Proofgold Proof

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