challenge_id stringclasses 487
values | source stringclasses 1
value | split stringclasses 2
values | theorem_name stringclasses 487
values | challenge_lean stringclasses 487
values | prover_id stringclasses 1
value | attempt int64 0 39 | stop_reason stringclasses 1
value | trace stringlengths 1.17k 47.5k | grade stringclasses 2
values | grade_detail stringclasses 3
values | curation_status stringclasses 4
values | n_valid int64 0 37 | n_invalid int64 0 39 | interval_low float64 0 0.84 | interval_high float64 0.08 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
aimeII_2001_p3 | minif2f | validation | aimeII_2001_p3 | import Mathlib.Algebra.BigOperators.Basic
import Mathlib.Data.Real.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Data.Nat.Log
import Mathlib.Data.Complex.Exponential
import Mathlib.NumberTheory.Divisors
import Mathlib.Data.ZMod.Defs
import Mathlib.Data.ZMod.Basic
import Mathlib.Topology.Basic
import Mathlib.Da... | deepseek-ai/DeepSeek-Prover-V2-7B | 0 | eos | ### Detailed Proof and Analysis
First, we need to understand the problem. We have a sequence of integers `x(n)` defined for all natural numbers `n`, with initial values:
- `x(1) = 211`,
- `x(2) = 375`,
- `x(3) = 420`,
- `x(4) = 523`,
and for `n ≥ 5`, it satisfies the recurrence relation:
`x(n) = x(n - 1) - x(n - 2) + ... | invalid | lean did not elaborate cleanly (status=error) | single_class | 0 | 3 | 0 | 0.195172 |
aimeII_2001_p3 | minif2f | validation | aimeII_2001_p3 | import Mathlib.Algebra.BigOperators.Basic
import Mathlib.Data.Real.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Data.Nat.Log
import Mathlib.Data.Complex.Exponential
import Mathlib.NumberTheory.Divisors
import Mathlib.Data.ZMod.Defs
import Mathlib.Data.ZMod.Basic
import Mathlib.Topology.Basic
import Mathlib.Da... | deepseek-ai/DeepSeek-Prover-V2-7B | 1 | eos | ### Detailed Proof and Analysis
First, we need to determine the values of `x 5`, `x 6`, ..., `x 975` using the recurrence relation:
\[ x_n = x_{n-1} - x_{n-2} + x_{n-3} - x_{n-4} \]
for \( n \geq 5 \). The initial conditions are:
1. \( x_1 = 211 \)
2. \( x_2 = 375 \)
3. \( x_3 = 420 \)
4. \( x_4 = 523 \)
#### Step 1:... | invalid | lean did not elaborate cleanly (status=error) | single_class | 0 | 3 | 0 | 0.195172 |
aimeII_2001_p3 | minif2f | validation | aimeII_2001_p3 | import Mathlib.Algebra.BigOperators.Basic
import Mathlib.Data.Real.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Data.Nat.Log
import Mathlib.Data.Complex.Exponential
import Mathlib.NumberTheory.Divisors
import Mathlib.Data.ZMod.Defs
import Mathlib.Data.ZMod.Basic
import Mathlib.Topology.Basic
import Mathlib.Da... | deepseek-ai/DeepSeek-Prover-V2-7B | 2 | eos | ### Detailed Proof and Analysis
First, we observe that the problem involves a recurrence relation for a sequence of integers indexed by natural numbers. The recurrence is not straightforward, as it's non-linear and depends on the previous four terms. The initial terms are given, and we need to compute \(x_{531} + x_{7... | invalid | lean did not elaborate cleanly (status=error) | single_class | 0 | 3 | 0 | 0.195172 |
aimeII_2020_p6 | minif2f | validation | aimeII_2020_p6 | import Mathlib.Algebra.BigOperators.Basic
import Mathlib.Data.Real.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Data.Nat.Log
import Mathlib.Data.Complex.Exponential
import Mathlib.NumberTheory.Divisors
import Mathlib.Data.ZMod.Defs
import Mathlib.Data.ZMod.Basic
import Mathlib.Topology.Basic
import Mathlib.Da... | deepseek-ai/DeepSeek-Prover-V2-7B | 0 | eos | ### Detailed Proof and Analysis
First, we need to understand the problem. We have a sequence \( t_n \) defined by:
