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Add Copilot skill architecture with 10 skills, 2 agents, and shared infra

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Introduce .github/skills/ with solve, prove, optimize, simplify,
encode, explain, benchmark, memory-safety, static-analysis, and
deeptest skills. Each skill follows a SKILL.md + scripts/ pattern
with Python scripts backed by a shared SQLite logging library
(z3db.py). Two orchestrator agents (z3-solver, z3-verifier) route
requests to the appropriate skills.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
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---
name: encode
description: Translate constraint problems into SMT-LIB2 or Z3 Python API code. Handles common problem classes including scheduling, graph coloring, arithmetic puzzles, and verification conditions.
---
Given a problem description (natural language, pseudocode, or a partial formulation), produce a complete, syntactically valid SMT-LIB2 encoding or Z3 Python script. The encoding should declare all variables, assert all constraints, and include the appropriate check-sat / get-model commands.
# Step 1: Identify the problem class
Common encodings:
| Problem class | Theory | Typical sorts |
|---------------|--------|---------------|
| Integer arithmetic | LIA / NIA | Int |
| Real arithmetic | LRA / NRA | Real |
| Bitvector operations | QF_BV | (_ BitVec N) |
| Arrays and maps | QF_AX | (Array Int Int) |
| Strings and regex | QF_S | String, RegLan |
| Uninterpreted functions | QF_UF | custom sorts |
| Mixed theories | AUFLIA, etc. | combination |
# Step 2: Generate the encoding
```bash
python3 scripts/encode.py --problem "Find integers x, y such that x^2 + y^2 = 25 and x > 0" --format smtlib2
python3 scripts/encode.py --problem "Schedule 4 tasks on 2 machines minimizing makespan" --format python
```
For `--format smtlib2`, the output is a complete .smt2 file ready for the **solve** skill.
For `--format python`, the output is a standalone Z3 Python script.
# Step 3: Validate the encoding
The script checks that the generated formula is syntactically valid by running a quick `z3 -in` parse check (no solving, just syntax). Parse errors are reported with the offending line.
# Parameters
| Parameter | Type | Required | Default | Description |
|-----------|------|----------|---------|-------------|
| problem | string | yes | | problem description |
| format | string | no | smtlib2 | output format: smtlib2 or python |
| output | path | no | stdout | write to file instead of stdout |
| validate | flag | no | on | run syntax check on the output |
| debug | flag | no | off | verbose tracing |
| db | path | no | .z3-agent/z3agent.db | logging database |