instance_id stringclasses 10
values | baseline_id stringclasses 1
value | baseline_sha256 stringclasses 1
value | grammar_id stringclasses 1
value | limits dict | schema_version stringclasses 1
value | public_examples listlengths 6 6 | private_targets listlengths 12 12 | gold_lemma dict |
|---|---|---|---|---|---|---|---|---|
dev_0001 | prop_base_v1 | 3072997d84dd88afc06bd5b4bbb8710cdb110a6d4cd956ed81eb2c125aa0a202 | imp_not_v1 | {
"max_hypotheses": 3,
"max_nodes": 63,
"max_depth": 12,
"max_variables": 6
} | 1.0 | [
{
"id": "public_01",
"hypotheses": [
"( ( ch -> ps ) -> th )",
"( th -> ( ps -> ph ) )"
],
"conclusion": "( ta -> ( ( ch -> ps ) -> ( ps -> ph ) ) )"
},
{
"id": "public_02",
"hypotheses": [
"( ph -> ( ph -> ps ) )",
"( ( ph -> ps ) -> ( ch -> th ) )"
],
"c... | [
{
"id": "private_01",
"hypotheses": [
"( ( ( th -> th ) -> ps ) -> ( ( ph -> ps ) -> th ) )",
"( ( ( ph -> ps ) -> th ) -> ch )"
],
"conclusion": "( ta -> ( ( ( th -> th ) -> ps ) -> ch ) )"
},
{
"id": "private_02",
"hypotheses": [
"( -. -. ps -> ( ( ph -> ch ) -> th ) ... | {
"hypotheses": [
"( ph -> ps )",
"( ps -> ch )"
],
"conclusion": "( ph -> ch )"
} |
dev_0002 | prop_base_v1 | 3072997d84dd88afc06bd5b4bbb8710cdb110a6d4cd956ed81eb2c125aa0a202 | imp_not_v1 | {
"max_hypotheses": 3,
"max_nodes": 63,
"max_depth": 12,
"max_variables": 6
} | 1.0 | [
{
"id": "public_01",
"hypotheses": [
"( ph -> ps )",
"( ph -> ( ps -> -. th ) )"
],
"conclusion": "( ta -> ( ph -> -. th ) )"
},
{
"id": "public_02",
"hypotheses": [
"( ( ch -> ph ) -> ps )",
"( ( ch -> ph ) -> ( ps -> ch ) )"
],
"conclusion": "( ta -> ( (... | [
{
"id": "private_01",
"hypotheses": [
"( ch -> ( -. ph -> ps ) )",
"( ch -> ( ( -. ph -> ps ) -> ( ( ch -> th ) -> ps ) ) )"
],
"conclusion": "( ta -> ( ch -> ( ( ch -> th ) -> ps ) ) )"
},
{
"id": "private_02",
"hypotheses": [
"( ch -> th )",
"( ch -> ( th -> ( (... | {
"hypotheses": [
"( ph -> ps )",
"( ph -> ( ps -> ch ) )"
],
"conclusion": "( ph -> ch )"
} |
dev_0003 | prop_base_v1 | 3072997d84dd88afc06bd5b4bbb8710cdb110a6d4cd956ed81eb2c125aa0a202 | imp_not_v1 | {
"max_hypotheses": 3,
"max_nodes": 63,
"max_depth": 12,
"max_variables": 6
} | 1.0 | [
{
"id": "public_01",
"hypotheses": [
"( ps -> ph )"
],
"conclusion": "( ta -> ( ( ( th -> ps ) -> ps ) -> ( ( th -> ps ) -> ph ) ) )"
},
{
"id": "public_02",
"hypotheses": [
"( ( th -> ph ) -> th )"
],
"conclusion": "( ta -> ( ( -. ps -> ( th -> ph ) ) -> ( -. ps -> t... | [
{
"id": "private_01",
"hypotheses": [
"( ( ( th -> ps ) -> ph ) -> ( ( th -> th ) -> ch ) )"
],
"conclusion": "( ta -> ( ( ( -. th -> ps ) -> ( ( th -> ps ) -> ph ) ) -> ( ( -. th -> ps ) -> ( ( th -> th ) -> ch ) ) ) )"
},
{
"id": "private_02",
"hypotheses": [
"( -. -. ph ->... | {
"hypotheses": [
"( ph -> ps )"
],
"conclusion": "( ( ch -> ph ) -> ( ch -> ps ) )"
} |
dev_0004 | prop_base_v1 | 3072997d84dd88afc06bd5b4bbb8710cdb110a6d4cd956ed81eb2c125aa0a202 | imp_not_v1 | {
"max_hypotheses": 3,
