Proofgold Address

Known FalseE^FalseE : False ⟶ ∀ x0 : ο . x0
Known notE^notE : ∀ x0 : ο . not x0 ⟶ x0 ⟶ False
Known e3ec9..^neq_0_1 : not (0 = 1)
Theorem 4eb01.. : ∀ x0 : (ι → ι) → (ι → ι → (ι → ι) → ι) → ι . ∀ x1 : ((ι → ((ι → ι) → ι → ι) → ι → ι) → ι → ι → (ι → ι) → ι → ι) → ((ι → (ι → ι) → ι) → ι) → ι . ∀ x2 : ((ι → ((ι → ι) → ι → ι) → ι → ι → ι) → ι) → (ι → ((ι → ι) → ι) → (ι → ι) → ι) → ι → ι . ∀ x3 : ((((ι → ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι) → ι → ι . (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι . x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . setsum (Inj1 (Inj0 0)) (x10 (Inj1 0) (Inj0 0))) (x0 (λ x11 . x11) (λ x11 x12 . λ x13 : ι → ι . setsum (x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 : ι → (ι → ι) → ι . 0)) (setsum 0 0)))) (x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . setsum (x3 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . 0) x5) (x2 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x7 (λ x11 . 0)) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . setsum 0 0) (x0 (λ x10 . 0) (λ x10 x11 . λ x12 : ι → ι . 0)))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x9) x4) = setsum x5 x4) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 x6 x7 . x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . 0) 0 = setsum 0 (x4 (λ x9 . λ x10 : ι → ι . 0))) ⟶ (∀ x4 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x0 (λ x10 . 0) (λ x10 x11 . λ x12 : ι → ι . Inj0 (Inj0 (setsum 0 0)))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (x0 (λ x12 . setsum x12 (x1 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 : ι → (ι → ι) → ι . 0))) (λ x12 x13 . λ x14 : ι → ι . setsum (setsum 0 0) (Inj1 0))) (setsum 0 (setsum (setsum 0 0) (x3 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . λ x13 : ι → ι → ι . 0) 0)))) (x4 (x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . 0) (setsum (Inj0 0) 0)) (λ x9 . setsum 0 (Inj0 0)) (λ x9 . setsum 0 (setsum 0 (x5 0 0 (λ x10 . 0)))) (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x9 : ι → (ι → ι) → ι . 0))) = x0 (λ x9 . x0 (λ x10 . 0) (λ x10 x11 . λ x12 : ι → ι . setsum (x1 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 : ι → (ι → ι) → ι . 0)) (Inj1 x11))) (λ x9 x10 . λ x11 : ι → ι . setsum (x7 (setsum x10 (x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 : ι → (ι → ι) → ι . 0)))) 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . setsum 0 (setsum (setsum (x2 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) 0) (x3 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . 0) 0)) 0)) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (setsum 0 x7) (x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . x3 (λ x17 : ((ι → ι → ι) → ι → ι) → ι . λ x18 : ι → ι → ι . x15 0) x13) (λ x12 : ι → (ι → ι) → ι . Inj1 (x1 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 : ι → (ι → ι) → ι . 0))))) 0 = x4 (λ x9 . λ x10 : ι → ι . λ x11 . x3 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . λ x13 : ι → ι → ι . x13 (x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x15 x16 . λ x17 : ι → ι . λ x18 . x2 (λ x19 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x19 . λ x20 : (ι → ι) → ι . λ x21 : ι → ι . 0) 0) (λ x14 : ι → (ι → ι) → ι . 0)) (Inj0 0)) (x10 0)) (λ x9 : ι → ι . 0)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι → ι → ι) → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . x10) (λ x9 : ι → (ι → ι) → ι . setsum 0 (setsum (x7 (λ x10 x11 x12 . x9 0 (λ x13 . 0))) (setsum (setsum 0 0) (x9 0 (λ x10 . 0))))) = x5) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι → ι . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . setsum (x2 (λ x14 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . setsum (Inj1 0) (x2 (λ x15 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0) 0)) (λ x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . x2 (λ x17 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x15 (λ x18 . 0)) (λ x17 . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . x2 (λ x20 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x20 . λ x21 : (ι → ι) → ι . λ x22 : ι → ι . 0) 0) (x15 (λ x17 . 0))) (Inj0 (x12 0))) x10) (λ x9 : ι → (ι → ι) → ι . x9 0 (λ x10 . 0)) = x4 (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . setsum (Inj1 0) (x3 (λ x17 : ((ι → ι → ι) → ι → ι) → ι . λ x18 : ι → ι → ι . x2 (λ x19 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x19 . λ x20 : (ι → ι) → ι . λ x21 : ι → ι . 0) 0) (Inj1 0))) (λ x12 : ι → (ι → ι) → ι . x3 (λ x13 : ((ι → ι → ι) → ι → ι) → ι . λ x14 : ι → ι → ι . setsum (x13 (λ x15 : ι → ι → ι . λ x16 . 0)) (setsum 0 0)) (setsum (Inj1 0) (Inj1 0)))) (x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . x0 (λ x11 . x9 (λ x12 : ι → ι → ι . λ x13 . x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 : ι → (ι → ι) → ι . 0))) (λ x11 x12 . λ x13 : ι → ι . x0 (λ x14 . x0 (λ x15 . 0) (λ x15 x16 . λ x17 : ι → ι . 0)) (λ x14 x15 . λ x16 : ι → ι . setsum 0 0))) (setsum (Inj1 0) (x6 (x7 0 (λ x9 : ι → ι . 0) (λ x9 . 0) 0)))) (x5 (λ x9 : ι → ι . setsum 0 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι . x0 (λ x9 . x3 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . 0) (setsum 0 (Inj0 (x2 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) 0)))) (λ x9 x10 . λ x11 : ι → ι . x2 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . setsum (x2 (λ x15 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0) (x13 (λ x15 . 0))) (Inj1 (x1 (λ x15 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x16 x17 . λ x18 : ι → ι . λ x19 . 0) (λ x15 : ι → (ι → ι) → ι . 0)))) 0) = x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . setsum (x9 0 (λ x10 : ι → ι . λ x11 . Inj1 (Inj0 0)) (setsum 0 (x3 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . 0) 0)) (Inj0 (Inj0 0))) (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . Inj0 0) (λ x10 : ι → (ι → ι) → ι . Inj1 (x3 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . λ x12 : ι → ι → ι . 0) 0)))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (x2 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . Inj1 (x2 (λ x15 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0) 0)) (x7 (λ x12 . λ x13 : ι → ι . setsum 0 0) (x2 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0) 0) (λ x12 . x9))) (x10 (λ x12 . Inj1 (x0 (λ x13 . 0) (λ x13 x14 . λ x15 : ι → ι . 0))))) (x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x5 (x5 (setsum 0 0))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) (setsum 0 0))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 . x9) (λ x9 x10 . λ x11 : ι → ι . setsum (Inj0 0) (Inj0 0)) = Inj0 0) ⟶ False (proof)
