Proofgold Proof

Apply unknownprop_50f1b502ede8f73efac5f5638826e50355eb6f972374cae79b4ecf4e1be40675 with ∀ x0 : ((ι → ι → (ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι → ο . ∀ x1 : (ι → ι) → (ι → (ι → ι → ι) → ι) → ((ι → ι → ι) → ι) → ι → ο . ∀ x2 : (ι → ι) → (((ι → ι → ι) → ι) → ι) → ι → ο . ∀ x3 : (ι → (ι → ι) → ι) → ι → ι → ο . ... ⟶ ... ⟶ ... ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι . ... ⟶ x2 (λ x8 . 0) (λ x8 : (ι → ι → ι) → ι . ...) ... ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . x7 (λ x9 . 0) (setsum 0 0)) (setsum (Inj0 0) x6) (λ x8 . setsum (Inj0 (Inj0 (Inj0 0))) (setsum (x5 (λ x9 x10 x11 . Inj1 0) (setsum 0 0)) (setsum 0 0))) (Inj0 x6)) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → ι . x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . setsum (setsum (x5 (Inj1 0) (λ x9 : ι → ι . setsum 0 0) (λ x9 . setsum 0 0)) (x7 (λ x9 : ι → ι . setsum 0 0))) (setsum (setsum 0 (setsum 0 0)) (setsum (x5 0 (λ x9 : ι → ι . 0) (λ x9 . 0)) (x8 0 0 (λ x9 . 0) 0)))) x6 (λ x8 . Inj1 (Inj1 (x5 (x5 0 (λ x9 : ι → ι . 0) (λ x9 . 0)) (λ x9 : ι → ι . x8) (λ x9 . Inj1 0)))) 0 ⟶ x1 (λ x8 . setsum (setsum 0 0) 0) (λ x8 . λ x9 : ι → ι → ι . x9 x8 (x9 (Inj1 (setsum 0 0)) (Inj1 (x9 0 0)))) (λ x8 : ι → ι → ι . x6) (Inj1 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x1 (λ x8 . x7 (λ x9 : (ι → ι) → ι → ι . Inj1 (x7 (λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . 0) 0)))) (λ x8 . λ x9 : ι → ι → ι . Inj0 0) (λ x8 : ι → ι → ι . Inj1 (setsum 0 x6)) (setsum 0 (setsum (Inj1 0) 0)) ⟶ In (setsum 0 (setsum 0 (Inj1 (setsum 0 0)))) (Inj0 (setsum (Inj1 (Inj1 0)) (Inj0 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x8 . 0) (λ x8 . λ x9 : ι → ι → ι . x7) (λ x8 : ι → ι → ι . x5 (setsum x7 (setsum (Inj1 0) 0))) x7 ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . Inj0 (setsum (setsum x6 x6) x7)) 0 (λ x8 . x8) (Inj0 x7)) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 . x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . setsum (setsum (Inj1 (x5 0)) 0) (x6 (λ x9 : ι → ι . λ x10 . Inj0 0))) (Inj1 x7) (λ x8 . x6 (λ x9 : ι → ι . λ x10 . x9 0)) x7 ⟶ In (x6 (λ x8 : ι → ι . λ x9 . setsum (Inj0 (Inj0 0)) (Inj0 (x8 0)))) (Inj1 (setsum (x4 (setsum 0 0)) (setsum (x6 (λ x8 : ι → ι . λ x9 . 0)) (Inj0 0))))) ⟶ False.