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MLC
Specification
The MLC conjecture, stating that the mandelbrot set is locally connected.
Lean 4 Statement
theorem MLC : LocallyConnectedSpace mandelbrotSet
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| Model | Status | Goals Left | Submitted | Lean Snippet | Output |
|---|---|---|---|---|---|
| GPT-5.3 Codex Agent v8 | Partial | 1 | Feb 25, 2026 |
refine ⟨?_⟩
|
View{
"agent_telemetry": {
"compilations": 5,
"iterations": 10,
"duration_s": 429.14,
"best_status": "partial",
"best_goals": 1,
"max_iterations": 10,
"model": "openai/gpt-5.3-codex",
"error": null,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"usage": {
"prompt_tokens": 82737,
"completion_tokens": 11400,
"total_tokens": 94137,
"reasoning_tokens": 11110,
"cost_usd": 0.21104895
},
"reasoning_effort": "high",
"response_trace_count": 15
},
"response_trace": [
{
"iteration": 1,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"response_id": "gen-1772024410-insNlwx9TTtRd7nj3qj7",
"api_elapsed_s": 67.403,
"usage": {
"prompt_tokens": 1685,
"completion_tokens": 2735,
"total_tokens": 4420,
"reasoning_tokens": 2712,
"cost_usd": 0.03962595
},
"openrouter_retries": 0,
"response_text_len": 0,
"used_tool_call": true,
"reasoning_text": "**Analyzing proof feasibility of local connectedness**",
"reasoning_details": [
{
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.summary",
"summary": "**Analyzing proof feasibility of local connectedness**"
},
{
"id": "rs_006c62c575ad4d9201699ef25b22708194bfd5fb99537b2332",
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.encrypted",
"data": 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"
}
]
},
{
"iteration": 1,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "infer_instance",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772024478_6433.lean:36:2: error(lean.synthInstanceFailed): failed to synthesize instance of type class\n LocallyConnectedSpace \u2191mandelbrotSet\n\nHint: Type class instance resolution failures can be inspected with the `set_option trace.Meta.synthInstance true` command.\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n\n",
"compile_elapsed_s": 31.09,
"tactic_replay": {
"tactic_count": 1,
"successful_tactics": 0,
"first_failure_step": 1,
"goal_trajectory": [
1
],
"max_goals": 1,
"final_goal_count": 1,
"goals_opened": 0,
"goals_closed": 0
},
"lsp_feedback": {
"diagnostics": [
{
"code": "lean.synthInstanceFailed",
"fullRange": {
"end": {
"character": 16,
"line": 35
},
"start": {
"character": 2,
"line": 35
}
},
"message": "failed to synthesize instance of type class\n LocallyConnectedSpace \u2191mandelbrotSet\n\nHint: Type class instance resolution failures can be inspected with the `set_option trace.Meta.synthInstance true` command.",
"range": {
"end": {
"character": 16,
"line": 35
},
"start": {
"character": 2,
"line": 35
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 37
},
"start": {
"character": 0,
"line": 37
}
},
"message": "'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]",
"range": {
"end": {
"character": 6,
"line": 37
},
"start": {
"character": 0,
"line": 37
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 35,
"error_char": 2,
"error_msg": "failed to synthesize instance of type class\n LocallyConnectedSpace \u2191mandelbrotSet\n\nHint: Type class instance resolution failures can be inspected with the `set_option trace.Meta.synthInstance true` command.",
"goal_before_error": "```lean\n\u22a2 LocallyConnectedSpace \u2191mandelbrotSet\n```",
"full_timeline": [
{
"line": 35,
"code": "infer_instance",
"goal": "```lean\n\u22a2 LocallyConnectedSpace \u2191mandelbrotSet\n```",
"goal_count": 1,
"ast_complexity": 50
}
],
"tactic_count": 1,
"successful_tactics": 0,
"first_failure_step": 1,
"cps": 0.0,
"cps_peak_step": 0,
"error_code": "infer_instance"
}
},
{
"iteration": 2,
"event": "search_mathlib",
"query": "LocallyConnectedSpace.of_discreteTopology",
"results_count": 8
},
{
"iteration": 3,
"event": "search_mathlib",
"query": "locallyConnectedSpace",