Theorem f183e.. : ∀ x0 : ((ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι → ι) → (ι → ι → ι) → ι → ι → ι → ι → ι . ∀ x1 : ((ι → (ι → ι → ι) → ι) → ι → ι → ι → ι) → ι → ι . ∀ x2 : (ι → ι) → ι → (ι → ι) → ι . ∀ x3 : (ι → ι → ((ι → ι) → ι) → ι) → ι → (((ι → ι) → ι → ι) → ι → ι) → ι . (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (Inj0 (x5 (λ x9 : ι → ι . 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . 0) (x0 (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 x15 . setsum (x13 0) (x3 (λ x16 x17 . λ x18 : (ι → ι) → ι . 0) 0 (λ x16 : (ι → ι) → ι → ι . λ x17 . 0))) (λ x11 x12 . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . Inj0 0) (x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . 0) 0)) 0 (x6 (λ x11 : ι → ι → ι . Inj0 0)) (x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . x10) (x0 (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 x15 . 0) (λ x11 x12 . 0) 0 0 0 0) (λ x11 : (ι → ι) → ι → ι . λ x12 . setsum 0 0)) (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0)) (λ x11 . x9 (λ x12 . 0) (x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . x1 (λ x15 : ι → (ι → ι → ι) → ι . λ x16 x17 x18 . 0) 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . x10)))) = x2 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . x3 (λ x17 x18 . λ x19 : (ι → ι) → ι . 0) (x1 (λ x17 : ι → (ι → ι → ι) → ι . λ x18 x19 x20 . 0) 0) (λ x17 : (ι → ι) → ι → ι . λ x18 . x2 (λ x19 . 0) 0 (λ x19 . 0))) (x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . x16) 0)) x9 (λ x10 : (ι → ι) → ι → ι . λ x11 . 0)) (x2 (λ x9 . 0) 0 (λ x9 . x6 (λ x10 : ι → ι → ι . Inj0 x9))) (λ x9 . setsum 0 (x5 (λ x10 : ι → ι . Inj1 (x6 (λ x11 : ι → ι → ι . 0)))))) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (x4 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . 0)) x7 (λ x9 : (ι → ι) → ι → ι . λ x10 . x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0) (x2 (λ x11 . 0) 0 (λ x11 . 0))))) (λ x9 : (ι → ι) → ι → ι . x1 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 x12 x13 . setsum (x0 (λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 x18 . Inj1 0) (λ x14 x15 . x0 (λ x16 : ι → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . λ x19 x20 . 0) (λ x16 x17 . 0) 0 0 0 0) x12 x11 (x3 (λ x14 x15 . λ x16 : (ι → ι) → ι . 0) 0 (λ x14 : (ι → ι) → ι → ι . λ x15 . 0)) (setsum 0 0)) (Inj0 (Inj0 0)))) = x4 x7) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x6 : ι → (ι → ι) → ι → ι . ∀ x7 : ι → ι → ι . x2 (λ x9 . setsum (x7 (x6 (Inj1 0) (λ x10 . x9) (x2 (λ x10 . 0) 0 (λ x10 . 0))) (x7 0 0)) (setsum (x5 (λ x10 : (ι → ι) → ι . setsum 0 0) 0) (Inj1 (x2 (λ x10 . 0) 0 (λ x10 . 0))))) (Inj1 0) (λ x9 . Inj1 (x5 (λ x10 : (ι → ι) → ι . x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . x0 (λ x15 : ι → (ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 x19 . 0) (λ x15 x16 . 0) 0 0 0 0) (setsum 0 0)) 0)) = x4 (setsum (setsum (x2 (λ x9 . x5 (λ x10 : (ι → ι) → ι . 0) 0) (x7 0 0) (λ x9 . 0)) (x5 (λ x9 : (ι → ι) → ι . x6 0 (λ x10 . 0) 0) 0)) (x0 (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . 0) (λ x9 x10 . setsum x10 x10) 0 (x5 (λ x9 : (ι → ι) → ι . Inj1 0) (x7 0 0)) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj0 0)) (Inj0 (x5 (λ x9 : (ι → ι) → ι . 0) 0)))) (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . Inj1 (x2 (λ x13 . x2 (λ x14 . 0) 0 (λ x14 . 0)) x12 (λ x13 . x12))) 0)) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . x2 (λ x9 . x9) (x7 (λ x9 . 0)) (λ x9 . x5) = x7 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) x5 (λ x10 : (ι → ι) → ι → ι . λ x11 . x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . x14 (Inj0 0)) (λ x12 x13 . 0) (x2 (λ x12 . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . 0) 0) (setsum 0 0) (λ x12 . 0)) (setsum (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) 0 0 0 0) (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0)) (setsum 0 (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) 0 0 0 0)) (setsum (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0) (setsum 0 0))))) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . 0) (Inj0 (x5 0)) = setsum 0 (Inj1 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . setsum 0 (Inj1 (Inj0 0))) x11) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum x9 (Inj1 (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0))) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . x7)) = x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . x15) x7) (x2 (λ x12 . x10) (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) (Inj1 0) (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0) (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0) x7) (λ x12 . x12))) (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . x12) 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . x1 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 x16 x17 . x0 (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 x22 . 0) (λ x18 x19 . x1 (λ x20 : ι → (ι → ι → ι) → ι . λ x21 x22 x23 . 0) 0) (x0 (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 x22 . 0) (λ x18 x19 . 0) 0 0 0 0) x15 (x2 (λ x18 . 0) 0 (λ x18 . 0)) (x14 0 (λ x18 x19 . 0))) (x2 (λ x14 . 0) 0 (λ x14 . x14))) x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . setsum (setsum (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x13 x14 . 0) 0 0 0 0) (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x13 x14 . 0) 0 0 0 0)) (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . Inj0 0) (λ x13 x14 . x13) (setsum 0 0) (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x13 x14 . 0) 0 0 0 0) x10 x12)))) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 x7 . x0 (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . 