{"id":"https://openalex.org/W7155007204","doi":"https://doi.org/10.48550/arxiv.2604.15839","title":"Discover and Prove: An Open-source Agentic Framework for Hard Mode Automated Theorem Proving in Lean 4","display_name":"Discover and Prove: An Open-source Agentic Framework for Hard Mode Automated Theorem Proving in Lean 4","publication_year":2026,"publication_date":"2026-04-17","ids":{"openalex":"https://openalex.org/W7155007204","doi":"https://doi.org/10.48550/arxiv.2604.15839"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.15839","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.15839","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.15839","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134039240","display_name":"Chengwu Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Chengwu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134073540","display_name":"Yichun Yin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yin, Yichun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134026754","display_name":"Ye Yuan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuan, Ye","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020017704","display_name":"Jiaxuan Xie","orcid":"https://orcid.org/0009-0009-6920-7804"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Jiaxuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134090326","display_name":"Botao Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Botao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134041657","display_name":"Siqi Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Siqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102723742","display_name":"Jianhao Shen","orcid":"https://orcid.org/0000-0002-4977-7959"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shen, Jianhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134056334","display_name":"Yan Xu","orcid":"https://orcid.org/0000-0002-0503-183X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Yan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134085193","display_name":"Lifeng Shang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shang, Lifeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134065788","display_name":"Ming Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Ming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.09950000047683716,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.09950000047683716,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.09769999980926514,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.06960000097751617,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.6915000081062317},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.6912999749183655},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.5375000238418579},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4778999984264374},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.4763000011444092},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.45980000495910645},{"id":"https://openalex.org/keywords/formal-verification","display_name":"Formal verification","score":0.4327999949455261},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.42669999599456787},{"id":"https://openalex.org/keywords/goto","display_name":"Goto","score":0.3887999951839447}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6996999979019165},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.6915000081062317},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.6912999749183655},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.5375000238418579},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5077999830245972},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4778999984264374},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.4763000011444092},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.45980000495910645},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.4462999999523163},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.4327999949455261},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.42669999599456787},{"id":"https://openalex.org/C114094675","wikidata":"https://www.wikidata.org/wiki/Q750997","display_name":"Goto","level":2,"score":0.3887999951839447},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.3840000033378601},{"id":"https://openalex.org/C75606506","wikidata":"https://www.wikidata.org/wiki/Q1049183","display_name":"Formal methods","level":2,"score":0.3797000050544739},{"id":"https://openalex.org/C90329073","wikidata":"https://www.wikidata.org/wiki/Q914232","display_name":"Ask price","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C127576917","wikidata":"https://www.wikidata.org/wiki/Q624630","display_name":"Competitor analysis","level":2,"score":0.35850000381469727},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.3305000066757202},{"id":"https://openalex.org/C159718280","wikidata":"https://www.wikidata.org/wiki/Q5526353","display_name":"Gas meter prover","level":3,"score":0.32409998774528503},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.3240000009536743},{"id":"https://openalex.org/C2780608745","wikidata":"https://www.wikidata.org/wiki/Q367293","display_name":"Convention","level":2,"score":0.32089999318122864},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3034999966621399},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C97399411","wikidata":"https://www.wikidata.org/wiki/Q825367","display_name":"Coin flipping","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C2985583900","wikidata":"https://www.wikidata.org/wiki/Q722617","display_name":"Formal description","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C94966114","wikidata":"https://www.wikidata.org/wiki/Q29256","display_name":"Black box","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C2780339515","wikidata":"https://www.wikidata.org/wiki/Q3074698","display_name":"Arrow","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2572000026702881},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.2554999887943268}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.15839","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.15839","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.15839","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.15839","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Most":[0],"ATP":[1,83,117],"benchmarks":[2,182],"embed":[3],"the":[4,8,23,42,49,54,121,124,143,166],"final":[5],"answer":[6,55,163],"within":[7],"formal":[9,59,170],"statement":[10],"--":[11,18,154],"a":[12,19,58,176],"convention":[13],"we":[14,66,71,86],"call":[15,41],"\"Easy":[16],"Mode\"":[17],"design":[20],"that":[21,95,158,179],"simplifies":[22],"task":[24],"relative":[25],"to":[26,34,103,137,146,186],"what":[27],"human":[28],"competitors":[29],"face":[30],"and":[31,74],"may":[32],"lead":[33],"optimistic":[35],"estimates":[36],"of":[37,80,123],"model":[38],"capability.":[39],"We":[40],"stricter,":[43],"more":[44],"realistic":[45],"setting":[46],"\"Hard":[47],"Mode\":":[48],"system":[50,145],"must":[51],"independently":[52],"discover":[53,104],"before":[56],"constructing":[57],"proof.":[60],"To":[61],"enable":[62],"Hard":[63,77,108,152,180],"Mode":[64,78,109,113,153,181],"research,":[65],"make":[67],"two":[68,81],"contributions.":[69],"First,":[70],"release":[72],"MiniF2F-Hard":[73],"FIMO-Hard,":[75],"expert-reannotated":[76],"variants":[79],"widely-used":[82],"benchmarks.":[84],"Second,":[85],"introduce":[87],"Discover":[88],"And":[89],"Prove":[90],"(DAP),":[91],"an":[92],"agentic":[93],"framework":[94],"uses":[96],"LLM":[97],"natural-language":[98],"reasoning":[99],"with":[100],"explicit":[101],"self-reflection":[102],"answers,":[105],"then":[106],"rewrites":[107],"statements":[110],"into":[111],"Easy":[112],"ones":[114],"for":[115],"existing":[116],"provers.":[118],"DAP":[119],"sets":[120],"state":[122],"art:":[125],"on":[126,139,165],"CombiBench":[127],"it":[128,141],"raises":[129],"solved":[130],"problems":[131,168],"from":[132],"7":[133],"(previous":[134],"SOTA,":[135],"Pass@16)":[136],"10;":[138],"PutnamBench":[140],"is":[142],"first":[144],"formally":[147],"prove":[148],"36":[149],"theorems":[150],"in":[151],"while":[155],"simultaneously":[156],"revealing":[157],"state-of-the-art":[159],"LLMs":[160],"exceed":[161],"80%":[162],"accuracy":[164],"same":[167],"where":[169],"provers":[171],"manage":[172],"under":[173],"10%,":[174],"exposing":[175],"substantial":[177],"gap":[178],"are":[183],"uniquely":[184],"suited":[185],"measure.":[187]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-21T00:00:00"}
