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Predicate Logic · vibeeval | DecimalAI

scienceby vibeeval

Predicate Logic

vibeeval/predicate-logic

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for predicate logic in mathematical logic

SkillScore95Maintained

Automatic

Research pack

Last verified 8/3/2026

What it changes

Passed 21 of 22 test cases with the skill, and 15 of 22 without it.

Without skill68%

With skill95%

Checks it passed that the model alone missed

Uses `sympy_compute.py`
Uses the `sat` subcommand
Uses `ForAll([x], P(x))` syntax

and 3 more in the full report

6 fixed15 passed either way1 still failing0 broke

Pass-rate lift: +27 pp
Tokens: -5%
Agent turns: 0%
Response time: -45%

Model gemini-3.6-flashMeasured 8/3/2026v121 of 22 cases passed with skill

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-predicate-logic/SKILL.md https://app.decimal.ai/s/vibeeval-predicate-logic/SKILL.md

Want it pinned and updatable? pip install "decimalai>=0.15", then decimalai skills add vibeeval-predicate-logic, 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-predicate-logic/ and pins it in .decimal/skills.lock

decimalai skills add vibeeval-predicate-logic

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

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

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

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

One of 6 test cases the skill fixed. Same model, same prompt, with and without the skill.

1 of 6

Prompt

Provide the complete command-line tool invocation using `uv run` to generate a model for `Exists([x], P(x))` using `z3_solve.py`.

What was checked, without and with the skill
Checked	Without skill	With skill
Includes `uv run python -m runtime.harness scripts/z3_solve.py model "Exists([x], P(x))"`	Missed	Passed

case-18 · 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.md60 linessingle file

Predicate Logic

When to Use

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

Decision Tree

Quantifier Analysis
- Identify: ForAll (universal), Exists (existential)
- Scope of quantifiers and free/bound variables
- z3_solve.py prove "ForAll([x], P(x)) implies P(a)"
Prenex Normal Form
- Move all quantifiers to front
- Standardize variables to avoid capture
- sympy_compute.py simplify "prenex(formula)"
Skolemization (for Exists)
- Replace existential quantifiers with Skolem functions
- Exists x. P(x) -> P(c) or P(f(y)) depending on scope
- Needed for resolution-based proofs
Resolution Proof
- Convert to CNF, negate conclusion
- Apply resolution rule until empty clause or saturation
- z3_solve.py prove "resolution_valid"
Model Theory
- Construct countermodel to refute invalid argument
- Finite model for finite domain
- z3_solve.py model "Exists([x], P(x) & Not(Q(x)))"

Tool Commands

Z3_Forall

uv run python -m runtime.harness scripts/z3_solve.py prove "ForAll([x], Implies(P(x), Q(x)))"

Track record

Benchmark

21 / 22

test cases passed, vs 15 / 22 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/predicate-logic/SKILL.md

View on GitHub ↗

License MITImported 8/1/2026Version v1

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See it in action

What's inside

Predicate Logic

When to Use

Decision Tree

Tool Commands

Z3_Forall

Track record

Benchmark

Adoption

SkillSafety

Source

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