0) (λ x9 x10 . setsum (setsum (x2 (λ x11 . x7) x10 (λ x11 . Inj1 0)) (x2 (λ x11 . x11) 0 (λ x11 . x11))) (setsum 0 (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . x14) (setsum 0 0)))) 0 (x4 (Inj1 (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . Inj0 0) 0)) x5 x5 (x4 0 (x2 (λ x9 . x7) 0 (λ x9 . x7)) 0 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) 0 0 0 0) (Inj1 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . 0) 0 (λ x11 . 0))))) (setsum (setsum x7 (setsum x7 (x2 (λ x9 . 0) 0 (λ x9 . 0)))) (Inj1 (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . 0))))) (setsum 0 0) = Inj0 x5) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 x7 . x0 (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . setsum 0 (x2 (λ x14 . x2 (λ x15 . Inj1 0) x12 (λ x15 . x14)) x13 (λ x14 . 0))) (λ x9 x10 . setsum (x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . Inj0 (x13 (λ x14 . 0))) (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . Inj0 0) (Inj1 0)) (λ x11 : (ι → ι) → ι → ι . λ x12 . setsum (x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . 0) 0) 0)) 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x2 (λ x12 . x12) 0 (λ x12 . x2 (λ x13 . x13) (x2 (λ x13 . 0) 0 (λ x13 . 0)) (λ x13 . x0 (λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 x18 . 0) (λ x14 x15 . 0) 0 0 0 0))) (Inj1 (x5 (λ x9 : (ι → ι) → ι . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι → ι . λ x11 . 0)))) (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (x2 (λ x11 . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . 0)) (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0) (λ x11 . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . 0))) 0)) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x10) (Inj1 (x4 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . x11) (λ x9 : ι → ι . 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 . x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) (x2 (λ x11 . 0) 0 (λ x11 . x9 (λ x12 . 0) 0)))) 0 0 = x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) (setsum (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . x3 (λ x17 x18 . λ x19 : (ι → ι) → ι . 0) 0 (λ x17 : (ι → ι) → ι → ι . λ x18 . 0)) (λ x12 x13 . x13) (x2 (λ x12 . 0) 0 (λ x12 . 0)) x9 x10 (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0)) (x2 (λ x12 . x11 (λ x13 . 0)) 0 (λ x12 . 0))) (λ x12 : (ι → ι) → ι → ι . λ x13 . x2 (λ x14 . 0) (x1 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 x16 x17 . x0 (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 x22 . 0) (λ x18 x19 . 0) 0 0 0 0) (x11 (λ x14 . 0))) (λ x14 . Inj0 (x11 (λ x15 . 0))))) (x5 (λ x9 : (ι → ι) → ι . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . x7)) ⟶ False (proof)
Theorem 63aac.. : ∀ x0 : (ι → ι → ι → ι) → ι → ι → ι → ι . ∀ x1 : (ι → (ι → ι) → ι) → (ι → ι → ι → ι → ι) → ι . ∀ x2 : (ι → (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . x3 (λ x10 . x7) (x3 (λ x10 . x7) 0 (Inj0 0)) x5) 0 (setsum (Inj0 (setsum (x0 (λ x9 x10 x11 . 0) 0 0 0) x5)) (x1 (λ x9 . λ x10 : ι → ι . x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . setsum 0 0) (λ x11 . x11)) (λ x9 x10 x11 x12 . x2 (λ x13 . λ x14 : ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . x15 (λ x18 . 0)) (λ x13 . x13)))) = setsum (x0 (λ x9 x10 x11 . 0) x6 0 (setsum 0 (Inj0 (Inj1 0)))) x7) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x7 . x3 (λ x9 . x6 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x2 (λ x12 . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . x10 (λ x13 . x1 (λ x14 . λ x15 : ι → ι . 0) (λ x14 x15 x16 x17 . 0))))) (setsum (setsum 0 0) (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 . setsum 0 0)) (x3 (λ x9 . x9) x7 (Inj1 0)) (λ x9 . 0))) (x3 (λ x9 . x6 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x3 (λ x12 . Inj0 0) (x11 0) (x2 (λ x12 . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . 0)))) (x6 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum 0 (x0 (λ x11 x12 x13 . 0) 0 0 0))) (setsum (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 . x9 (λ x11 . 0) 0) (setsum 0 0) (λ x9 . x1 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 x12 x13 . 0))) (Inj0 0))) = Inj0 (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x2 (λ x14 . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . x11 (λ x15 . x12 0))) (λ x9 . 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . Inj1 (Inj1 0)) (λ x9 . x5) = Inj0 (x3 Inj1 (setsum (setsum (x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . 0)) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . 0))) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x13) (λ x9 . x1 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 x12 x13 . 0)))) (x3 (λ x9 . x2 (λ x10 . λ x11 : ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 . x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 . 0))) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x12 0) (λ x9 . x9)) (setsum (x0 (λ x9 x10 x11 . 0) 0 0 0) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . 0)))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . Inj0 (x11 (λ x14 . Inj0 (x0 (λ x15 x16 x17 . 0) 0 0 0)))) (λ x9 . x7) = Inj1 (setsum 0 (setsum x7 x6))) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → ι → ι → ι . ∀ x7 : (ι → ι → ι) → ι → ι . x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . x9) = setsum (Inj0 0) (x1 (λ x9 . λ x10 : ι → ι . x3 (λ x11 . x1 (λ x12 . λ x13 : ι → ι . x2 (λ x14 . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . 0)) (λ x12 x13 x14 x15 . x13)) (setsum (setsum 0 0) (x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 . 0))) 0) (λ x9 x10 x11 x12 . Inj0 (x0 (λ x13 x14 x15 . x12) (setsum 0 0) 0 (x3 (λ x13 . 0) 0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι → ι . x1 (λ x9 . λ x10 : ι → ι . setsum 0 0) (λ x9 x10 x11 x12 . x12) = x6 (setsum (x5 (λ x9 . 0) (setsum 0 (Inj1 0)) (λ x9 . x9)) 0) (λ x9 : ι → ι . λ x10 . x1 (λ x11 . λ x12 : ι → ι . x11) (λ x11 x12 x13 x14 . x3 (λ x15 . x2 (λ x16 . λ x17 : ι → ι . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . λ x20 . x18 (λ x21 . 