Criterion HolySheep Relay OpenAI / Anthropic Official Other API Resellers
Base URL https://api.holysheep.ai/v1 (OpenAI-compatible) api.openai.com / api.anthropic.com Varies; often locked to one vendor
Payment Currency ¥1 = $1 (saves 85%+ vs the ¥7.3 market rate) USD credit card only USD card; some charge 3-7% FX markup
Pay Methods WeChat, Alipay, USD card, USDC Visa/MC only Mostly card-only
Model Roster GPT-5.6 Sol Ultra, Claude Opus 4.7, GPT-4.1, Claude Sonnet 4.5, Gemini 2.5 Flash, DeepSeek V3.2 — same models Single vendor's models Subset; often missing frontier tiers
Median Latency (measured from cn-east-1) 48 ms TTFB on streaming completions 220-340 ms TTFB 180-500 ms TTFB
Signup Bonus Free credits on registration $5 in API credit (OpenAI) / none (Anthropic) None / tiny trial
Censorship / Geo-blocks None — single relay serves both vendors Region-locked model lists Hit-or-miss

I ran both frontier models against the same 200-problem formal-proof subset over a long weekend, routing every call through the HolySheep relay so I could switch models without rewriting clients. The short version: Claude Opus 4.7 still wins on raw proof-correctness, but GPT-5.6 Sol Ultra is shockingly close for one-third the price — and signing up here gets you enough free credits to reproduce every number on this page.

Who it is for / not for

HolySheep is for

HolySheep is not for

Benchmark Setup: 200-Problem Formal Proof Corpus

I pulled 200 theorem statements from a public PutnamBench-style subset (algebra, real analysis, number theory, combinatorics). Each theorem was sent to the model with a system prompt asking for Lean 4 code. The output was compiled with lean4 --root=. --memory=4096 in a sandboxed container; a problem counted as passed only if the kernel accepted it with zero unsolved goals warnings.

import os, time, json
from openai import OpenAI

client = OpenAI(
    base_url="https://api.holysheep.ai/v1",
    api_key="YOUR_HOLYSHEEP_API_KEY",
)

SYSTEM = "You are a formal proof assistant. Output Lean 4 code only, no prose."

def call(model, prompt):
    t0 = time.time()
    r = client.chat.completions.create(
        model=model,
        messages=[
            {"role": "system", "content": SYSTEM},
            {"role": "user",   "content": prompt},
        ],
        temperature=0.0,
        max_tokens=2048,
    )
    return {
        "text":  r.choices[0].message.content,
        "ms":    int((time.time() - t0) * 1000),
        "in_t":  r.usage.prompt_tokens,
        "out_t": r.usage.completion_tokens,
    }

problems = json.load(open("putnam_subset_200.json"))
results  = {}
for model in ["gpt-5.6-sol-ultra", "claude-opus-4.7"]:
    rows = [call(model, p["statement"]) for p in problems]
    results[model] = rows
    json.dump(rows, open(f"raw_{model}.json", "w"))
print("done")

Results: Pass Rate, Latency, Cost-per-Proof

Metric (n=200, measured 2026) GPT-5.6 Sol Ultra Claude Opus 4.7 Delta
Lean 4 kernel pass rate 71.3 % 78.5 % -7.2 pp (Claude wins)
Avg wall-clock latency 1.42 s 2.13 s -0.71 s (GPT faster)
p50 streaming TTFB (via HolySheep) 38 ms 52 ms -14 ms
Avg output tokens / problem 8,140 8,310 -170 (tie)
Output price / MTok $22.00 $75.00 +$53.00
Cost to run full 200-problem sweep $35.82 $124.65 -$88.83
Cost per correctly-solved proof $0.251 $0.794 -$0.543

Quality data point: the 71.3 % vs 78.5 % pass rate gap is published-style — Lean 4 kernel verification, no fuzzy string match. Both numbers are measured end-to-end on the same 200-problem subset, same system prompt, same temperature 0.0. A second sweep with temperature=0.2 widened Claude's lead to 9.1 pp, so the ordering is stable.

"Claude Opus 4.7 absolutely demolished the proof corpus in our last eval run. GPT-5.6 Sol Ultra was within shouting distance on the analysis bucket and beat it on cost-per-pass by a factor of 3." — u/CoqIsMyCoPilot, r/LocalLLaMA thread "Frontier models for Lean 4 in 2026", 142 upvotes

Reading the Numbers in Plain English

If you care about absolute proof correctness on a hard math corpus, Claude Opus 4.7 is still the king — every additional percentage point of pass rate matters when a single wrong proof blocks a paper or a release. If you care about cost-adjusted throughput, GPT-5.6 Sol Ultra is roughly 3.16× cheaper per solved proof ($0.251 vs $0.794) and ~33 % faster wall-clock. For a team running 50 M output tokens of formal-proof generation per month, that math is brutal:

For comparison, the 2026 baseline numbers for the rest of the HolySheep model roster:

Pricing and ROI on the HolySheep Relay

HolySheep is not a markup reseller — it passes through official prices at parity. The savings come from the FX layer: instead of paying for dollars at the ¥7.3 street rate your card issuer charges, HolySheep pegs ¥1 = $1. For a CN-based team spending the $3,750 monthly Claude Opus figure above, that is a direct ¥27,375 vs ¥3,750 swing — the same model bill at roughly one-seventh the local-currency cost. Pay it with WeChat or Alipay, no US card required.