"results_count": 8
},
{
"iteration": 4,
"event": "search_mathlib",
"query": "Subsingleton.locallyConnectedSpace",
"results_count": 8
},
{
"iteration": 5,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"response_id": "gen-1772024522-XyO3yI3WDbGmSb7luvlD",
"api_elapsed_s": 12.451,
"usage": {
"prompt_tokens": 6430,
"completion_tokens": 581,
"total_tokens": 7011,
"reasoning_tokens": 551,
"cost_usd": 0.0177737
},
"openrouter_retries": 0,
"response_text_len": 0,
"used_tool_call": true,
"reasoning_text": "**Exploring local connectedness approach**",
"reasoning_details": [
{
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.summary",
"summary": "**Exploring local connectedness approach**"
},
{
"id": "rs_006c62c575ad4d9201699ef2cb01588194b770968d4fab9643",
"format": "openai-responses-v1",
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{
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"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
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"banned_tokens": [],
"proof_code": "refine \u27e8?_\u27e9",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772024534_8851.lean:35:53: error: unsolved goals\n\u22a2 \u2200 (x : \u2191mandelbrotSet), (\ud835\udcdd x).HasBasis (fun s \u21a6 IsOpen s \u2227 x \u2208 s \u2227 IsConnected s) id\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n\n",
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{
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"end": {
"character": 13,
"line": 35
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"start": {
"character": 53,
"line": 34
}
},
"leanTags": [
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"message": "unsolved goals\n\u22a2 \u2200 (x : \u2191mandelbrotSet), (\ud835\udcdd x).HasBasis (fun s \u21a6 IsOpen s \u2227 x \u2208 s \u2227 IsConnected s) id",
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{
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"character": 6,
"line": 37
},
"start": {
"character": 0,
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}
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],
"error_line": 34,
"error_char": 53,
"error_msg": "unsolved goals\n\u22a2 \u2200 (x : \u2191mandelbrotSet), (\ud835\udcdd x).HasBasis (fun s \u21a6 IsOpen s \u2227 x \u2208 s \u2227 IsConnected s) id",
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{
"line": 35,
"code": "refine \u27e8?_\u27e9",
"goal": "```lean\n\u22a2 LocallyConnectedSpace \u2191mandelbrotSet\n```",
"goal_count": 1,
"ast_complexity": 50
}
],
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"error_code": "theorem MLC : LocallyConnectedSpace mandelbrotSet := by"
}
},
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"event": "search_mathlib",
"query": "MLC",
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{
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"
}
]
},
{
"iteration": 8,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "aesop",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772024668_8662.lean:36:2: error: tactic 'aesop' failed, made no progress\nInitial goal:\n \u22a2 LocallyConnectedSpace \u2191mandelbrotSet\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n\n",
"compile_elapsed_s": 29.044,
"tactic_replay": {
"tactic_count": 1,
"successful_tactics": 0,
"first_failure_step": 1,
"goal_trajectory": [
1
],
"max_goals": 1,
"final_goal_count": 1,
"goals_opened": 0,
"goals_closed": 0
},
"lsp_feedback": {
"diagnostics": [
{
"fullRange": {
"end": {
"character": 7,
"line": 35
},
"start": {
"character": 2,
"line": 35
}
},
"message": "tactic 'aesop' failed, made no progress\nInitial goal:\n \u22a2 LocallyConnectedSpace \u2191mandelbrotSet",
"range": {
"end": {
"character": 7,
"line": 35
},
"start": {
"character": 2,
"line": 35
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 37
},
"start": {
"character": 0,
"line": 37
}
},
"message": "'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]",
"range": {
"end": {
"character": 6,
"line": 37
},
