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Proof Theory · vibeeval | DecimalAI

scienceby vibeeval

Proof Theory

vibeeval/proof-theory

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for proof theory in mathematical logic

SkillScore86Maintained

Automatic

Research pack

Last verified 8/3/2026

What it changes

Passed 17 of 20 test cases with the skill, and 14 of 20 without it.

Without skill68%

With skill86%

Checks it passed that the model alone missed

Passes Implies(derivable(phi), valid(phi)) as the theorem string.
Includes uv run python -m runtime.harness scripts/cc_math/z3_solve.py prove.
Executes uv run python -m runtime.harness scripts/cc_math/z3_solve.py prove "P(0)".

and 2 more in the full report

4 fixed15 passed either way3 still failing0 broke

Pass-rate lift: +18 pp
Tokens: +6%
Agent turns: 0%
Response time: -19%

Model gemini-3.6-flashMeasured 8/3/2026v119 of 22 cases passed with skill · 20 comparable

Tokens, turns and time describe resource use, not a dollar price.

Use this skill

Save it into your project's skills folder. Claude Code picks it up in its next session.

curl -fsSL --create-dirs -o .claude/skills/vibeeval-proof-theory/SKILL.md https://app.decimal.ai/s/vibeeval-proof-theory/SKILL.md

Want it pinned and updatable? pip install "decimalai>=0.15", then decimalai skills add vibeeval-proof-theory, and start Claude Code with claude --plugin-dir "$(git rev-parse --show-toplevel)/.agents"

1 · One-time — install the CLI (docs ↗)

pip install "decimalai>=0.15"

2 · Get the skill — writes .agents/skills/vibeeval-proof-theory/ and pins it in .decimal/skills.lock

decimalai skills add vibeeval-proof-theory

No CLI? Get the same file — curl · raw file

curl -fsSL --create-dirs -o .claude/skills/vibeeval-proof-theory/SKILL.md https://app.decimal.ai/s/vibeeval-proof-theory/SKILL.md

Raw file: /s/vibeeval-proof-theory/SKILL.md ↗ · machine-readable summary at /s/vibeeval-proof-theory.json ↗

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

One of 2 test cases the skill fixed. Same model, same prompt, with and without the skill.

1 of 2

Prompt

Write the exact terminal command to execute verification of a formal proof structure using the math scratchpad harness script.

What was checked, without and with the skill
Checked	Without skill	With skill
Executes uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py verify.	Missed	Passed

case-17 · gemini-3.6-flash · 8/3/2026 · answers are capped and redacted

What's inside

The instructions your model reads when the skill loads.

SKILL.md62 linessingle file

Proof Theory

When to Use

Use this skill when working on proof-theory problems in mathematical logic.

Decision Tree

Proof Strategy Selection
- Direct proof: assume premises, derive conclusion
- Proof by contradiction: assume negation, derive false
- Proof by cases: split on disjunction
- Induction: base case + inductive step
Structural Induction
- Define well-founded ordering on structures
- Base: prove for minimal elements
- Step: assume for smaller, prove for current
- z3_solve.py prove "induction_principle"
Cut Elimination
- Gentzen's Hauptsatz: cuts can be eliminated
- Subformula property: only subformulas appear
- Useful for proof normalization
Completeness/Soundness Check
- Soundness: if provable then valid
- Completeness: if valid then provable
- z3_solve.py prove "soundness_theorem"
Proof Verification
- Check each step follows from rules
- Verify dependencies are satisfied
- math_scratchpad.py verify "proof_steps"

Tool Commands

Z3_Induction_Base

Track record

Benchmark

17 / 20

test cases passed, vs 14 / 20 without

Adoption

Users: 0
Times used: 0

Safety and source details

SkillSafety

✓ 3 of 3 passed

Code scan15 of 15 checks clean

0 critical · 0 warning · 0 info — scanner v4 — 8/1/2026

View 15 scanner checks

live_secretremote_code_executionreverse_shelldata_exfiltrationssrf_metadataagent_snoopinganti_refusaldestructive_commandsobfuscated_unicodeunicode_homoglyphopaque_blobsuspicious_urltool_overreachtrigger_abuseprompt_injection_phrasing

IntentSafe

LLM judge · does the skill do what it claims

ContentClean

LLM judge · policy & harmful-content review

Source

Imported

vibeeval / vibecosystem

skills/math/mathematical-logic/proof-theory/SKILL.md

View on GitHub ↗

License MITImported 8/1/2026Version v1

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See it in action

What's inside

Proof Theory

When to Use

Decision Tree

Tool Commands

Z3_Induction_Base

Track record

Benchmark

Adoption

SkillSafety

Source

Other skills for the same job

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