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Datasets:
HyperCactus0
/
LeanTransitionCorpus

Tasks:
Text Generation
Tags:
lean
lean4
automated-theorem-proving
theorem-proving
formal-mathematics
mathematics
License:
Dataset card Data Studio Files
xet
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1
HyperCactus0 commited on
Commit
d17e0a9
·
verified ·
1 Parent(s): e62dcd8

Record 18 verified HPC batch manifests

Browse files
Files changed (18) hide show
  1. manifests/batches/oproofs/s00000-r00002888-n000004.json +78 -0
  2. manifests/batches/oproofs/s00000-r00002912-n000004.json +58 -0
  3. manifests/batches/oproofs/s00000-r00002948-n000004.json +51 -0
  4. manifests/batches/oproofs/s00000-r00002988-n000004.json +51 -0
  5. manifests/batches/oproofs/s00000-r00002996-n000004.json +51 -0
  6. manifests/batches/oproofs/s00000-r00003008-n000004.json +44 -0
  7. manifests/batches/oproofs/s00000-r00003016-n000004.json +58 -0
  8. manifests/batches/oproofs/s00000-r00003020-n000004.json +44 -0
  9. manifests/batches/oproofs/s00000-r00003024-n000004.json +51 -0
  10. manifests/batches/oproofs/s00000-r00003028-n000004.json +44 -0
  11. manifests/batches/oproofs/s00000-r00003032-n000004.json +44 -0
  12. manifests/batches/oproofs/s00000-r00003048-n000004.json +51 -0
  13. manifests/batches/oproofs/s00000-r00003052-n000004.json +44 -0
  14. manifests/batches/oproofs/s00000-r00003056-n000004.json +44 -0
  15. manifests/batches/oproofs/s00000-r00003072-n000004.json +44 -0
  16. manifests/batches/oproofs/s00000-r00003084-n000004.json +51 -0
  17. manifests/batches/oproofs/s00000-r00003092-n000004.json +44 -0
  18. manifests/batches/oproofs/s00000-r00003104-n000004.json +44 -0
manifests/batches/oproofs/s00000-r00002888-n000004.json ADDED
@@ -0,0 +1,78 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "oproofs/s00000-r00002888-n000004",
4
+ "batch_fingerprint": "1502a69f3bd427e5fc923914c88f384d708948982604aad98589fe8419db017f",
5
+ "evidence": {
6
+ "batch_fingerprint": "1502a69f3bd427e5fc923914c88f384d708948982604aad98589fe8419db017f",
7
+ "contamination_matches": [],
8
+ "corpus_duplicate_proofs": [],
9
+ "failures": [
10
+ {
11
+ "id": "oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2891",
12
+ "index": 2891,
13
+ "reason": "missing_trace",
14
+ "selection": {
15
+ "file_path": "Full/Proof_002891.lean",
16
+ "id": "oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2891",
17
+ "index": 2891,
18
+ "metadata": {
19
+ "declaration_kind": "theorem",
20
+ "source_dataset": "oproofs",
21
+ "source_row": 2891,
22
+ "source_shard": 0,
23
+ "source_statement_fingerprint": "191da16135ba73235d32d2393513624caa041ffd7785e9c20c090ac30274ba0f",
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+ "theorem_name": "lean_workbook_21104",
25
+ "theorem_ordinal": 0
26
+ },
27
+ "source_sha256": "8f57359cc6838a42d2a7f3b1bd25bb8f729898c3edc2a173e249d40e362c226a"
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+ },
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+ "source_file": "Full/Proof_002891.lean"
30
+ }
31
+ ],
32
+ "input_proofs": 4,
33
+ "input_units": 4,
34
+ "pretrace_duplicate_proofs": [],
35
+ "proofs": 3,
36
+ "published_proofs": 3,
37
+ "published_transitions": 17,
38
+ "replay_failures": [],
39
+ "trace_mode": "individual",
40
+ "transitions": 17,
41
+ "validation_failures": [],
42
+ "validation_rejected_proofs": 0,
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+ "zero_transition_proofs": 0
44
+ },
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+ "shards": [
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+ {
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+ "path": "data/train/pd8/oproofs-s00000-r00002888-n000004-0000-489c197c7f37896e.parquet",
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+ "sha256": "489c197c7f37896e14fe6b1ffdde5faa9b11b721dcfecc6c6f1cd9ccad054367",
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+ "bytes": 270338,
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+ "rows": 6,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ },
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+ {
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+ "path": "data/internal_test/pd8/oproofs-s00000-r00002888-n000004-0000-ecd8ff647d0fd287.parquet",
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+ "sha256": "ecd8ff647d0fd2871f67958da88461d57b699af04110ded2927c0fdb3c837f22",
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+ "bytes": 1102879,
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+ "rows": 7,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ },
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+ {
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+ "path": "data/internal_test/pd8/oproofs-s00000-r00002888-n000004-0001-c13cdaf413178c72.parquet",
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+ "sha256": "c13cdaf413178c72490e86167083a41d6f6356bd3a34499604c874a881672de1",
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+ "bytes": 756093,
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+ "rows": 4,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ }
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+ ],
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+ "proof_ids": [
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2888",
