Proofgold Proof

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