Proofgold Proof

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