Proofgold Proof

Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with ∀ x0 : ((ι → ι → (ι → ι) → ι) → ι) → ι → ι → ο . ∀ x1 : (ι → ι) → ι → ο . ∀ x2 : ((((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι) → ι) → ι → (ι → ι → ι) → ο . ∀ x3 : (ι → (ι → ι) → ι) → (((ι → ι) → ι) → ι) → ο . (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x3 (λ x8 . λ x9 : ι → ι . x9 (Inj1 ...)) ...) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι → ι) → ι . ∀ x7 . In (setsum (Inj0 (setsum (Inj0 0) 0)) (Inj1 0)) (Inj0 x7) ⟶ x3 (λ x8 . λ x9 : ι → ι . x8) (λ x8 : (ι → ι) → ι . Inj0 (setsum (setsum (setsum 0 0) 0) (setsum (setsum 0 0) 0))) ⟶ x3 (λ x8 . λ x9 : ι → ι . 0) (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : (ι → ι) → ι → ι . x1 (λ x8 . x5) (setsum x5 (x6 (Inj1 0) (Inj1 (Inj0 0)))) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x6 (x8 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0)) 0) (x6 0 x4) (λ x8 x9 . Inj1 (x7 (λ x10 . Inj1 x9) 0))) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 x6 x7 . x2 (λ x8 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . Inj1 0) 0 (λ x8 x9 . setsum (Inj0 0) x7) ⟶ In (Inj0 (Inj0 (setsum x6 (Inj0 0)))) (Inj0 (setsum (Inj0 (setsum 0 0)) (setsum (x4 0 0 (λ x8 . 0) 0) x7)))) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x7 . In (Inj1 x5) (Inj1 (setsum (Inj1 (x6 (λ x8 x9 : ι → ι . λ x10 . 0) (λ x8 x9 . 0))) (Inj1 (setsum 0 0)))) ⟶ x1 (λ x8 . x6 (λ x9 x10 : ι → ι . λ x11 . Inj0 0) (λ x9 x10 . setsum (Inj0 0) 0)) (setsum 0 (setsum (setsum 0 (setsum 0 0)) (setsum 0 0))) ⟶ x1 (λ x8 . 0) (setsum 0 (Inj0 0))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x8 . 0) (Inj1 (setsum (Inj1 (setsum 0 0)) (Inj1 0))) ⟶ False) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . In x5 (setsum (setsum 0 0) (Inj1 (setsum (Inj0 0) x4))) ⟶ x1 (λ x8 . x7) (Inj1 0) ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι . setsum (setsum x7 0) (x6 0)) 0 (setsum (Inj0 (setsum 0 (Inj0 0))) 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . x0 (λ x8 : ι → ι → (ι → ι) → ι . 0) (setsum 0 (Inj0 (setsum x5 (Inj1 0)))) (setsum (Inj0 (setsum (setsum 0 0) (setsum 0 0))) (Inj0 (Inj1 0))) ⟶ In (Inj1 (Inj1 (Inj1 0))) (setsum 0 (setsum 0 (Inj1 0)))) ⟶ False.