- \( t_1 = 20 \)
- \( t_2 = 21 \)
- For \( n \geq 3 \), \( t_n = \frac{5 \cdot t_{n-1} + 1}{25 \cdot t_{n-2}} \)
We are to compute \( \text{den}(t_{2020}) + \text{num}(t_{2020}) \) where:
1. \( \text{den... | invalid | lean did not elaborate cleanly (status=error) | single_class | 0 | 3 | 0 | 0.195172 |
aimeII_2020_p6 | minif2f | validation | aimeII_2020_p6 | import Mathlib.Algebra.BigOperators.Basic
import Mathlib.Data.Real.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Data.Nat.Log
import Mathlib.Data.Complex.Exponential
import Mathlib.NumberTheory.Divisors
import Mathlib.Data.ZMod.Defs
import Mathlib.Data.ZMod.Basic
import Mathlib.Topology.Basic
import Mathlib.Da... | deepseek-ai/DeepSeek-Prover-V2-7B | 1 | eos | ### Detailed Proof and Analysis
First, let's understand the problem and the sequence `t(n)`:
1. **Initial Terms**:
- `t(1) = 20`
- `t(2) = 21`
2. **Recurrence Relation for `n ≥ 3`**:
- `t(n) = (5 * t(n - 1) + 1) / (25 * t(n - 2))`
Our goal is to compute `t(2020)` and show that its numerator and denominator... | invalid | lean did not elaborate cleanly (status=error) | single_class | 0 | 3 | 0 | 0.195172 |
aimeII_2020_p6 | minif2f | validation | aimeII_2020_p6 | import Mathlib.Algebra.BigOperators.Basic
import Mathlib.Data.Real.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Data.Nat.Log
import Mathlib.Data.Complex.Exponential
import Mathlib.NumberTheory.Divisors
import Mathlib.Data.ZMod.Defs
import Mathlib.Data.ZMod.Basic
import Mathlib.Topology.Basic
import Mathlib.Da... | deepseek-ai/DeepSeek-Prover-V2-7B | 2 | eos | ### Detailed Proof and Analysis
First, we observe the sequence defined by:
- \( t_1 = 20 \),
- \( t_2 = 21 \),
- For \( n \geq 3 \), \( t_n = \frac{5 \cdot t_{n-1} + 1}{25 \cdot t_{n-2}} \).
We need to compute the denominator and numerator of \( t_{2020} \) (in reduced form) and show that \( \text{den} + \text{num} =... | invalid | lean did not elaborate cleanly (status=error) | single_class | 0 | 3 | 0 | 0.195172 |
aimeI_2000_p7 | minif2f | validation | aimeI_2000_p7 | import Mathlib.Algebra.BigOperators.Basic
import Mathlib.Data.Real.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Data.Nat.Log
import Mathlib.Data.Complex.Exponential
import Mathlib.NumberTheory.Divisors
import Mathlib.Data.ZMod.Defs
import Mathlib.Data.ZMod.Basic
import Mathlib.Topology.Basic
import Mathlib.Da... | deepseek-ai/DeepSeek-Prover-V2-7B | 0 | eos | ### Detailed Proof and Analysis
First, we need to understand the problem and the given conditions. We have three positive real numbers \( x, y, z \) such that:
1. \( x \cdot y \cdot z = 1 \),
2. \( x + \frac{1}{z} = 5 \),
3. \( y + \frac{1}{x} = 29 \),
4. \( z + \frac{1}{y} = m \) (where \( m \) is a rational number w... | invalid | lean did not elaborate cleanly (status=error) | single_class | 0 | 3 | 0 | 0.195172 |
aimeI_2000_p7 | minif2f | validation | aimeI_2000_p7 | "import Mathlib.Algebra.BigOperators.Basic\nimport Mathlib.Data.Real.Basic\nimport Mathlib.Data.Comp(...TRUNCATED) | deepseek-ai/DeepSeek-Prover-V2-7B | 1 | eos | "### Detailed Proof and Analysis\n\nFirst, let's carefully restate and understand the problem.\n\n**(...TRUNCATED) | invalid | lean did not elaborate cleanly (status=error) | single_class | 0 | 3 | 0 | 0.195172 |
aimeI_2000_p7 | minif2f | validation | aimeI_2000_p7 | "import Mathlib.Algebra.BigOperators.Basic\nimport Mathlib.Data.Real.Basic\nimport Mathlib.Data.Comp(...TRUNCATED) | deepseek-ai/DeepSeek-Prover-V2-7B | 2 | eos | "### Detailed Proof and Analysis\n\n#### Understanding the Problem\nWe have three positive real numb(...TRUNCATED) | invalid | lean did not elaborate cleanly (status=error) | single_class | 0 | 3 | 0 | 0.195172 |