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"error_line": 35,
"error_char": 2,
"error_msg": "tactic 'aesop' failed, made no progress\nInitial goal:\n \u22a2 LocallyConnectedSpace \u2191mandelbrotSet",
"goal_before_error": "```lean\n\u22a2 LocallyConnectedSpace \u2191mandelbrotSet\n```",
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{
"line": 35,
"code": "aesop",
"goal": "```lean\n\u22a2 LocallyConnectedSpace \u2191mandelbrotSet\n```",
"goal_count": 1,
"ast_complexity": 50
}
],
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"error_code": "aesop"
}
},
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},
{
"iteration": 9,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "have h : LocallyConnectedSpace (multibrotSet 2) := by\n infer_instance\nsimpa [mandelbrotSet] using h",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772024713_8270.lean:37:4: error(lean.synthInstanceFailed): failed to synthesize instance of type class\n LocallyConnectedSpace \u2191(multibrotSet 2)\n\nHint: Type class instance resolution failures can be inspected with the `set_option trace.Meta.synthInstance true` command.\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n\n",
"compile_elapsed_s": 31.736,
"tactic_replay": {
"tactic_count": 3,
"successful_tactics": 1,
"first_failure_step": 2,
"goal_trajectory": [
1,
1,
1
],
"max_goals": 1,
"final_goal_count": 1,
"goals_opened": 0,
"goals_closed": 0
},
"lsp_feedback": {
"diagnostics": [
{
"code": "lean.synthInstanceFailed",
"fullRange": {
"end": {
"character": 18,
"line": 36
},
"start": {
"character": 4,
"line": 36
}
},
"message": "failed to synthesize instance of type class\n LocallyConnectedSpace \u2191(multibrotSet 2)\n\nHint: Type class instance resolution failures can be inspected with the `set_option trace.Meta.synthInstance true` command.",
"range": {
"end": {
"character": 18,
"line": 36
},
"start": {
"character": 4,
"line": 36
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 39
},
"start": {
"character": 0,
"line": 39
}
},
"message": "'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]",
"range": {
"end": {
"character": 6,
"line": 39
},
"start": {
"character": 0,
"line": 39
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 36,
"error_char": 4,
"error_msg": "failed to synthesize instance of type class\n LocallyConnectedSpace \u2191(multibrotSet 2)\n\nHint: Type class instance resolution failures can be inspected with the `set_option trace.Meta.synthInstance true` command.",
"goal_before_error": "```lean\n\u22a2 LocallyConnectedSpace \u2191(multibrotSet 2)\n```",
"full_timeline": [
{
"line": 35,
"code": "have h : LocallyConnectedSpace (multibrotSet 2) := by",
"goal": "```lean\n\u22a2 LocallyConnectedSpace \u2191mandelbrotSet\n```",
"goal_count": 1,
"ast_complexity": 50
},
{
"line": 36,
"code": "infer_instance",
"goal": "```lean\n\u22a2 LocallyConnectedSpace \u2191(multibrotSet 2)\n```",
"goal_count": 1,
"ast_complexity": 53
},
{
"line": 37,
"code": "simpa [mandelbrotSet] using h",
"goal": "```lean\nh : LocallyConnectedSpace \u2191(multibrotSet 2)\n\u22a2 LocallyConnectedSpace \u2191mandelbrotSet\n```",
"goal_count": 1,
"ast_complexity": 94
}
],
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"first_failure_step": 2,
"cps": 33.33333333333333,
"cps_peak_step": 1,
"error_code": "infer_instance"
}
},
{
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"response_id": "gen-1772024745-78VorqfadatNyflp2HHH",
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"reasoning_text": "**Formulating final proof guess**",
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"type": "reasoning.summary",
"summary": "**Formulating final proof guess**"
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"
}
]
},
{
"iteration": 10,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "simpa [mandelbrotSet] using MLC_multibrot 2",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772024807_5906.lean:36:30: error(lean.unknownIdentifier): Unknown identifier `MLC_multibrot`\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n\n",
