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Require Import ZArith.
Require Import Lia.
Open Scope Z_scope.
Lemma two_x_eq_1 : forall x, 2 * x = 1 -> False.
Proof.
intros.
lia.
Qed.
Lemma two_x_y_eq_1 : forall x y, 2 * x + 2 * y = 1 -> False.
Proof.
intros.
lia.
Qed.
Lemma two_x_y_z_eq_1 : forall x y z, 2 * x + 2 * y + 2 * z= 1 -> False.
Proof.
intros.
lia.
Qed.
Lemma omega_nightmare : forall x y, 27 <= 11 * x + 13 * y <= 45 -> -10 <= 7 * x - 9 * y <= 4 -> False.
Proof.
intros ; intuition auto.
lia.
Qed.
Lemma compact_proof : forall z,
(z < 0) ->
(z >= 0) ->
(0 >= z \/ 0 < z) -> False.
Proof.
intros.
lia.
Qed.
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