Proofgold Proof

Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with ∀ x0 : (ι → ι) → ι → ο . ∀ x1 : (ι → (ι → ι) → ι → (ι → ι) → ι → 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) → ι → ο . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι . In (Inj1 ...) ... ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x12) (λ x8 : ι → (ι → ι) → ι . x5 0) ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . Inj1 (Inj1 (setsum (setsum 0 0) (Inj0 0)))) (x5 (setsum (Inj1 (Inj1 0)) 0))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι . ∀ x5 x6 x7 . x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . setsum (x8 (λ x12 x13 x14 . Inj1 (Inj1 0)) (λ x12 . Inj0 0) (x10 (x10 0 0) 0)) (Inj1 0)) x7 ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) x7) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι) → ι) → ι → ι . x2 (λ x8 . x7 (λ x9 : ι → ι . 0) (Inj0 (setsum 0 0))) 0 (Inj1 0) (Inj0 (setsum (x5 (Inj1 0) (λ x8 : ι → ι . x7 (λ x9 : ι → ι . 0) 0)) (x6 x4))) ⟶ x2 (λ x8 . Inj0 0) (setsum x4 (Inj0 (x5 0 (λ x8 : ι → ι . setsum 0 0)))) x4 0) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x8 . 0) (Inj0 (Inj1 x4)) (Inj0 (setsum (Inj0 0) 0)) (setsum (setsum x4 0) 0) ⟶ In x7 (Inj1 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (ι → ι → ι) → ι → ι → ι . x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . setsum 0 (Inj0 (Inj1 (x10 0 0)))) (Inj1 0) ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x12) (λ x8 : ι → (ι → ι) → ι . x5 0 (setsum (Inj0 (setsum 0 0)) 0) (λ x9 . x6) (x8 (setsum (Inj1 0) 0) (λ x9 . 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι → ι . ∀ x7 . x1 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x8 : ι → (ι → ι) → ι . 0) ⟶ False) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . In (Inj1 (Inj0 (setsum 0 (x6 (λ x8 x9 x10 . 0))))) (Inj0 (setsum x4 0)) ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) x7 ⟶ x0 (λ x8 . Inj0 (Inj0 (setsum (x5 0) (Inj1 0)))) (Inj1 0)) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 . In (Inj1 0) x4 ⟶ x0 (λ x8 . setsum 0 (Inj0 (x6 (λ x9 : ι → ι . λ x10 . 0)))) (setsum x7 x7) ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) (Inj1 (Inj1 x5))) ⟶ False.