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+Require Import Coq.Reals.Reals Coq.nsatz.Nsatz.
+Local Open Scope R.
+
+Goal forall x y : R,
+ x*x = y * y ->
+ x*x = -y * -y ->
+ x*(x*x) = 0 -> (* The associativity does not actually matter, *)
+ (x*x)*x = 0. (* just otherwise [assumption] would solve the goal. *)
+Proof.
+ nsatz.
+Qed.