70
+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2889",
71
+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2890"
72
+ ],
73
+ "proof_keys": [
74
+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002888.lean\",\"18f3bb88a5e4326f5bf8f4c77f3a8411cf408cbc9c8cddfb5bc96fdcc7e00afe\",0,\"lean_workbook_12555\"]",
75
+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002889.lean\",\"e7b821f3b4fef6c883c585d6e6cc268682c615310a47b1743fa40a4027c797ac\",0,\"lean_workbook_12414\"]",
76
+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002890.lean\",\"8adb32f89e51b3292f4a467a8473191766fbb22b982c07563287b94552a8a1de\",0,\"lean_workbook_21471\"]"
77
+ ]
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+ }
manifests/batches/oproofs/s00000-r00002912-n000004.json ADDED
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1
+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "oproofs/s00000-r00002912-n000004",
4
+ "batch_fingerprint": "99fc0c1f1e436a011cf208988a8f88658c1010f1e15e7dfc290aa535dd654563",
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+ "evidence": {
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+ "batch_fingerprint": "99fc0c1f1e436a011cf208988a8f88658c1010f1e15e7dfc290aa535dd654563",
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+ "contamination_matches": [],
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+ "corpus_duplicate_proofs": [],
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+ "failures": [],
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+ "input_proofs": 4,
11
+ "input_units": 4,
12
+ "pretrace_duplicate_proofs": [],
13
+ "proofs": 4,
14
+ "published_proofs": 4,
15
+ "published_transitions": 23,
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+ "replay_failures": [],
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+ "trace_mode": "individual",
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+ "transitions": 23,
19
+ "validation_failures": [],
20
+ "validation_rejected_proofs": 0,
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+ "zero_transition_proofs": 0
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+ },
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+ "shards": [
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+ {
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+ "path": "data/train/p9f/oproofs-s00000-r00002912-n000004-0000-2216922c36d13971.parquet",
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+ "sha256": "2216922c36d13971a31a31506b2e060a56f525359e6d460c69c1f6ca67046baa",
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+ "bytes": 1363873,
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+ "rows": 13,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ },
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+ {
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+ "path": "data/train/p9f/oproofs-s00000-r00002912-n000004-0001-c46836492d8e78c5.parquet",
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+ "sha256": "c46836492d8e78c5ba99d6053eeb233e3620d32f47c0e9e3bc9f5858c74637fe",
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+ "bytes": 274327,
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+ "rows": 3,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ },
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+ {
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+ "path": "data/internal_test/p9f/oproofs-s00000-r00002912-n000004-0000-c8196f3a7bea9d8b.parquet",
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+ "sha256": "c8196f3a7bea9d8be0587740dccfe9c025b3b50588ff783b04b34d85ea2d2c1d",
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+ "bytes": 203705,
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+ "rows": 7,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ }
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+ ],
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+ "proof_ids": [
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2912",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2913",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2914",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2915"
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+ ],
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+ "proof_keys": [
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002912.lean\",\"cc6462bb2ab062126fde448160fcfaf8603a8dbd4f27821aa7148147b5577972\",0,\"lean_workbook\"]",
54
+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002913.lean\",\"f7a928c60cebf1659e3dbcea92efd9978a952540767da26f18473d27939135e1\",0,\"lean_workbook_12769\"]",
55
+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002914.lean\",\"35791d38bfda1b5885506de04b9bba368be1596e64a05bb2d4dcde12a3502339\",0,\"lean_workbook\"]",
56
+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002915.lean\",\"cc6ce9a34324252013d21dfbfdf01177061d0008461fd4defdee8134e3f2498b\",0,\"lean_workbook\"]"
57
+ ]
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+ }
manifests/batches/oproofs/s00000-r00002948-n000004.json ADDED
@@ -0,0 +1,51 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "oproofs/s00000-r00002948-n000004",
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+ "batch_fingerprint": "6f78acf79b6a19fd62f0b1832f86d405c8b450d42782e4f067c61887a1c7db31",