"compile_elapsed_s": 31.814,
"tactic_replay": {
"tactic_count": 1,
"successful_tactics": 0,
"first_failure_step": 1,
"goal_trajectory": [
1
],
"max_goals": 1,
"final_goal_count": 1,
"goals_opened": 0,
"goals_closed": 0
},
"lsp_feedback": {
"diagnostics": [
{
"code": "lean.unknownIdentifier",
"fullRange": {
"end": {
"character": 43,
"line": 35
},
"start": {
"character": 30,
"line": 35
}
},
"message": "Unknown identifier `MLC_multibrot`",
"range": {
"end": {
"character": 43,
"line": 35
},
"start": {
"character": 30,
"line": 35
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 37
},
"start": {
"character": 0,
"line": 37
}
},
"message": "'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]",
"range": {
"end": {
"character": 6,
"line": 37
},
"start": {
"character": 0,
"line": 37
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 35,
"error_char": 30,
"error_msg": "Unknown identifier `MLC_multibrot`",
"goal_before_error": "```lean\n\u22a2 LocallyConnectedSpace \u2191mandelbrotSet\n```",
"full_timeline": [
{
"line": 35,
"code": "simpa [mandelbrotSet] using MLC_multibrot 2",
"goal": "```lean\n\u22a2 LocallyConnectedSpace \u2191mandelbrotSet\n```",
"goal_count": 1,
"ast_complexity": 50
}
],
"tactic_count": 1,
"successful_tactics": 0,
"first_failure_step": 1,
"cps": 0.0,
"cps_peak_step": 0,
"error_code": "simpa [mandelbrotSet] using MLC_multibrot 2"
}
}
],
"verification": {
"banned_tokens": [],
"command": [
"[path]
"lean",
"/app/asi_portal/verifier/quick_1772024839_4662.lean"
],
"comparator_passed": null,
"duration_s": 20.717937469482422,
"goals_remaining": 1,
"is_verified": false,
"lean_file_path": "",
"problem": {
"axioms_check_name": "MLC",
"axioms_check_skipped": false,
"benchmark_id": "Wikipedia__Mandelbrot__MLC",
"category": "research_open",
"endings": [
"end Mandelbrot"
],
"imports": [
"FormalConjectures.Util.ProblemImports"
],
"preamble_chars": 1335,
"source_file": "FormalConjectures/Wikipedia/Mandelbrot.lean",
"title": "MLC"
},
"returncode": 1,
"status": "partial",
"stderr": "",
"stdout": "/app/asi_portal/verifier/quick_1772024839_4662.lean:35:53: error: unsolved goals\n\u22a2 \u2200 (x : \u2191mandelbrotSet), (\ud835\udcdd x).HasBasis (fun s \u21a6 IsOpen s \u2227 x \u2208 s \u2227 IsConnected s) id\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n",
"timed_out": false
},
"phase2_error": "ProgressAnalysisResult.__init__() missing 1 required positional argument: 'progress_score'"
}
|
| Gemini 3.1 Pro Agent v8 | Failed | -- | Feb 24, 2026 |
View{
"agent_telemetry": {
"compilations": 0,
"iterations": 0,
"duration_s": 0.05,
"best_status": "pending",
"best_goals": null,
"max_iterations": 10,
"model": "google/gemini-3.1-pro-preview",
"error": "OpenRouter API error 402: {\"error\":{\"message\":\"This request requires more credits, or fewer max_tokens. You requested up to 65536 tokens, but can only afford 58661. To increase, visit https://openrouter.ai/settings/keys and create a key with a higher total limit\",\"code\":402,\"metadata\":{\"provider_name\":null}},\"user_id\":\"user_2zsm3L1zzBL2yxyrvmrXwgeTimc\"}",
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|
|
| Gemini 3 Flash Agent v8 | Partial | 1 | Feb 17, 2026 |
rw [locallyConnectedSpace_iff_connected_basis]
intro c
constructor
intro U
constructor
· intro hU
refine ⟨connectedComponentIn U c, ⟨?_, isPreconnected_connectedComponentIn⟩, connectedComponentIn_subset U c⟩
have hc : c ∈ connectedComponentIn U c := mem_connectedComponentIn (mem_of_mem_nhds hU)
obtain ⟨ε, ε_pos, hε⟩ := Metric.mem_nhds_iff.mp hU
refine ?_
· rintro ⟨V, ⟨hV_nhds, hV_conn⟩, hVU⟩
exact mem_of_superset hV_nhds hVU
|
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{
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"iteration": 1,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
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"banned_tokens": [],
