Proofgold Proof

Apply unknownprop_50f1b502ede8f73efac5f5638826e50355eb6f972374cae79b4ecf4e1be40675 with ∀ x0 : (((((ι → ι) → ι → ι) → ι) → ι → ι → ι) → ι) → ι → (ι → (ι → ι) → ι) → ο . ∀ x1 : (ι → ι) → ((((ι → ι) → ι → ι) → ι) → ι) → (ι → 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 → ι → ι) → (ι → ι) → ι → ι) → ι → ι) → ι → ι → ο . ... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι . In (Inj0 (Inj1 (setsum 0 (Inj0 0)))) (Inj1 (setsum (setsum (setsum 0 0) 0) (x7 (λ x8 . x7 (λ x9 . 0) ...) ...))) ⟶ x3 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum (setsum (setsum (setsum 0 0) (setsum 0 0)) 0) (x7 (λ x11 . x10) (λ x11 : ι → ι . λ x12 . x9 (λ x13 x14 . 0) (λ x13 . setsum 0 0) (setsum 0 0)))) (Inj1 (Inj1 (setsum (Inj0 0) (setsum 0 0)))) (Inj0 x4) ⟶ x1 (λ x8 . Inj1 (x5 0 (λ x9 : ι → ι . λ x10 . x10))) (λ x8 : ((ι → ι) → ι → ι) → ι . Inj0 (Inj1 (setsum (setsum 0 0) (Inj1 0)))) (λ x8 x9 . Inj0 (x7 (λ x10 . setsum (setsum 0 0) (Inj0 0)) (λ x10 : ι → ι . λ x11 . Inj1 (x10 0)))) (x7 (λ x8 . 0) (λ x8 : ι → ι . λ x9 . setsum (x6 (λ x10 . 0)) 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x1 (λ x8 . 0) (λ x8 : ((ι → ι) → ι → ι) → ι . 0) (λ x8 x9 . Inj1 (setsum x6 x8)) 0 ⟶ In (Inj1 (setsum 0 (setsum (setsum 0 0) (setsum 0 0)))) (Inj0 (setsum (Inj1 x6) (x4 (λ x8 . 0))))) ⟶ (∀ x4 x5 x6 x7 . In x7 (setsum (Inj0 (setsum 0 (setsum 0 0))) x6) ⟶ x2 (λ x8 . Inj0 (setsum (Inj0 x8) (setsum (setsum 0 0) 0))) (Inj0 (setsum x5 0)) (λ x8 x9 : ι → ι . λ x10 . Inj0 (Inj1 (setsum (setsum 0 0) x7))) (λ x8 : ι → ι . λ x9 . Inj1 (setsum 0 (setsum 0 (setsum 0 0)))) ⟶ x0 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . Inj0 x7) (Inj1 x5) (λ x8 . λ x9 : ι → ι . 0)) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 . x0 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . setsum (setsum (setsum 0 (Inj0 0)) 0) (Inj1 (Inj1 (setsum 0 0)))) (setsum (Inj1 (setsum x5 0)) x7) (λ x8 . λ x9 : ι → ι . setsum (Inj1 (setsum (x6 (λ x10 : (ι → ι) → ι → ι . 0)) x8)) x7) ⟶ x1 (λ x8 . setsum (Inj1 (Inj1 x7)) x8) (λ x8 : ((ι → ι) → ι → ι) → ι . 0) (λ x8 x9 . setsum x9 (setsum (Inj1 (setsum 0 0)) x9)) (Inj0 (x6 (λ x8 : (ι → ι) → ι → ι . setsum (setsum 0 0) 0)))) ⟶ False.