, assistant
Default—
Fieldmessages[].contentTypestringRequirementRequiredValues & limitsDefault—
Fieldmax_tokensTypeintegerRequirementRequiredValues & limitsDefault—
FieldstreamTypebooleanRequirementOptionalValues & limitsDefaultfalse
Input material combinations

Text · UTF-8 text

messages[].content string

Method parameters and lifecycle
ParameterContract
Parametercontent_typeContractapplication/json
ParameterrequiredContractmodel, messages, max_tokens
Parameteroptional_controlsContractstream
Parametermaterial_typesContracttext
Parametertext_file_materialContractRead 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

ConfigurationRate scheduleCharge
ConfigurationBase token ratesRate scheduleBase rateCharge
Input · Input tokens $0.0012 / 1K tokens
Output · Output tokens $0.0046 / 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

Complete minimal JSON bodycurl · use your UTF-8 documentPython · save the complete result
{
  "model": "deepseek/deepseek-prover-v2-671b",
  "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/deepseek-prover-v2-671b', '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/deepseek-prover-v2-671b', '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
FieldType
FieldidTypestring
FieldmodelTypestring
Fieldcontent[]Typetext|thinking|tool_use|other content block
Fieldstop_reasonTypestring|null
FieldusageTypeobject
Errors and next steps
ResponseConditionNext step
Response400 · invalid_request_errorConditionInvalid required fields, material representation or parameter valueNext stepCorrect the indicated fields before a new creation request.

Aliases

Model aliases

Ailoot Ultra deepseek/deepseek-prover-v2-671b

Method path aliases

Use the method paths shown above.

Related caller IDs

deepseek/deepseek-prover-v2-671b

FAQ · deepseek/deepseek-prover-v2-671b
What inputs and results are available?

POST /v1/chat/completions · deepseek/deepseek-prover-v2-671b: text → text

POST /v1/messages · deepseek/deepseek-prover-v2-671b: text → json, sse

Which fields does the request use?

POST /v1/chat/completions · deepseek/deepseek-prover-v2-671b: model, messages, stream, modalities, provider

POST /v1/messages · deepseek/deepseek-prover-v2-671b: model, messages, max_tokens, stream

What limits apply?

POST /v1/chat/completions · deepseek/deepseek-prover-v2-671b: messages.min_items: 1

More details

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