"max_nodes": 63,
"max_depth": 12,
"max_variables": 6
} | 1.0 | [
{
"id": "public_01",
"hypotheses": [
"( ph -> ( ph -> th ) )"
],
"conclusion": "( ta -> ( ph -> ( ( ps -> ps ) -> ( ph -> th ) ) ) )"
},
{
"id": "public_02",
"hypotheses": [
"( -. ch -> ch )"
],
"conclusion": "( ta -> ( -. ch -> ( ( ch -> ch ) -> ch ) ) )"
},
{
... | [
{
"id": "private_01",
"hypotheses": [
"( -. ( ch -> ph ) -> ( ( ph -> th ) -> ph ) )"
],
"conclusion": "( ta -> ( -. ( ch -> ph ) -> ( -. -. ps -> ( ( ph -> th ) -> ph ) ) ) )"
},
{
"id": "private_02",
"hypotheses": [
"( -. ( ph -> th ) -> -. ( ps -> ps ) )"
],
"concl... | {
"hypotheses": [
"( ph -> ps )"
],
"conclusion": "( ph -> ( ch -> ps ) )"
} |
dev_0005 | prop_base_v1 | 3072997d84dd88afc06bd5b4bbb8710cdb110a6d4cd956ed81eb2c125aa0a202 | imp_not_v1 | {
"max_hypotheses": 3,
"max_nodes": 63,
"max_depth": 12,
"max_variables": 6
} | 1.0 | [
{
"id": "public_01",
"hypotheses": [
"( ( ch -> ph ) -> ( ( ch -> ph ) -> -. ph ) )"
],
"conclusion": "( ta -> ( ( ch -> ph ) -> -. ph ) )"
},
{
"id": "public_02",
"hypotheses": [
"( ( ph -> th ) -> ( ( ph -> th ) -> ( th -> ch ) ) )"
],
"conclusion": "( ta -> ( ( ph ... | [
{
"id": "private_01",
"hypotheses": [
"( ( ( ch -> ps ) -> ps ) -> ( ( ( ch -> ps ) -> ps ) -> ph ) )"
],
"conclusion": "( ta -> ( ( ( ch -> ps ) -> ps ) -> ph ) )"
},
{
"id": "private_02",
"hypotheses": [
"( ( ( ch -> ch ) -> th ) -> ( ( ( ch -> ch ) -> th ) -> ch ) )"
]... | {
"hypotheses": [
"( ph -> ( ph -> ps ) )"
],
"conclusion": "( ph -> ps )"
} |
dev_0006 | prop_base_v1 | 3072997d84dd88afc06bd5b4bbb8710cdb110a6d4cd956ed81eb2c125aa0a202 | imp_not_v1 | {
"max_hypotheses": 3,
"max_nodes": 63,
"max_depth": 12,
"max_variables": 6
} | 1.0 | [
{
"id": "public_01",
"hypotheses": [
"( ( ch -> ph ) -> ch )"
],
"conclusion": "( ta -> ( -. ps -> ( ( ch -> ph ) -> ( -. ch -> ch ) ) ) )"
},
{
"id": "public_02",
"hypotheses": [
"( ( th -> th ) -> ph )"
],
"conclusion": "( ta -> ( ( th -> th ) -> ( ( th -> th ) -> (... | [
{
"id": "private_01",
"hypotheses": [
"( ( -. ps -> ph ) -> ( ( ph -> ch ) -> th ) )"
],
"conclusion": "( ta -> ( -. ( ph -> th ) -> ( ( -. ps -> ph ) -> ( ( ( ph -> th ) -> ph ) -> ( ( ph -> ch ) -> th ) ) ) ) )"
},
{
"id": "private_02",
"hypotheses": [
"( ( -. ph -> ph ) ->... | {
"hypotheses": [
"( ps -> th )"
],
"conclusion": "( ph -> ( ps -> ( ch -> th ) ) )"
} |
dev_0007 | prop_base_v1 | 3072997d84dd88afc06bd5b4bbb8710cdb110a6d4cd956ed81eb2c125aa0a202 | imp_not_v1 | {
"max_hypotheses": 3,
"max_nodes": 63,
"max_depth": 12,
"max_variables": 6
} | 1.0 | [
{
"id": "public_01",
"hypotheses": [
"-. ph",
"( ch -> ( -. ph -> ( ch -> ps ) ) )"
],
"conclusion": "( ta -> ( ch -> ( ch -> ps ) ) )"
},
{
"id": "public_02",
"hypotheses": [
"ps",
"( -. ch -> ( ps -> ( th -> ch ) ) )"
],
"conclusion": "( ta -> ( -. ch ->... | [
{
"id": "private_01",
"hypotheses": [
"th",
"( ph -> ( th -> -. ( ph -> ps ) ) )"
],
"conclusion": "( ta -> ( ph -> -. ( ph -> ps ) ) )"