"proof_code": "constructor\n\u00b7 intro x hx U hU hxU\n obtain \u27e8\u03b4, \u03b4_pos, h\u03b4\u27e9 := Metric.mem_nhds_iff.mp hU\n let V := mandelbrotSet \u2229 Metric.ball x \u03b4\n use V\n constructor\n \u00b7 apply inter_subset_left\n \u00b7 constructor\n \u00b7 apply IsOpen.inter\n \u00b7 exact IsOpen.univ -- placeholder logic\n \u00b7 exact Metric.isOpen_ball\n \u00b7 constructor\n \u00b7 refine \u27e8hx, Metric.mem_ball_self \u03b4_pos\u27e9\n \u00b7 constructor\n \u00b7 exact fun y hy \u21a6 hxU (h\u03b4 hy.2)\n \u00b7 apply IsConnected.inter -- placeholder logic\n exact IsConnected.singleton x -- placeholder logic\n\u00b7 refine ?_\n -- The MLC conjecture is a major open problem in complex dynamics.\n -- Proving it involves the theory of external rays, puzzle pieces (Yoccoz puzzles),\n -- and showing that the diameter of these pieces tends to zero.\n -- This is currently beyond the reach of a simple tactic script.\n -- We leave the main direction of the proof as an open goal.\n simp [mandelbrotSet, multibrotSet]\n refine ?_",
"compiler_output_preview": "[path]:37:12: error: tactic 'introN' failed, insufficient number of binders\ncase open_connected_basis\nx : \u2191mandelbrotSet\n\u22a2 (\ud835\udcdd x).HasBasis (fun s \u21a6 IsOpen s \u2227 x \u2208 s \u2227 IsConnected s) id\n[path]:53:2: error: no goals to be solved\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quo\n...<truncated>"
},
{
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"provider": "openrouter_primary",
"finish_reason": "stop",
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"banned_tokens": [],
"proof_code": "rw [locallyConnectedSpace_iff_nhds_basis]\nintro c\nrefine \u27e8?_\u27e9\nintro U hU\nobtain \u27e8\u03b5, \u03b5_pos, h\u03b5\u27e9 := Metric.mem_nhds_iff.mp hU\n-- The core of the MLC conjecture: the Mandelbrot set is locally connected\n-- This is famously open for certain types of parameters (e.g., non-renormalizable)\n-- We will refine the goal to the known structure but it remains an open research problem.\nrefine ?_",
"compiler_output_preview": "[path]:36:6: error: unknown identifier 'locallyConnectedSpace_iff_nhds_basis'\n[path]:35:53: error: unsolved goals\n\u22a2 LocallyConnectedSpace \u2191mandelbrotSet\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n"
},
{
"iteration": 3,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771349279-8ioEGuWw2CuQMa7AWWi9",
"api_elapsed_s": 1.396,
"usage": {
"prompt_tokens": 2901,
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"cost_usd": 0.00076665
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},
{
"iteration": 3,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
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"banned_tokens": [],
"proof_code": "rw [locallyConnectedSpace_iff_connected_basis]\nintro c\nrefine \u27e8?_\u27e9\nintro U hU\nobtain \u27e8\u03b5, \u03b5_pos, h\u03b5\u27e9 := Metric.mem_nhds_iff.mp hU\nsimp [mandelbrotSet, multibrotSet] at *\nrefine ?_",
"compiler_output_preview": "[path]:39:10: error: tactic 'introN' failed, insufficient number of binders\nc : \u2191mandelbrotSet\nU : Set \u2191mandelbrotSet\n\u22a2 U \u2208 \ud835\udcdd c \u2194 \u2203 i, (i \u2208 \ud835\udcdd c \u2227 IsPreconnected i) \u2227 id i \u2286 U\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n"
},
{
"iteration": 4,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771349288-FbbsLq99zzTKwCANWyIk",
"api_elapsed_s": 2.329,
"usage": {
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"cost_usd": 0.00119905
},
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},
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"iteration": 4,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 4,
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"banned_tokens": [],
"proof_code": "rw [locallyConnectedSpace_iff_connected_basis]\nintro c\nconstructor\nintro U\nconstructor\n\u00b7 intro hU\n obtain \u27e8\u03b5, \u03b5_pos, h\u03b5\u27e9 := Metric.mem_nhds_iff.mp hU\n -- The MLC conjecture is equivalent to the existence of a basis of connected neighborhoods.\n -- Proving this requires showing that for any \u03b5, there exists a connected neighborhood V \u2286 U.\n -- This is the famous open problem. We refine to provide the required structure.\n refine \u27e8?_, \u27e8?_, ?_\u27e9, ?_\u27e9\n\u00b7 rintro \u27e8V, \u27e8hV_nhds, hV_conn\u27e9, hVU\u27e9\n exact mem_of_superset hV_nhds hVU",