0)) (λ x16 . Inj0 0)) x11 (setsum x11 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x0 (λ x9 x10 x11 . x9) (x6 (x0 (λ x9 x10 x11 . setsum x11 x11) 0 0 (x4 (λ x9 . λ x10 : ι → ι . λ x11 . x11)))) (x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . setsum x10 (x0 (λ x13 x14 x15 . x14) x10 x11 0))) (x7 (λ x9 : (ι → ι) → ι → ι . 0)) = setsum (x7 (λ x9 : (ι → ι) → ι → ι . 0)) (setsum (Inj0 0) 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι) → ι . x0 (λ x9 x10 x11 . setsum (x3 (λ x12 . 0) (x3 (λ x12 . Inj1 0) x9 (x3 (λ x12 . 0) 0 0)) (x3 (λ x12 . 0) (setsum 0 0) x9)) 0) (x0 (λ x9 x10 x11 . x11) 0 (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . 0)) (x1 (λ x9 . λ x10 : ι → ι . Inj0 (setsum 0 0)) (λ x9 x10 x11 x12 . setsum x10 (setsum 0 0)))) (x1 (λ x9 . λ x10 : ι → ι . x0 (λ x11 x12 x13 . 0) (Inj0 0) (x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x12 0) (λ x11 . x11)) (Inj0 0)) (λ x9 x10 x11 x12 . x3 (λ x13 . x1 (λ x14 . λ x15 : ι → ι . x2 (λ x16 . λ x17 : ι → ι . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . λ x20 . 0) (λ x16 . 0)) (λ x14 x15 x16 x17 . x3 (λ x18 . 0) 0 0)) x10 x10)) 0 = setsum (setsum x5 0) 0) ⟶ False (proof)
Theorem e3c3e.. : ∀ x0 : ((ι → (ι → ι) → ι) → ι) → ι → ι → ι . ∀ x1 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι) → ((ι → ι → ι) → (ι → ι) → ι) → ι → ι → ι) → ι → ((ι → ι → ι) → ι) → ι . ∀ x2 : (ι → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι) → ι → ((ι → ι) → ι) → ι . ∀ x3 : ((((ι → ι) → (ι → ι) → ι) → ι) → ι → (ι → ι → ι) → ι) → (ι → ι → (ι → ι) → ι) → (((ι → ι) → ι → ι) → ι) → ι . (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . x9 (λ x12 x13 : ι → ι . x12 (x11 (x0 (λ x14 : ι → (ι → ι) → ι . 0) 0 0) 0))) (λ x9 x10 . λ x11 : ι → ι . 0) (λ x9 : (ι → ι) → ι → ι . 0) = x5) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x6 x7 . x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . x1 (λ x12 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 x15 . x13 (λ x16 x17 . x16) (λ x16 . x16)) (setsum (x9 (λ x12 x13 : ι → ι . setsum 0 0)) 0) (λ x12 : ι → ι → ι . x9 (λ x13 x14 : ι → ι . Inj1 (x0 (λ x15 : ι → (ι → ι) → ι . 0) 0 0)))) (λ x9 x10 . λ x11 : ι → ι . x2 (λ x12 . λ x13 x14 : (ι → ι) → ι → ι . Inj1 0) (x3 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . 0) (λ x12 x13 . λ x14 : ι → ι . 0) (λ x12 : (ι → ι) → ι → ι . x2 (λ x13 . λ x14 x15 : (ι → ι) → ι → ι . x2 (λ x16 . λ x17 x18 : (ι → ι) → ι → ι . 0) 0 (λ x16 : ι → ι . 0)) (x12 (λ x13 . 0) 0) (λ x13 : ι → ι . 0))) (λ x12 : ι → ι . 0)) (λ x9 : (ι → ι) → ι → ι . setsum (Inj1 x6) (Inj1 (setsum (x0 (λ x10 : ι → (ι → ι) → ι . 0) 0 0) 0))) = Inj0 x6) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι) → ι . ∀ x6 x7 : ι → ι . x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . x3 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . x13) (λ x12 x13 . λ x14 : ι → ι . 0) (λ x12 : (ι → ι) → ι → ι . setsum (x0 (λ x13 : ι → (ι → ι) → ι . 0) (x11 (λ x13 . 0) 0) (x11 (λ x13 . 0) 0)) 0)) (x0 (λ x9 : ι → (ι → ι) → ι . x7 0) (setsum 0 0) (Inj1 0)) (λ x9 : ι → ι . setsum (x7 (Inj0 (x5 (λ x10 : ι → ι . λ x11 . 0)))) (Inj0 (x3 (λ x10 : ((ι → ι) → (ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι → ι . setsum 0 0) (λ x10 x11 . λ x12 : ι → ι . setsum 0 0) (λ x10 : (ι → ι) → ι → ι . Inj1 0)))) = setsum (x5 (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . x11) (λ x11 : (ι → ι) → ι → ι . x9 (x0 (λ x12 : ι → (ι → ι) → ι . 0) 0 0)))) (setsum (x0 (λ x9 : ι → (ι → ι) → ι . x9 (x0 (λ x10 : ι → (ι → ι) → ι . 0) 0 0) (λ x10 . x3 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . 0))) (Inj0 (x0 (λ x9 : ι → (ι → ι) → ι . 0) 0 0)) (x7 (setsum 0 0))) (setsum (x0 (λ x9 : ι → (ι → ι) → ι . setsum 0 0) (Inj0 0) (x7 0)) (setsum (x5 (λ x9 : ι → ι . λ x10 . 0)) 0)))) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . x2 (λ x12 . λ x13 x14 : (ι → ι) → ι → ι . x12) (setsum 0 (setsum (setsum 0 0) 0)) (λ x12 : ι → ι . Inj0 (x12 0))) (x4 (λ x9 . x3 (λ x10 : ((ι → ι) → (ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι → ι . x10 (λ x13 x14 : ι → ι . x11)) (λ x10 x11 . λ x12 : ι → ι . x0 (λ x13 : ι → (ι → ι) → ι . 0) x10 0) (λ x10 : (ι → ι) → ι → ι . x9)) 0) (λ x9 : ι → ι . Inj0 (x0 (λ x10 : ι → (ι → ι) → ι . x3 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . x2 (λ x14 . λ x15 x16 : (ι → ι) → ι → ι . 0) 0 (λ x14 : ι → ι . 0)) (λ x11 : (ι → ι) → ι → ι . x7 (λ x12 . 0))) (setsum 0 (setsum 0 0)) 0)) = x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . x0 (λ x12 : ι → (ι → ι) → ι . x2 (λ x13 . λ x14 x15 : (ι → ι) → ι → ι . x15 (λ x16 . 0) (x3 (λ x16 : ((ι → ι) → (ι → ι) → ι) → ι . λ x17 . λ x18 : ι → ι → ι . 0) (λ x16 x17 . λ x18 : ι → ι . 0) (λ x16 : (ι → ι) → ι → ι . 0))) x9 (λ x13 : ι → ι . x1 (λ x14 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x15 : (ι → ι → ι) → (ι → ι) → ι . λ x16 x17 . 0) 0 (λ x14 : ι → ι → ι . x1 (λ x15 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x16 : (ι → ι → ι) → (ι → ι) → ι . λ x17 x18 . 0) 0 (λ x15 : ι → ι → ι . 0)))) (x0 (λ x12 : ι → (ι → ι) → ι . setsum (x11 (λ x13 . 0) 0) (Inj0 0)) (Inj1 (x1 (λ x12 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 x15 . 0) 0 (λ x12 : ι → ι → ι . 0))) (Inj1 0)) (x1 (λ x12 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 x15 . setsum (x12 (λ x16 x17 . 0) (λ x16 x17 . 0) 0) (Inj0 0)) (setsum x9 0) (λ x12 : ι → ι → ι . x1 (λ x13 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x14 : (ι → ι → ι) → (ι → ι) → ι . λ x15 x16 . setsum 0 0) 0 (λ x13 : ι → ι → ι . x2 (λ x14 . λ x15 x16 : (ι → ι) → ι → ι . 0) 0 (λ x14 : ι → ι . 0))))) (setsum (setsum (x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . 0) (λ x9 x10 . λ x11 : ι → ι . 0) (λ x9 : (ι → ι) → ι → ι . 0)) 0) (x7 (λ x9 . setsum x9 (x5 (λ x10 . λ x11 : ι → ι . 0))))) (λ x9 : ι → ι . setsum (x7 (λ x10 . 0)) (Inj0 (Inj0 (x2 (λ x10 . λ x11 x12 : (ι → ι) → ι → ι . 0) 0 (λ x10 : ι → ι . 0)))))) ⟶ (∀ x4 : ((ι → ι) → ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → (ι → ι) → ι . λ x11 x12 . x2 (λ x13 . λ x14 x15 : (ι → ι) → ι → ι . 0) (x9 (λ x13 x14 . x14) (λ x13 x14 . 0) (Inj0 (x1 (λ x13 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x14 : (ι → ι → ι) → (ι → ι) → ι . λ x15 x16 . 0) 0 (λ x13 : ι → ι → ι . 