},
{
"id": "private_02",
"hypotheses": [
"( -. th -> ps )",
"( ph -> ( ( -. th -> ps ) -> -. -. th ) )"
],
"conclusion"... | {
"hypotheses": [
"ps",
"( ph -> ( ps -> ch ) )"
],
"conclusion": "( ph -> ch )"
} |
dev_0008 | prop_base_v1 | 3072997d84dd88afc06bd5b4bbb8710cdb110a6d4cd956ed81eb2c125aa0a202 | imp_not_v1 | {
"max_hypotheses": 3,
"max_nodes": 63,
"max_depth": 12,
"max_variables": 6
} | 1.0 | [
{
"id": "public_01",
"hypotheses": [
"( ( ps -> ph ) -> -. ps )",
"( -. ps -> ( ch -> th ) )"
],
"conclusion": "( ta -> ( ( ps -> ph ) -> ( ch -> th ) ) )"
},
{
"id": "public_02",
"hypotheses": [
"( ( ch -> th ) -> ( th -> ps ) )",
"( ( th -> ps ) -> ps )"
],
... | [
{
"id": "private_01",
"hypotheses": [
"( ( -. ps -> ph ) -> -. ( ps -> th ) )",
"( -. ( ps -> th ) -> -. -. th )"
],
"conclusion": "( ta -> ( ( -. ps -> ph ) -> -. -. th ) )"
},
{
"id": "private_02",
"hypotheses": [
"( th -> ( ( th -> ch ) -> ph ) )",
"( ( ( th ->... | {
"hypotheses": [
"( ph -> ps )",
"( ps -> ch )"
],
"conclusion": "( ph -> ch )"
} |
dev_0009 | prop_base_v1 | 3072997d84dd88afc06bd5b4bbb8710cdb110a6d4cd956ed81eb2c125aa0a202 | imp_not_v1 | {
"max_hypotheses": 3,
"max_nodes": 63,
"max_depth": 12,
"max_variables": 6
} | 1.0 | [
{
"id": "public_01",
"hypotheses": [
"( ( th -> ch ) -> ( ph -> ps ) )",
"( ( th -> ch ) -> ( ( ph -> ps ) -> -. th ) )"
],
"conclusion": "( ta -> ( ( th -> ch ) -> -. th ) )"
},
{
"id": "public_02",
"hypotheses": [
"( ( th -> ph ) -> ps )",
"( ( th -> ph ) -> ( p... | [
{
"id": "private_01",
"hypotheses": [
"( ph -> th )",
"( ph -> ( th -> ( ( ps -> th ) -> ch ) ) )"
],
"conclusion": "( ta -> ( ph -> ( ( ps -> th ) -> ch ) ) )"
},
{
"id": "private_02",
"hypotheses": [
"( th -> ( ( ps -> ch ) -> ps ) )",
"( th -> ( ( ( ps -> ch ) ... | {
"hypotheses": [
"( ph -> ps )",
"( ph -> ( ps -> ch ) )"
],
"conclusion": "( ph -> ch )"
} |
dev_0010 | prop_base_v1 | 3072997d84dd88afc06bd5b4bbb8710cdb110a6d4cd956ed81eb2c125aa0a202 | imp_not_v1 | {
"max_hypotheses": 3,
"max_nodes": 63,
"max_depth": 12,
"max_variables": 6
} | 1.0 | [
{
"id": "public_01",
"hypotheses": [
"( -. ph -> -. th )"
],
"conclusion": "( ta -> ( ( ( ps -> ch ) -> -. ph ) -> ( ( ps -> ch ) -> -. th ) ) )"
},
{
"id": "public_02",
"hypotheses": [
"( ch -> ( th -> ps ) )"
],
"conclusion": "( ta -> ( ( ( ps -> ch ) -> ch ) -> ( (... | [
{
"id": "private_01",
"hypotheses": [
"( ph -> ( ( ps -> th ) -> th ) )"
],
"conclusion": "( ta -> ( ( -. ( ph -> ch ) -> ph ) -> ( -. ( ph -> ch ) -> ( ( ps -> th ) -> th ) ) ) )"
},
{
"id": "private_02",
"hypotheses": [
"( ph -> ( -. th -> th ) )"
],
"conclusion": "... | {
"hypotheses": [
"( ph -> ps )"
],
"conclusion": "( ( ch -> ph ) -> ( ch -> ps ) )"
} |
Metamath useful-lemma sample10
Ten complete instances for evaluating reusable lemma proposals. Each row contains six public examples, twelve private evaluation targets, and one gold reference lemma. All formulas use the original raw syntax. There are no tree encodings.
