minif2f-v1 / aime-1984-p15

aime-1984-p15

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal aime-1984-p15

What it runs

The Lean statement the swarm must prove — kernel-verified at Gate A. The trailing sorry is the open obligation a proof replaces.

goals/aime-1984-p15.lean

import Mathlib

set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat

theorem aime_1984_p15 (x y z w : ℝ)
    (h₀ :
      x ^ 2 / (2 ^ 2 - 1) + y ^ 2 / (2 ^ 2 - 3 ^ 2) + z ^ 2 / (2 ^ 2 - 5 ^ 2) +
          w ^ 2 / (2 ^ 2 - 7 ^ 2) =
        1)
    (h₁ :
      x ^ 2 / (4 ^ 2 - 1) + y ^ 2 / (4 ^ 2 - 3 ^ 2) + z ^ 2 / (4 ^ 2 - 5 ^ 2) +
          w ^ 2 / (4 ^ 2 - 7 ^ 2) =
        1)
    (h₂ :
      x ^ 2 / (6 ^ 2 - 1) + y ^ 2 / (6 ^ 2 - 3 ^ 2) + z ^ 2 / (6 ^ 2 - 5 ^ 2) +
          w ^ 2 / (6 ^ 2 - 7 ^ 2) =
        1)
    (h₃ :
      x ^ 2 / (8 ^ 2 - 1) + y ^ 2 / (8 ^ 2 - 3 ^ 2) + z ^ 2 / (8 ^ 2 - 5 ^ 2) +
          w ^ 2 / (8 ^ 2 - 7 ^ 2) =
        1) :
    x ^ 2 + y ^ 2 + z ^ 2 + w ^ 2 = 36 := by
  sorry

Runs (0)

No runs recorded for this suite yet — they appear here as the swarm attempts the benchmarks.