putnam-v1 / putnam-1962-a6

putnam-1962-a6

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1962-a6

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/putnam-1962-a6.lean

import Mathlib

theorem putnam_1962_a6 (S : Set ℚ)
(hSadd : ∀ a ∈ S, ∀ b ∈ S, a + b ∈ S)
(hSprod : ∀ a ∈ S, ∀ b ∈ S, a * b ∈ S)
(hScond : ∀ r : ℚ, (r ∈ S ∨ -r ∈ S ∨ r = 0) ∧ ¬(r ∈ S ∧ -r ∈ S) ∧ ¬(r ∈ S ∧ r = 0) ∧ ¬(-r ∈ S ∧ r = 0))
: S = { r : ℚ | r > 0 } := by
  sorry

Runs (0)

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