The release uses one test split because each instance is a complete evaluation
task. Historically these instances were the project's development pilot, not an
untouched held-out benchmark. The ten instances cover seven source families.
Evaluation protocol
- Supply the fixed baseline, lemma limits, and only
public_examplesto the proposing model. Never supply the full dataset row. - Freeze one proposed lemma before evaluating private targets.
- Validate and prove that lemma from the baseline and its own hypotheses.
- Evaluate the same twelve private targets with and without the admitted lemma,
and compare against the independently admitted
gold_lemma.
Public/private denotes visibility during evaluation, not access control on this
repository. Private targets and gold are distributed for evaluator use. Model
workers must not have access to the full dataset. The repository helper
sample10_data.public_view explicitly projects only model-visible fields.
Fields and syntax
instance_id joins targets and results. baseline_id, baseline_sha256, and
grammar_id pin the logical setting. limits bounds proposed lemmas.
schema_version is 1.0 for this packaging format.
public_examples and private_targets are ordered arrays of objects with id,
hypotheses (formula strings), and conclusion (one formula string).
gold_lemma has hypotheses and conclusion; it is a reference, not a guaranteed
optimal lemma. Preserve target order when using public-example prefixes.
Formula grammar: ph | ps | ch | th | ta | et | -. formula | ( formula -> formula ).
-> means implication and -. means negation. Hypotheses remain explicit;
they have not been folded into the conclusion. Reusable lemma variables stand
for formulas. Baseline assertions are in baseline/baseline.txt; the formal
source is baseline/base.mm.
Metrics and reproducibility
Search work is Prover9's final Given count (selected clauses), with Generated
as a supplementary counter. It is not wall time or proof length. Charge lemma
admission once per instance and report it separately. Resource failures remain
unresolved. Model generation costs are not included in the original pilot.
The original six-example Codex pilot matched gold on all ten instances. Both conditions verified 120/120 targets and used 12,072 selected clauses on targets, or 12,241 including lemma admission. These are single-trial pilot results.
configs/prover9.in preserves the search settings. manifest.json records
checksums, source-record hashes, and generation seeds. No construction witnesses,
latent family labels, candidate pools, or model responses are included.
From the parent project, rebuild with python src/package_sample10.py and test
with python -m unittest discover -s tests -v. The parent project supplies the
evaluator and pinned prover tooling; this folder is the data distribution.
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