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+ "evidence": {
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+ "batch_fingerprint": "6f78acf79b6a19fd62f0b1832f86d405c8b450d42782e4f067c61887a1c7db31",
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+ "contamination_matches": [],
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+ "corpus_duplicate_proofs": [],
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+ "failures": [],
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+ "input_proofs": 4,
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+ "input_units": 4,
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+ "pretrace_duplicate_proofs": [],
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+ "proofs": 4,
14
+ "published_proofs": 4,
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+ "published_transitions": 25,
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+ "replay_failures": [],
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+ "trace_mode": "individual",
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+ "transitions": 25,
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+ "validation_failures": [],
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+ "validation_rejected_proofs": 0,
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+ "zero_transition_proofs": 0
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+ },
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+ "shards": [
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+ {
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+ "path": "data/train/pa9/oproofs-s00000-r00002948-n000004-0000-a793bb0f1c1a7f27.parquet",
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+ "sha256": "a793bb0f1c1a7f27d63b0c156592812c1a23d122eb5b28942283ff9bbc49d96a",
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+ "bytes": 851688,
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+ "rows": 9,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ },
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+ {
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+ "path": "data/internal_test/pa9/oproofs-s00000-r00002948-n000004-0000-484fbc19c0278e04.parquet",
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+ "sha256": "484fbc19c0278e0492feadaddf5ad41614354ce41b195376bde4ddd4d8d51d0b",
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+ "bytes": 750316,
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+ "rows": 16,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ }
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+ ],
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+ "proof_ids": [
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2948",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2949",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2950",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2951"
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+ ],
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+ "proof_keys": [
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002948.lean\",\"9acc676e75d733242224ea1c603db47dbbb4e5a7fbe5db2c98b3b105abbfa40c\",0,\"lean_workbook\"]",
47
+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002949.lean\",\"c6fc190159265e3de98e8c4f13253b90b172daed190c1e2eb2f530873c6f9653\",0,\"lean_workbook\"]",
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002950.lean\",\"b8c3722c4c0013539b4927d41b5c91695c1f1d137509375d50f4f47ca105fa09\",0,\"company_profit_max\"]",
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002951.lean\",\"87904ffeb765fb7064ccdba284381a2389d3aede13cd29eed1a916c577dc66c4\",0,\"lean_workbook\"]"
50
+ ]
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+ }
manifests/batches/oproofs/s00000-r00002988-n000004.json ADDED
@@ -0,0 +1,51 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "oproofs/s00000-r00002988-n000004",
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+ "batch_fingerprint": "26f46bc01deab88780502ff382491fe3b49ec1c0f616f084822b1fd9141d1d06",
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+ "evidence": {
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+ "batch_fingerprint": "26f46bc01deab88780502ff382491fe3b49ec1c0f616f084822b1fd9141d1d06",
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+ "contamination_matches": [],
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+ "corpus_duplicate_proofs": [],
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+ "failures": [],
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+ "input_proofs": 4,
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+ "input_units": 4,
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+ "pretrace_duplicate_proofs": [],
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+ "proofs": 4,
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+ "published_proofs": 4,
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+ "published_transitions": 29,
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+ "replay_failures": [],
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+ "trace_mode": "individual",
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+ "transitions": 29,
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+ "validation_failures": [],