aime_1983_p1 | minif2f | test | aime_1983_p1 | "import Mathlib.Algebra.BigOperators.Basic\nimport Mathlib.Data.Real.Basic\nimport Mathlib.Data.Comp(...TRUNCATED) | deepseek-ai/DeepSeek-Prover-V2-7B | 0 | eos | "### Detailed Proof and Analysis\n\nFirst, we need to understand the problem and the given condition(...TRUNCATED) | invalid | lean did not elaborate cleanly (status=error) | single_class | 0 | 3 | 0 | 0.195172 |
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MiniF2F DeepSeek-Prover-V2 Traces
One row per proof attempt (trace) produced while screening MiniF2F problems with DeepSeek-Prover-V2-7B. Each row carries the generated proof text, its Lean grade, and the per-challenge curation decision.
Provenance
MiniF2F theorem statements -> DeepSeek-Prover-V2-7B generations (multiple seeded
attempts per problem) -> Lean elaboration + comparator grading (valid /
invalid / incomplete) -> per-challenge curation from a
Beta(0.1 + n_valid, 0.1 + n_invalid) posterior on the validity rate, whose
credible interval decides each challenge's status.
Columns
| column | description |
|---|---|
challenge_id |
MiniF2F problem id the trace attempts. |
source |
Constant "minif2f"; the upstream statement source. |
split |
MiniF2F split the problem belongs to (validation or test). |
theorem_name |
Name of the theorem/lemma the prover must complete. |
challenge_lean |
Self-contained Lean file (Mathlib header + theorem ... := by sorry) given to the prover. |
prover_id |
Constant "deepseek-ai/DeepSeek-Prover-V2-7B"; the model that generated the trace. |
attempt |
Zero-based attempt index for this challenge (each attempt a fresh seed). |
stop_reason |
Why generation stopped (e.g. stop, max_new_tokens). |
trace |
Full generated text (the model's proof attempt). |
grade |
Three-way grade from Lean elaboration: valid, invalid, or incomplete. |
grade_detail |
Human-readable grader detail for the grade. |
curation_status |
Per-challenge curation outcome: accepted, needs_more_info, out_of_band, or single_class. |
n_valid |
Per-challenge count of valid grades feeding the curation posterior. |
n_invalid |
Per-challenge count of invalid grades feeding the curation posterior. |
interval_low |
Low bound of the per-challenge Beta-posterior credible interval on the validity rate. |
interval_high |
High bound of the per-challenge Beta-posterior credible interval on the validity rate. |
Distributions
- Total rows (traces): 3940
- Distinct challenges: 487
Rows per grade:
invalid: 2404valid: 1536
Rows per split:
test: 2135validation: 1805
Curation status over challenges:
accepted: 24needs_more_info: 27out_of_band: 16single_class: 420
Curation status over rows:
accepted: 960needs_more_info: 1080out_of_band: 640single_class: 1260
Generation config
Trace-generation configuration used to produce this dataset:
prover_id: deepseek-ai/DeepSeek-Prover-V2-7Bmax_new_tokens: 32768temperature: 1.0top_p: 0.95base_seed: 0seed_per_attempt: base_seed + attemptmax_model_len: 16384dtype: auto
Caveats
incompletegrades are token-limited generations that produced no gradeable proof; they form no valid/invalid evidence and are excluded from the curation posterior counts.single_classchallenges never produced a contrasting pair (one ofn_validorn_invalidis zero), so no within-challenge validity contrast exists.out_of_bandchallenges do have a contrasting pair, but their validity-rate credible interval fell outside the informative band[0.2, 0.8].splitis recomputed by loading MiniF2F; a challenge absent from both splits is left null.
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