Proofgold Proof

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