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+ "validation_rejected_proofs": 0,
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+ "zero_transition_proofs": 0
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+ },
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+ "shards": [
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+ {
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+ "path": "data/train/pbd/oproofs-s00000-r00002988-n000004-0000-0ffbaae52136ae80.parquet",
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+ "sha256": "0ffbaae52136ae803c24d2105ca652049a7372d4dc3deb41f83bedaf3b7fd905",
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+ "bytes": 604808,
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+ "rows": 20,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ },
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+ {
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+ "path": "data/internal_test/pbd/oproofs-s00000-r00002988-n000004-0000-aaf4fbbfc03a817a.parquet",
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+ "sha256": "aaf4fbbfc03a817ac267cae0a40f42a7312a7269d8a3ad9f88974d615e65c4a4",
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+ "bytes": 499608,
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+ "rows": 9,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ }
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+ ],
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+ "proof_ids": [
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2988",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2989",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2990",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:2991"
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+ ],
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+ "proof_keys": [
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002988.lean\",\"e097c97c22a3a729d9dbbf5cca40cd966947e417fd45f2e427bc9eb8bde08e01\",0,\"divizibility_part1\"]",
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002989.lean\",\"6e3fababed2edf3aeb94bf5d680ffdcb15515ce2efd64d3892e37f19b4c693d5\",0,\"exists_pair_mod_10\"]",
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002990.lean\",\"676c550dd73785e5bd78d729f4313de2029cb577ff1b781bbdff951e2bf2dda9\",0,\"no_function_f_satisfying_f_f_x_eq_x_plus_one\"]",
49
+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_002991.lean\",\"bc86262f68955aed22aaec68638313973045f775f4a45be10031335c635146e7\",0,\"lean_workbook\"]"
50
+ ]
51
+ }
manifests/batches/oproofs/s00000-r00002996-n000004.json ADDED
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1
+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "oproofs/s00000-r00002996-n000004",
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+ "batch_fingerprint": "08c6de5e1e3789b19860bf3bbae7639bf34c68dffab9359cceb0c92b508ac0eb",
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+ "evidence": {
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+ "batch_fingerprint": "08c6de5e1e3789b19860bf3bbae7639bf34c68dffab9359cceb0c92b508ac0eb",
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+ "contamination_matches": [],
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+ "corpus_duplicate_proofs": [],
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+ "failures": [],
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+ "input_proofs": 4,
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+ "input_units": 4,
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+ "pretrace_duplicate_proofs": [],
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+ "proofs": 4,
14
+ "published_proofs": 4,
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+ "published_transitions": 21,
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+ "replay_failures": [],
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+ "trace_mode": "individual",
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+ "transitions": 21,
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+ "validation_failures": [],
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+ "validation_rejected_proofs": 0,
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+ "zero_transition_proofs": 0
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+ },
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+ "shards": [
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+ {
25
+ "path": "data/train/p66/oproofs-s00000-r00002996-n000004-0000-41ece63ad55e3268.parquet",
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+ "sha256": "41ece63ad55e3268e706e2c2e9eb230ce173e589b872c1ce49cbd7fe9f3bbaf1",
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+ "bytes": 534287,
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+ "rows": 18,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ },
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+ {
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+ "path": "data/internal_test/p66/oproofs-s00000-r00002996-n000004-0000-047fee5508e559c3.parquet",
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+ "sha256": "047fee5508e559c3073eef5b5d2d33cdef5ee748267c15d1a6ec913c6abb7b67",
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+ "bytes": 51097,
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+ "rows": 3,
