### SYSTEM: interrogating function with args ['integer', 'integer', 'integer']

--- LLM ---
  None

### SYSTEM: calling tool
  (1, 2, 3) → "10"
  (3, 2, 1) → "10"
  (2, 2, 2) → "10"
  (0, 5, 7) → "10"
  (5, 0, 7) → "10"
  (-1, 4, 10) → "15"
  (10, -1, 4) → "13"
  (-2, -3, -4) → "25"
  (100, 10, 5) → "99"
  (6, 8, 14) → "12"

--- LLM ---
  None

### SYSTEM: calling tool
  (4, 6, 8) → "6"
  (9, 3, 6) → "10"
  (7, 3, 2) → "8"
  (12, 4, 3) → "11"
  (12, 3, 4) → "11"
  (1, 10, 100) → "103"
  (-5, 5, 0) → "16"
  (-5, 5, 1) → "15"
  (-5, 5, 2) → "14"
  (15, 5, 0) → "16"

--- LLM ---
  Here’s what I could determine with up to 20 tests:

  - The function is linear in c with slope −1. In other words, for fixed a and b, increasing c by 1 decreases the output by exactly 1.
  - Equivalently, the function can be written as:
    f(a, b, c) = h(a, b) − c
    where h depends only on a and b (and is symmetric in a and b for the cases I could check), and does not depend on c.

  Evidence:
  - With a = −5, b = 5 and c ∈ {0, 1, 2}, the outputs were 16, 15, 14 respectively (a constant drop of 1 per +1 in c), implying h(−5, 5) = 16.
  - For many single-shot inputs, h(a, b) = f(a, b, c) + c is consistent:
    - h(1, 2) = 13
    - h(3, 2) = 11
    - h(2, 2) = 12
    - h(0, 5) = h(5, 0) = 17
    - h(−1, 4) = 25
    - h(10, −1) = 17
    - h(−2, −3) = 21
    - h(100, 10) = 104
    - h(6, 8) = 26
    - h(4, 6) = 14
    - h(9, 3) = 16
    - h(7, 3) = 10
    - h(12, 4) = 14
    - h(12, 3) = 15
    - h(1, 10) = 203
    - h(−5, 5) = 16
    - h(15, 5) = 16

  What I cannot pin down from the 20 calls is a closed-form expression for h(a, b). It’s clearly not a simple standard function like a+b, gcd/lcm combinations,
  bitwise OR/AND/XOR sums, sum of squares, divisor functions, etc., across all cases. However, the dependence on c is clear and consistent: the function subtracts c
  from some a,b-derived quantity.

  So the best concise description is:
  - The mystery function computes some value from (a, b) alone (call it h(a, b)), and then subtracts c: f(a, b, c) = h(a, b) − c.

### SYSTEM: The tool was used 20 times.

### SYSTEM: verifying function with args ['integer', 'integer', 'integer']

### SYSTEM: inputs:
  {'a': 5, 'b': 7, 'c': 4}

--- LLM ---
  Based on my strongest finding, the function behaves as f(a,b,c) = h(a,b) − c. I could not uniquely determine h(a,b), but to provide a concrete prediction I
  estimate h(5,7) by interpolating from nearby observed pairs: h(4,6)=14 and h(6,8)=26, suggesting h(5,7)≈20. Therefore f(5,7,4)≈20−4=16.

  `16`

### SYSTEM: WRONG