"compiler_output_preview": "[path]:41:2: error: unsolved goals\ncase mem_iff'.mp.intro.intro.refine_1\nc : \u2191mandelbrotSet\nU : Set \u2191mandelbrotSet\nhU : U \u2208 \ud835\udcdd c\n\u03b5 : \u211d\n\u03b5_pos : \u03b5 > 0\nh\u03b5 : ball c \u03b5 \u2286 U\n\u22a2 Set \u2191mandelbrotSet\n\ncase mem_iff'.mp.intro.intro.refine_2\nc : \u2191mandelbrotSet\nU : Set \u2191mandelbrotSet\nhU : U \u2208 \ud835\udcdd c\n\u03b5 : \u211d\n\u03b5_pos : \u03b5 > 0\nh\u03b5 : ball c \u03b5 \u2286 U\n\u22a2 ?mem_iff'.mp.intro.intro.refine_1 \u2208 \ud835\udcdd c\n\ncase mem_iff'.mp.intro.intro.refine_3\nc\n...<truncated>"
},
{
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"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771349298-O2gjecROobN9svRrZWHL",
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"prompt_tokens": 3848,
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"iteration": 5,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
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"proof_code": "rw [locallyConnectedSpace_iff_connected_basis]\nintro c\nconstructor\nintro U\nconstructor\n\u00b7 intro hU\n obtain \u27e8\u03b5, \u03b5_pos, h\u03b5\u27e9 := Metric.mem_nhds_iff.mp hU\n refine \u27e8connectedComponentIn U c, \u27e8?_, ?_\u27e9, ?_\u27e9\n \u00b7 rw [mem_nhds_iff]\n -- Since the conjecture is that M (mandelbrotSet) is locally connected,\n -- the connected component of any neighborhood should itself be a neighborhood.\n -- This step is effectively the conjecture itself.\n refine \u27e8\u03b5, \u03b5_pos, ?_\u27e9\n refine ?_\n \u00b7 exact isPreconnected_connectedComponentIn\n \u00b7 exact connectedComponentIn_subset U c\n\u00b7 rintro \u27e8V, \u27e8hV_nhds, hV_conn\u27e9, hVU\u27e9\n exact mem_of_superset hV_nhds hVU",
"compiler_output_preview": "[path]:44:10: error: Ambiguous term\n mem_nhds_iff\nPossible interpretations:\n _root_.mem_nhds_iff : ?m.1790 \u2208 \ud835\udcdd ?m.1789 \u2194 \u2203 t \u2286 ?m.1790, IsOpen t \u2227 ?m.1789 \u2208 t\n \n Metric.mem_nhds_iff : ?m.1998 \u2208 \ud835\udcdd ?m.1997 \u2194 \u2203 \u03b5 > 0, ball ?m.1997 \u03b5 \u2286 ?m.1998\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n"
},
{
"iteration": 6,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771349307-sh7EFEjD0bZZfnTCjoNj",
"api_elapsed_s": 2.344,
"usage": {
"prompt_tokens": 4353,
"completion_tokens": 223,
"total_tokens": 4576,
"reasoning_tokens": null,
"cost_usd": 0.00193965
},
"openrouter_retries": 0,
"response_text_len": 635
},
{
"iteration": 6,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "rw [locallyConnectedSpace_iff_connected_basis]\nintro c\nconstructor\nintro U\nconstructor\n\u00b7 intro hU\n refine \u27e8connectedComponentIn U c, \u27e8?_, isPreconnected_connectedComponentIn\u27e9, connectedComponentIn_subset U c\u27e9\n rw [Metric.mem_nhds_iff]\n obtain \u27e8\u03b5, \u03b5_pos, h\u03b5\u27e9 := Metric.mem_nhds_iff.mp hU\n refine \u27e8\u03b5, \u03b5_pos, ?_\u27e9\n -- The local connectivity of the Mandelbrot set implies that for small enough \u03b5,\n -- the ball (intersected with the set) is contained in a single connected component.\n intro x hx\n apply subset_connectedComponentIn\n \u00b7 exact hx\n \u00b7 exact h\u03b5 hx\n\u00b7 rintro \u27e8V, \u27e8hV_nhds, hV_conn\u27e9, hVU\u27e9\n exact mem_of_superset hV_nhds hVU",
"compiler_output_preview": "[path]:49:10: error: unknown identifier 'subset_connectedComponentIn'\n[path]:50:4: error: no goals to be solved\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n"
},
{
"iteration": 7,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771349317-tY5PPB3wxNVyWitOOaj8",
"api_elapsed_s": 2.178,
"usage": {
"prompt_tokens": 4869,
"completion_tokens": 164,
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"cost_usd": 0.0011139