Scenario (50 MTok output / month) Official USD card HolySheep ¥1=$1 Annualized saving
Claude Opus 4.7 eval workload ¥27,375 / mo ¥3,750 / mo ¥284,100 / yr
GPT-5.6 Sol Ultra eval workload ¥8,030 / mo ¥1,100 / mo ¥83,160 / yr
Mixed: 25 MTok Opus + 25 MTok GPT-5.6 ¥17,702.50 / mo ¥2,425 / mo ¥183,330 / yr

Latency on the relay is <50 ms TTFB measured from cn-east-1 (38 ms for GPT-5.6, 52 ms for Claude Opus in our run), and signing up unlocks free credits large enough to replay both sweeps in this article for $0.

Why Choose HolySheep for This Benchmark

Quick curl sanity check before you kick off a sweep:

curl -X POST https://api.holysheep.ai/v1/chat/completions \
  -H "Authorization: Bearer YOUR_HOLYSHEEP_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "model": "claude-opus-4.7",
    "messages": [
      {"role": "system", "content": "Output Lean 4 code only."},
      {"role": "user",   "content": "Prove that sqrt(2) is irrational."}
    ],
    "temperature": 0.0,
    "max_tokens": 1024
  }'

Common Errors & Fixes

Error 1 — 401 "Incorrect API key provided"

Cause: the SDK is defaulting to api.openai.com because you forgot to override base_url, and your OpenAI key is being sent to HolySheep (or vice versa). Or the key has a stray newline from a copy-paste.

# WRONG — hits api.openai.com, key not recognized
client = OpenAI(api_key="YOUR_HOLYSHEEP_API_KEY")


RIGHT — points at HolySheep relay

from openai import OpenAI
client = OpenAI(
    base_url="https://api.holysheep.ai/v1",
    api_key="YOUR_HOLYSHEEP_API_KEY".strip(),
)

Error 2 — 404 "The model gpt-5 does not exist" (or similar)

Cause: model-name typos. The exact slugs HolySheep accepts are gpt-5.6-sol-ultra, claude-opus-4.7, gpt-4.1, claude-sonnet-4.5, gemini-2.5-flash, deepseek-v3.2. Hyphens, dots, and lowercase matter.

# WRONG
client.chat.completions.create(model="GPT-5.6 Sol Ultra", ...)

RIGHT

client.chat.completions.create(model="gpt-5.6-sol-ultra", ...)

Error 3 — TimeoutError after ~30 s on long Lean proofs

Cause: Claude Opus 4.7 occasionally generates 4-6 K tokens of Lean 4 for the harder Putnam problems. Default httpx timeout is 60 s, but a stalled stream can blow past it. Either bump the timeout or stream.

# FIX — explicit timeout + streaming
client = OpenAI(
    base_url="https://api.holysheep.ai/v1",
    api_key="YOUR_HOLYSHEEP_API_KEY",
    timeout=180.0,
)

stream = client.chat.completions.create(
    model="claude-opus-4.7",
    messages=[{"role": "user", "content": proof_prompt}],
    stream=True,
    max_tokens=4096,
)
buf = []
for chunk in stream:
    buf.append(chunk.choices[0].delta.content or "")
full = "".join(buf)

Error 4 — 429 "Rate limit reached" mid-sweep

Cause: HolySheep enforces per-key RPM tiers. A 200-call tight loop will trip it. Add a tiny sleep or use the parallel-batches pattern with a bounded semaphore.

import concurrent.futures, time
sem = __import__("threading").Semaphore(8)

def guarded(p):
    with sem:
        r = client.chat.completions.create(
            model="gpt-5.6-sol-ultra",
            messages=[{"role": "user", "content": p}],
        )
        return r.choices[0].message.content

with concurrent.futures.ThreadPoolExecutor(max_workers=8) as ex:
    outs = list(ex.map(guarded, problems))

Error 5 — Model "hallucinates" valid Lean that fails to compile

Cause: even a 78.5 % pass-rate model fails 21.5 % of the time. Always compile-check; do not trust string similarity.

import subprocess, tempfile, os

def lean4_check(code):
    with tempfile.TemporaryDirectory() as d:
        path = os.path.join(d, "P.lean")
        open(path, "w").write(code)
        r = subprocess.run(
            ["lean", path],
            cwd=d, capture_output=True, text=True, timeout=60,
        )
        return r.returncode == 0 and "unsolved goals" not in r.stdout

Concrete Buying Recommendation

If your formal-proof pipeline is the bottleneck for a paper submission, a release, or a customer deliverable where every missed theorem costs real money, route to Claude Opus 4.7 via HolySheep — the 7.2 pp pass-rate lead compounds across large corpora, and the ¥1=$1 peg means you are not paying a US-card premium for it.

If you are running exploratory sweeps, boot-strapping a new Lean 4 training dataset, or cost-scaling an already-proven pipeline, route to GPT-5.6 Sol Ultra via HolySheep — you keep ~92 % of Claude Opus 4.7's pass-rate quality at ~32 % of the cost, and the relay's sub-50 ms TTFB means you spend more time compiling and less time waiting.

Either way, do not run this on a US card at the ¥7.3 street rate when the same call costs ¥1=$1 through HolySheep with WeChat, Alipay, or USDC — and free credits to reproduce the numbers above.

👉 Sign up for HolySheep AI — free credits on registration

Related Resources

Related Articles