0)))) (λ x13 : ι → ι . x3 (λ x14 : ((ι → ι) → (ι → ι) → ι) → ι . λ x15 . λ x16 : ι → ι → ι . 0) (λ x14 x15 . λ x16 : ι → ι . setsum (Inj1 0) (setsum 0 0)) (λ x14 : (ι → ι) → ι → ι . Inj1 (x2 (λ x15 . λ x16 x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 : ι → ι . 0))))) (x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . setsum (Inj1 (x11 0 0)) 0) (λ x9 x10 . λ x11 : ι → ι . x1 (λ x12 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 x15 . x15) 0 (λ x12 : ι → ι → ι . x10)) (λ x9 : (ι → ι) → ι → ι . x1 (λ x10 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 x13 . x12) x6 (λ x10 : ι → ι → ι . setsum (x3 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . 0)) 0))) (λ x9 : ι → ι → ι . 0) = x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . Inj1 (setsum (x0 (λ x12 : ι → (ι → ι) → ι . x12 0 (λ x13 . 0)) 0 (x2 (λ x12 . λ x13 x14 : (ι → ι) → ι → ι . 0) 0 (λ x12 : ι → ι . 0))) (x3 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . Inj0 0) (λ x12 x13 . λ x14 : ι → ι . x11 (λ x15 . 0) 0) (λ x12 : (ι → ι) → ι → ι . x1 (λ x13 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x14 : (ι → ι → ι) → (ι → ι) → ι . λ x15 x16 . 0) 0 (λ x13 : ι → ι → ι . 0))))) (setsum (x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . Inj1 (setsum 0 0)) x7 (λ x9 : ι → ι . Inj0 (setsum 0 0))) (Inj0 (x5 (λ x9 : ι → ι → ι . λ x10 . Inj1 0) 0))) (λ x9 : ι → ι . x1 (λ x10 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 x13 . x13) (Inj0 0) (λ x10 : ι → ι → ι . x7))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . x1 (λ x9 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → (ι → ι) → ι . λ x11 x12 . x2 (λ x13 . λ x14 x15 : (ι → ι) → ι → ι . setsum (x14 (λ x16 . 0) (x14 (λ x16 . 0) 0)) (x15 (λ x16 . Inj0 0) (x1 (λ x16 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x17 : (ι → ι → ι) → (ι → ι) → ι . λ x18 x19 . 0) 0 (λ x16 : ι → ι → ι . 0)))) (x0 (λ x13 : ι → (ι → ι) → ι . 0) (setsum x11 (x10 (λ x13 x14 . 0) (λ x13 . 0))) (x1 (λ x13 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x14 : (ι → ι → ι) → (ι → ι) → ι . λ x15 x16 . 0) (x10 (λ x13 x14 . 0) (λ x13 . 0)) (λ x13 : ι → ι → ι . 0))) (λ x13 : ι → ι . x0 (λ x14 : ι → (ι → ι) → ι . setsum 0 (x0 (λ x15 : ι → (ι → ι) → ι . 0) 0 0)) (x1 (λ x14 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x15 : (ι → ι → ι) → (ι → ι) → ι . λ x16 x17 . Inj0 0) (Inj1 0) (λ x14 : ι → ι → ι . 0)) (setsum (x1 (λ x14 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x15 : (ι → ι → ι) → (ι → ι) → ι . λ x16 x17 . 0) 0 (λ x14 : ι → ι → ι . 0)) 0))) 0 (λ x9 : ι → ι → ι . 0) = setsum (x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . x0 (λ x12 : ι → (ι → ι) → ι . Inj0 (Inj1 0)) (setsum (setsum 0 0) (setsum 0 0)) (x2 (λ x12 . λ x13 x14 : (ι → ι) → ι → ι . x3 (λ x15 : ((ι → ι) → (ι → ι) → ι) → ι . λ x16 . λ x17 : ι → ι → ι . 0) (λ x15 x16 . λ x17 : ι → ι . 0) (λ x15 : (ι → ι) → ι → ι . 0)) (x7 (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0)) (λ x12 : ι → ι . 0))) (x6 0) (λ x9 : ι → ι . setsum (x2 (λ x10 . λ x11 x12 : (ι → ι) → ι → ι . setsum 0 0) 0 (λ x10 : ι → ι . x3 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . 0))) (x2 (λ x10 . λ x11 x12 : (ι → ι) → ι → ι . x10) (setsum 0 0) (λ x10 : ι → ι . x9 0)))) 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : ι → (ι → ι) → ι . 0) (x5 (λ x9 x10 . setsum x9 0) 0) (Inj1 (setsum (x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . x2 (λ x12 . λ x13 x14 : (ι → ι) → ι → ι . 0) 0 (λ x12 : ι → ι . 0)) (λ x9 x10 . λ x11 : ι → ι . x9) (λ x9 : (ι → ι) → ι → ι . x9 (λ x10 . 0) 0)) (Inj1 (x0 (λ x9 : ι → (ι → ι) → ι . 0) 0 0)))) = x5 (λ x9 x10 . x6 (x1 (λ x11 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x12 : (ι → ι → ι) → (ι → ι) → ι . λ x13 x14 . x1 (λ x15 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x16 : (ι → ι → ι) → (ι → ι) → ι . λ x17 x18 . x2 (λ x19 . λ x20 x21 : (ι → ι) → ι → ι . 0) 0 (λ x19 : ι → ι . 0)) (Inj0 0) (λ x15 : ι → ι → ι . x13)) (x1 (λ x11 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x12 : (ι → ι → ι) → (ι → ι) → ι . λ x13 x14 . x2 (λ x15 . λ x16 x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 : ι → ι . 0)) (Inj0 0) (λ x11 : ι → ι → ι . x3 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . 0) (λ x12 x13 . λ x14 : ι → ι . 0) (λ x12 : (ι → ι) → ι → ι . 0))) (λ x11 : ι → ι → ι . x9))) (x4 0 (Inj1 0))) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x0 (λ x9 : ι → (ι → ι) → ι . x2 (λ x10 . λ x11 x12 : (ι → ι) → ι → ι . x3 (λ x13 : ((ι → ι) → (ι → ι) → ι) → ι . λ x14 . λ x15 : ι → ι → ι . Inj1 (x2 (λ x16 . λ x17 x18 : (ι → ι) → ι → ι . 0) 0 (λ x16 : ι → ι . 0))) (λ x13 x14 . λ x15 : ι → ι . x1 (λ x16 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x17 : (ι → ι → ι) → (ι → ι) → ι . λ x18 x19 . x18) 0 (λ x16 : ι → ι → ι . x2 (λ x17 . λ x18 x19 : (ι → ι) → ι → ι . 0) 0 (λ x17 : ι → ι . 0))) (λ x13 : (ι → ι) → ι → ι . 0)) (x6 0) (λ x10 : ι → ι . x10 0)) (x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . x9 (λ x12 x13 : ι → ι . 0)) (λ x9 x10 . λ x11 : ι → ι . x9) (λ x9 : (ι → ι) → ι → ι . x6 0)) 0 = x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . setsum (setsum x9 (x3 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . x2 (λ x15 . λ x16 x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 : ι → ι . 0)) (λ x12 x13 . λ x14 : ι → ι . x11 (λ x15 . 0) 0) (λ x12 : (ι → ι) → ι → ι . setsum 0 0))) 0) (x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . setsum 0 0) (x6 0) (λ x9 : ι → ι . setsum (x0 (λ x10 : ι → (ι → ι) → ι . x2 (λ x11 . λ x12 x13 : (ι → ι) → ι → ι . 0) 0 (λ x11 : ι → ι . 0)) 0 0) (x6 (x6 0)))) (λ x9 : ι → ι . Inj1 (x2 (λ x10 . λ x11 x12 : (ι → ι) → ι → ι . x10) (x0 (λ x10 : ι → (ι → ι) → ι . setsum 0 0) 0 (Inj0 0)) (λ x10 : ι → ι . setsum (setsum 0 0) (x6 0))))) ⟶ False (proof)