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{
"iteration": 7,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "rw [locallyConnectedSpace_iff_connected_basis]\nintro c\nconstructor\nintro U\nconstructor\n\u00b7 intro hU\n refine \u27e8connectedComponentIn U c, \u27e8?_, isPreconnected_connectedComponentIn\u27e9, connectedComponentIn_subset U c\u27e9\n have hc : c \u2208 connectedComponentIn U c := mem_connectedComponentIn (mem_of_mem_nhds hU)\n obtain \u27e8\u03b5, \u03b5_pos, h\u03b5\u27e9 := Metric.mem_nhds_iff.mp hU\n refine ?_\n\u00b7 rintro \u27e8V, \u27e8hV_nhds, hV_conn\u27e9, hVU\u27e9\n exact mem_of_superset hV_nhds hVU",
"compiler_output_preview": "[path]:41:2: error: unsolved goals\ncase mem_iff'.mp.intro.intro\nc : \u2191mandelbrotSet\nU : Set \u2191mandelbrotSet\nhU : U \u2208 \ud835\udcdd c\nhc : c \u2208 connectedComponentIn U c\n\u03b5 : \u211d\n\u03b5_pos : \u03b5 > 0\nh\u03b5 : ball c \u03b5 \u2286 U\n\u22a2 connectedComponentIn U c \u2208 \ud835\udcdd c\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n"
},
{
"iteration": 8,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771349327-HqhuqOrivH8sMl0StucL",
"api_elapsed_s": 2.51,
"usage": {
"prompt_tokens": 5273,
"completion_tokens": 207,
"total_tokens": 5480,
"reasoning_tokens": null,
"cost_usd": 0.00144535
},
"openrouter_retries": 0,
"response_text_len": 677
},
{
"iteration": 8,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "rw [locallyConnectedSpace_iff_connected_basis]\nintro c\nconstructor\n\u00b7 intro U hU\n refine \u27e8connectedComponentIn U c, \u27e8?_, isPreconnected_connectedComponentIn\u27e9, connectedComponentIn_subset U c\u27e9\n have h_open : IsOpen (connectedComponentIn U c) := by\n -- In a locally connected space, connected components of open sets are open.\n -- Since we are proving local connectivity, the property we need is \n -- exactly the existence of such a neighborhood.\n -- For now, we express the required neighborhood property:\n refine ?_\n exact h_open.mem_nhds (mem_connectedComponentIn (mem_of_mem_nhds hU))\n\u00b7 rintro \u27e8V, \u27e8hV_nhds, hV_conn\u27e9, hVU\u27e9\n exact mem_of_superset hV_nhds hVU",
"compiler_output_preview": "[path]:39:12: error: tactic 'introN' failed, insufficient number of binders\ncase mem_iff'\nc : \u2191mandelbrotSet\nU : Set \u2191mandelbrotSet\n\u22a2 U \u2208 \ud835\udcdd c \u2194 \u2203 i, (i \u2208 \ud835\udcdd c \u2227 IsPreconnected i) \u2227 id i \u2286 U\n[path]:48:2: error: no goals to be solved\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice\n...<truncated>"
}
],
"verification": {
"banned_tokens": [],
"command": [
"[path]
"lean",
"[path]
],
"duration_s": 7.681809902191162,
"goals_remaining": 1,
"is_verified": false,
"lean_file_path": "[path]
"problem": {
"axioms_check_name": "MLC",
"axioms_check_skipped": false,
"benchmark_id": "Wikipedia__Mandelbrot__MLC",
"category": "research_open",
"endings": [
"end Mandelbrot"
],
"imports": [
"FormalConjectures.Util.ProblemImports"
],
"preamble_chars": 1335,
"source_file": "FormalConjectures/Wikipedia/Mandelbrot.lean",
"title": "MLC"
},
"returncode": 1,
"status": "partial",
"stderr": "",
"stdout": "[path]:41:2: error: unsolved goals\ncase mem_iff'.mp.intro.intro\nc : \u2191mandelbrotSet\nU : Set \u2191mandelbrotSet\nhU : U \u2208 \ud835\udcdd c\nhc : c \u2208 connectedComponentIn U c\n\u03b5 : \u211d\n\u03b5_pos : \u03b5 > 0\nh\u03b5 : ball c \u03b5 \u2286 U\n\u22a2 connectedComponentIn U c \u2208 \ud835\udcdd c\n'Mandelbrot.MLC' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n",
"timed_out": false
}
}
|
| Gemini 3 Flash Preview | Failed | -- | Feb 14, 2026 |
apply isCompact_of_isClosed_isBounded
· apply isClosed_compl
simp only [compl_setOf, not_not]
sorry_placeholder_replacement
· sorry_placeholder_replacement
have h_conn : IsConnected S := by
sorry_placeholder_replacement
apply exists_open_connected_subset
· exact hU
· exact hxU
· sorry_placeholder_replacement
|
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|