Proofgold Proof

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