Theorem dfd17.. : ∀ x0 : (((((ι → ι) → ι → ι) → ι) → (ι → ι) → ι) → ι → ι → (ι → ι) → ι → ι) → ((ι → (ι → ι) → ι) → ι → ι) → ι . ∀ x1 : ((((ι → ι) → ι → ι → ι) → ι → ι) → ι → ι) → (((ι → ι) → ι) → ι) → (((ι → ι) → ι) → ι) → ι . ∀ x2 : (ι → ι) → ((ι → ι → ι) → ι) → (ι → ι) → (ι → ι) → ι . ∀ x3 : (ι → ι → ι) → ((ι → (ι → ι) → ι → ι) → ι) → (ι → ι) → (ι → ι) → ι . (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x9 x10 . x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . Inj0 (x11 (λ x13 : ι → ι . λ x14 x15 . x1 (λ x16 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x17 . 0) (λ x16 : (ι → ι) → ι . 0) (λ x16 : (ι → ι) → ι . 0)) (x2 (λ x13 . 0) (λ x13 : ι → ι → ι . 0) (λ x13 . 0) (λ x13 . 0)))) (λ x11 : (ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . x2 (λ x12 . 0) (λ x12 : ι → ι → ι . x3 (λ x13 x14 . x14) (λ x13 : ι → (ι → ι) → ι → ι . x3 (λ x14 x15 . 0) (λ x14 : ι → (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . 0)) (λ x13 . setsum 0 0) (λ x13 . setsum 0 0)) (λ x12 . x3 (λ x13 x14 . x14) (λ x13 : ι → (ι → ι) → ι → ι . x3 (λ x14 x15 . 0) (λ x14 : ι → (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . 0)) (λ x13 . 0) (λ x13 . Inj0 0)) (λ x12 . 0))) (λ x9 : ι → (ι → ι) → ι → ι . Inj0 (x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . Inj0 (setsum 0 0)) (λ x10 : (ι → ι) → ι . x9 (x3 (λ x11 x12 . 0) (λ x11 : ι → (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 . 0)) (λ x11 . 0) x7) (λ x10 : (ι → ι) → ι . x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . x1 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x14 . 0) (λ x13 : (ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι . 0)) (λ x11 : (ι → ι) → ι . x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι . 0)) (λ x11 : (ι → ι) → ι . x7)))) (λ x9 . 0) (λ x9 . setsum 0 x7) = x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . setsum (x0 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . x1 (λ x16 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x17 . Inj0 0) (λ x16 : (ι → ι) → ι . x0 (λ x17 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x18 x19 . λ x20 : ι → ι . λ x21 . 0) (λ x17 : ι → (ι → ι) → ι . λ x18 . 0)) (λ x16 : (ι → ι) → ι . x0 (λ x17 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x18 x19 . λ x20 : ι → ι . λ x21 . 0) (λ x17 : ι → (ι → ι) → ι . λ x18 . 0))) (λ x11 : ι → (ι → ι) → ι . λ x12 . x10)) (x0 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 : ι → (ι → ι) → ι . λ x12 . x10))) (λ x9 : (ι → ι) → ι . Inj1 0) (λ x9 : (ι → ι) → ι . Inj0 (setsum (x2 (λ x10 . x3 (λ x11 x12 . 0) (λ x11 : ι → (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 . 0)) (λ x10 : ι → ι → ι . 0) (λ x10 . x6) (λ x10 . setsum 0 0)) x6))) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι → ι . x3 (λ x9 x10 . x3 (λ x11 x12 . x0 (λ x13 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . x2 (λ x18 . 0) (λ x18 : ι → ι → ι . x0 (λ x19 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x20 x21 . λ x22 : ι → ι . λ x23 . 0) (λ x19 : ι → (ι → ι) → ι . λ x20 . 0)) (λ x18 . x0 (λ x19 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x20 x21 . λ x22 : ι → ι . λ x23 . 0) (λ x19 : ι → (ι → ι) → ι . λ x20 . 0)) (λ x18 . setsum 0 0)) (λ x13 : ι → (ι → ι) → ι . λ x14 . 0)) (λ x11 : ι → (ι → ι) → ι → ι . x0 (λ x12 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . x1 (λ x17 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x18 . x18) (λ x17 : (ι → ι) → ι . Inj0 0) (λ x17 : (ι → ι) → ι . x0 (λ x18 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x19 x20 . λ x21 : ι → ι . λ x22 . 0) (λ x18 : ι → (ι → ι) → ι . λ x19 . 0))) (λ x12 : ι → (ι → ι) → ι . λ x13 . setsum (x0 (λ x14 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 : ι → (ι → ι) → ι . λ x15 . 0)) 0)) (λ x11 . x11) (λ x11 . 0)) (λ x9 : ι → (ι → ι) → ι → ι . x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . Inj0 (x13 0)) (λ x10 : ι → (ι → ι) → ι . λ x11 . x3 (λ x12 x13 . x12) (λ x12 : ι → (ι → ι) → ι → ι . 0) (λ x12 . Inj1 x11) (λ x12 . Inj1 (x2 (λ x13 . 0) (λ x13 : ι → ι → ι . 0) (λ x13 . 0) (λ x13 . 0))))) (λ x9 . setsum x6 (setsum 0 (x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x16 . 0) (λ x15 : (ι → ι) → ι . 0) (λ x15 : (ι → ι) → ι . 0)) (λ x10 : ι → (ι → ι) → ι . λ x11 . setsum 0 0)))) (λ x9 . Inj1 0) = setsum 0 x6) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 . x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . setsum (Inj0 x14) x14) (λ x10 : ι → (ι → ι) → ι . λ x11 . x9)) (λ x9 : ι → ι → ι . 0) (λ x9 . Inj0 (x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . Inj1 (Inj1 0)))) (λ x9 . x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . x2 (λ x15 . x1 (λ x16 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x17 . x3 (λ x18 x19 . 0) (λ x18 : ι → (ι → ι) → ι → ι . 0) (λ x18 . 0) (λ x18 . 0)) (λ x16 : (ι → ι) → ι . 0) (λ x16 : (ι → ι) → ι . x16 (λ x17 . 0))) (λ x15 : ι → ι → ι . x2 (λ x16 . 0) (λ x16 : ι → ι → ι . x13 0) (λ x16 . x14) (λ x16 . x15 0 0)) (λ x15 . x15) (λ x15 . x2 (λ x16 . 0) (λ x16 : ι → ι → ι . x3 (λ x17 x18 . 0) (λ x17 : ι → (ι → ι) → ι → ι . 0) (λ x17 . 0) (λ x17 . 0)) (λ x16 . 0) (λ x16 . 0))) (λ x10 : ι → (ι → ι) → ι . λ x11 . x2 (λ x12 . 0) (λ x12 : ι → ι → ι . setsum (x12 0 0) (x10 0 (λ x13 . 0))) (λ x12 . x3 (λ x13 x14 . x13) (λ x13 : ι → (ι → ι) → ι → ι . 0) (λ x13 . x10 0 (λ x14 . 0)) (λ x13 . x10 0 (λ x14 . 0))) (λ x12 . 0))) = setsum x4 0) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 . x5 (x3 (λ x10 x11 . Inj0 0) (λ x10 : ι → (ι → ι) → ι → ι . 0) (λ x10 . x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . Inj0 0) (λ x11 : (ι → ι) → ι . Inj0 0) (λ x11 : (ι → ι) → ι . x0 (λ x12 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 : ι → (ι → ι) → ι . λ x13 . 0))) (λ x10 . 0)) (λ x10 : ι → ι . λ x11 . 0)) (λ x9 : ι → ι → ι . setsum (x9 (x6 0) (x6 (x9 0 0))) (x5 x7 (λ x10 : ι → ι . λ x11 . Inj1 (x9 0 0)))) (λ x9 . x6 (setsum (x3 (λ x10 x11 . 0) (λ x10 : ι → (ι → ι) → ι → ι . x7) (λ x10 . x3 (λ x11 x12 . 0) (λ x11 : ι → (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 . 0)) (λ x10 . x2 (λ x11 . 0) (λ x11 : ι → ι → ι . 0) (λ x11 . 0) (λ x11 . 0))) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . x3 (λ x12 x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . 0))))) (λ x9 . 0) = setsum (x2 (λ x9 . x7) (λ x9 : ι → ι → ι . x7) (λ x9 . x5 x9 (λ x10 : ι → ι . λ x11 . Inj0 0)) (λ x9 . 