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+ "revision": "e62dcd87cea2cf00aec0850c35b83a3d53e8f2af"
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+ }
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+ ],
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+ "proof_ids": [
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+ "sha256": "f4244f2fde9db25d76545c66691bb0e2877d55b5f84ff9619125cf1b9614f98f",
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+ }
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+ ],
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+ "proof_ids": [
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:3092",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:3093",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:3094",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:3095"
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+ ],
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+ "proof_keys": [
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_003092.lean\",\"a64886015652a749641438bb9d6b9258cf58929d18f77a07c45c3ad696aa4911\",0,\"lean_workbook\"]",
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_003093.lean\",\"0fce9964b1b3e1a2d60a33c2b10bd4d325f8303e1852f1da59ab9a702d6ece06\",0,\"involution_condition\"]",
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_003094.lean\",\"f64e879d2cc464f18fda125bd9b3e0d4c8ae135ac8fce0c08b147344a85bf268\",0,\"exists_function_not_periodic\"]",
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_003095.lean\",\"229f07eff1d86f0bb1ba7e31693e389fa24ff83bb6f94f8f070e196ba0c7b97f\",0,\"a_minus_b_value\"]"
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+ ]
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+ }
manifests/batches/oproofs/s00000-r00003104-n000004.json ADDED
@@ -0,0 +1,44 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "oproofs/s00000-r00003104-n000004",
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+ "batch_fingerprint": "0bd7dc016870814ee41636404d7f52afe2a7a09f93c81cdc17be360ddbc53e4c",
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+ "evidence": {
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+ "batch_fingerprint": "0bd7dc016870814ee41636404d7f52afe2a7a09f93c81cdc17be360ddbc53e4c",
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+ "contamination_matches": [],
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+ "corpus_duplicate_proofs": [],
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+ "failures": [],
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+ "input_proofs": 4,
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+ "input_units": 4,
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+ "pretrace_duplicate_proofs": [],
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+ "proofs": 4,
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+ "published_proofs": 4,
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+ "published_transitions": 11,
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+ "replay_failures": [],
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+ "trace_mode": "individual",
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+ "transitions": 11,
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+ "validation_failures": [],
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+ "validation_rejected_proofs": 0,
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+ "zero_transition_proofs": 0
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+ },
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+ "shards": [
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+ {
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+ "path": "data/train/p4a/oproofs-s00000-r00003104-n000004-0000-82e83bdaa1f94e22.parquet",
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+ "sha256": "82e83bdaa1f94e22f461de536ed7b85a7bed0226917824a2779baad0d7d23b86",
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+ }
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+ ],
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+ "proof_ids": [
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:3105",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:3106",
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+ "oproofs:oproofs:3bae0c06157639c0a673679635c669d19c99e906:0:3107"
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+ ],
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+ "proof_keys": [
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_003104.lean\",\"fefb0dfcc29a444b01fe18543572cf452bd86a4dc06668900684f1c6dd280ff2\",0,\"exists_n_digit_prime\"]",
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_003105.lean\",\"fab9b5cb853d89c8edac2aa8186dd18a980b1f19aca7ffe41354c614d6f7ae02\",0,\"interest_rate_calculation\"]",
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_003106.lean\",\"211a4d87b35ed1ca4a8c0d1cab48a6b6696e1475f164eb97b2148a417b4fa0c1\",0,\"lean_workbook\"]",
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+ "[\"oproofs\",\"3bae0c06157639c0a673679635c669d19c99e906\",\"Full/Proof_003107.lean\",\"9a0ddb47bb1e2064ac08fe4604e1044c1ae2d8004d715d86104710a9e7393393\",0,\"exists_prime_dividing_u_2014_plus_2009\"]"
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+ ]
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+ }