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