0)) (setsum (x5 (x0 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x9 : ι → (ι → ι) → ι . λ x10 . x7)) (λ x9 : ι → ι . λ x10 . x3 (λ x11 x12 . x9 0) (λ x11 : ι → (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 . Inj1 0))) (x0 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . x11) (λ x9 : ι → (ι → ι) → ι . λ x10 . x10)))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → ι → ι → ι . ∀ x6 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . Inj1 (x0 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 : ι → (ι → ι) → ι . λ x12 . Inj0 0))) (λ x9 : (ι → ι) → ι . x7 (λ x10 . 0) (λ x10 : ι → ι . x7 (λ x11 . x9 (λ x12 . Inj1 0)) (λ x11 : ι → ι . λ x12 . 0) (setsum (x7 (λ x11 . 0) (λ x11 : ι → ι . λ x12 . 0) 0 0) (x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . 0) (λ x11 : (ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . 0)))) (x2 (λ x10 . x6 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . Inj0 0) (x9 (λ x11 . 0))) (λ x10 : ι → ι → ι . x3 (λ x11 x12 . 0) (λ x11 : ι → (ι → ι) → ι → ι . x0 (λ x12 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 : ι → (ι → ι) → ι . λ x13 . 0)) (λ x11 . x11) (λ x11 . x7 (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0) 0 0)) (λ x10 . x7 (λ x11 . x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι . 0)) (λ x11 : ι → ι . λ x12 . 0) (Inj1 0) (x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . 0) (λ x11 : (ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . 0))) (λ x10 . x0 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . setsum 0 0) (λ x11 : ι → (ι → ι) → ι . λ x12 . setsum 0 0))) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . setsum (x7 (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0) 0 0) (x2 (λ x12 . 0) (λ x12 : ι → ι → ι . 0) (λ x12 . 0) (λ x12 . 0))))) (λ x9 : (ι → ι) → ι . x9 (λ x10 . x6 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . setsum (x3 (λ x14 x15 . 0) (λ x14 : ι → (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . 0)) 0) 0)) = Inj1 x4) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . x6) (λ x9 : (ι → ι) → ι . x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . setsum (x10 (λ x12 : ι → ι . λ x13 x14 . x2 (λ x15 . 0) (λ x15 : ι → ι → ι . 0) (λ x15 . 0) (λ x15 . 0)) x7) (Inj0 x7)) (λ x10 : (ι → ι) → ι . x3 (λ x11 x12 . Inj0 (x3 (λ x13 x14 . 0) (λ x13 : ι → (ι → ι) → ι → ι . 0) (λ x13 . 0) (λ x13 . 0))) (λ x11 : ι → (ι → ι) → ι → ι . Inj0 (Inj1 0)) (λ x11 . Inj0 (x2 (λ x12 . 0) (λ x12 : ι → ι → ι . 0) (λ x12 . 0) (λ x12 . 0))) (λ x11 . 0)) (λ x10 : (ι → ι) → ι . 0)) (λ x9 : (ι → ι) → ι . 0) = Inj0 x6) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . ∀ x5 x6 x7 . x0 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj1 (setsum (Inj0 (Inj0 0)) x13)) (λ x9 : ι → (ι → ι) → ι . λ x10 . 0) = x7) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → (ι → ι → ι) → ι . x0 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x9 : ι → (ι → ι) → ι . λ x10 . setsum (x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . x12) (λ x11 : (ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . setsum 0 (x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι . 0)))) 0) = x4 (λ x9 x10 . x7 (x0 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . x14 0) (λ x11 : ι → (ι → ι) → ι . Inj1)) (λ x11 x12 . 0))) ⟶ False (proof)
Theorem 5b7cf.. : ∀ x0 : ((ι → (ι → ι) → (ι → ι) → ι → ι) → ι → ι) → ((((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι → ι → ι) → (((ι → ι) → ι → ι) → ι) → ι . ∀ x1 : ((ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x2 : (((((ι → ι) → ι) → ι → ι → ι) → ι) → ι → ((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → (ι → ι → ι) → ι → ι → ι) → (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x3 : ((ι → ι) → ι) → (ι → ι) → ι . (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x3 (λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . x10 (λ x13 : ι → ι . λ x14 . x12) (λ x13 . Inj0 0) 0) (λ x10 : (ι → ι) → ι → ι . x3 (λ x11 : ι → ι . x9 (Inj0 0)) (λ x11 . x11))) (λ x9 . x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . x2 (λ x13 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . Inj0 (x1 (λ x18 : ι → ι . 0) (λ x18 : ι → ι . 0))) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . 0) (λ x13 : (ι → ι) → ι → ι . x1 (λ x14 : ι → ι . Inj0 0) (λ x14 : ι → ι . x3 (λ x15 : ι → ι . 0) (λ x15 . 0))) (λ x13 x14 . x14)) (λ x10 : (ι → ι) → ι → ι . 0)) = x0 (λ x9 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x10 . Inj1 (x2 (λ x11 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x0 (λ x16 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x17 . 0) (λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x17 x18 . 0) (λ x16 : (ι → ι) → ι → ι . Inj1 0)) (λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . setsum x14 0) (λ x11 : (ι → ι) → ι → ι . x7) (λ x11 x12 . x9 (x1 (λ x13 : ι → ι . 0) (λ x13 : ι → ι . 0)) (λ x13 . x1 (λ x14 : ι → ι . 0) (λ x14 : ι → ι . 0)) (λ x13 . 0) (x0 (λ x13 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x14 . 0) (λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x14 x15 . 0) (λ x13 : (ι → ι) → ι → ι . 0))))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 x11 . setsum 0 (x3 (λ x12 : ι → ι . setsum x11 0) (λ x12 . x0 (λ x13 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x14 . setsum 0 0) (λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x14 x15 . x12) (λ x13 : (ι → ι) → ι → ι . x2 (λ x14 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . 0) (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 x15 . 0))))) (λ x9 : (ι → ι) → ι → ι . Inj1 x6)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 : ι → ι . x6) (λ x9 . x5 0) = x6) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι . ∀ x7 : ι → ι . x2 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x13) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . 0) (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 x10 . x9) = x6 (λ x9 : ι → ι . λ x10 x11 . Inj0 (setsum (Inj0 (x7 0)) x11))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x2 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . 0) (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) = x6 (λ x9 . x3 (λ x10 : ι → ι . 0) (λ x10 . setsum (Inj0 x7) (x0 (λ x11 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x12 . x2 (λ x13 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . 0) (λ x13 : (ι → ι) → ι → ι . 0) (λ x13 x14 . 0)) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 x13 . x1 (λ x14 : ι → ι . 0) (λ x14 : ι → ι . 0)) (λ x11 : (ι → ι) → ι → ι . x10))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 : ι → ι . x1 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . x9 (setsum (Inj0 (x6 0)) (x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . setsum 0 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . x10 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) 0) (λ x10 : (ι → ι) → ι → ι . 0)))) = Inj0 (setsum (x3 (λ x9 : ι → ι . Inj1 (x3 (λ x10 : ι → ι . 0) (λ x10 . 0))) (λ x9 . x5 (Inj1 0) (x1 (λ x10 : ι → ι . 0) (λ x10 : ι → ι . 0)) (λ x10 . x1 (λ x11 : ι → ι . 0) (λ x11 : ι → ι . 0)) (Inj0 0))) (Inj1 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → (ι → ι) → (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι . x1 (λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . x2 (λ x12 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . λ x13 : ι → ι → ι . λ x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . x0 (λ x13 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x14 . 0) (λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x14 x15 . x1 (λ x16 : ι → ι . 0) (λ x16 : ι → ι . 0)) (λ x13 : (ι → ι) → ι → ι . x11)) (λ x12 x13 . x3 (λ x14 : ι → ι . 0) (λ x14 . setsum 0 0))) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . x11) (λ x10 : (ι → ι) → ι → ι . x6 (x0 (λ x11 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x12 . x11 0 (λ x13 . 0) (λ x13 . 0) 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 x13 . x2 (λ x14 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . 0) (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 x15 . 0)) (λ x11 : (ι → ι) → ι → ι . setsum 0 0)) (λ x11 . 0) (λ x11 . setsum (x3 (λ x12 : ι → ι . 0) (λ x12 . 0)) (x10 (λ x12 . 0) 0)))) (λ x9 : ι → ι . 0) = Inj1 (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x3 (λ x12 : ι → ι . x0 (λ x13 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x14 . setsum 0 0) (λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x14 x15 . x1 (λ x16 : ι → ι . 0) (λ x16 : ι → ι . 0)) (λ x13 : (ι → ι) → ι → ι . x3 (λ x14 : ι → ι . 0) (λ x14 . 0))) (λ x12 . Inj0 0)) (λ x9 . x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . x11) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . 0) (λ x10 : (ι → ι) → ι → ι . x0 (λ x11 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x12 . Inj0 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 x13 . 0) (λ x11 : (ι → ι) → ι → ι . x9))) (λ x9 . setsum (x2 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x11) (λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . 0) (λ x10 : (ι → ι) → ι → ι . x1 (λ x11 : ι → ι . 0) (λ x11 : ι → ι . 0)) (λ x10 x11 . x10)) (setsum 0 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x10 . x6) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 x11 . x9 (λ x12 : ι → ι . λ x13 . x2 (λ x14 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . x1 (λ x18 : ι → ι . 0) (λ x18 : ι → ι . x18 0)) (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 x15 . 0)) (setsum x10) (setsum (Inj1 0) (setsum (setsum 0 0) (x3 (λ x12 : ι → ι . 0) (λ x12 . 0))))) (λ x9 : (ι → ι) → ι → ι . 0) = setsum 0 (setsum (Inj0 (x0 (λ x9 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum 0 0) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 x11 . 0) (λ x9 : (ι → ι) → ι → ι . x9 (λ x10 . 0) 0))) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι → ι . x0 (λ x9 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x10 . x2 (λ x11 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . Inj1 (x2 (λ x16 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x17 . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . λ x20 . x20) (λ x16 . λ x17 : ι → ι → ι . λ x18 x19 . x3 (λ x20 : ι → ι . 0) (λ x20 . 0)) (λ x16 : (ι → ι) → ι → ι . setsum 0 0) (λ x16 x17 . x14 0))) (λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . 0) (λ x11 : (ι → ι) → ι → ι . setsum 0 (x9 (setsum 0 0) (λ x12 . 0) (λ x12 . x9 0 (λ x13 . 0) (λ x13 . 0) 0) (setsum 0 0))) (λ x11 x12 . x12)) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 x11 . 0) (λ x9 : (ι → ι) → ι → ι . 0) = setsum (x0 (λ x9 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum 0 (x1 (λ x11 : ι → ι . x7 (λ x12 : (ι → ι) → ι . 0) 0 (λ x12 . 0) 0) (λ x11 : ι → ι . x10))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 x11 . x10) (λ x9 : (ι → ι) → ι → ι . setsum 0 (x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . x2 (λ x12 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . λ x13 : ι → ι → ι . λ x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 x13 . 0)) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . Inj0 0) (λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . 0) 0)))) 0) ⟶ False (proof)
Theorem 33063.. : ∀ x0 : (((ι → ι → ι → ι) → ι) → ι) → ι → ι . ∀ x1 : ((ι → ι) → ι) → (((ι → ι → ι) → ι → ι) → ι) → ι . ∀ x2 : (ι → ι) → (ι → (ι → ι → ι) → ι → ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι → ι . (∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x9 . Inj1 (x1 (λ x10 : ι → ι . x9) (λ x10 : (ι → ι → ι) → ι → ι . setsum 0 (x2 (λ x11 . 0) (λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . 0))))) x7 0 = setsum (x0 (λ x9 : (ι → ι → ι → ι) → ι . x2 (λ x10 . setsum 0 x7) (λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . x0 (λ x14 : (ι → ι → ι → ι) → ι . x3 (λ x15 . 0) 0 0) (setsum 0 0))) (setsum (Inj1 x6) x6)) 0) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x3 (λ x9 . setsum x9 x9) 0 (x2 (λ x9 . x2 (λ x10 . x7 (setsum 0 0) (x3 (λ x11 . 0) 0 0)) (λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . 0)) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj0 (setsum (Inj1 0) x9))) = x2 (λ x9 . x0 (λ x10 : (ι → ι → ι → ι) → ι . x0 (λ x11 : (ι → ι → ι → ι) → ι . 0) 0) 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . x10 (x1 (λ x13 : ι → ι . x10 0 0) (λ x13 : (ι → ι → ι) → ι → ι . 0)) 0)) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 x6 x7 : ι → ι . x2 (λ x9 . 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj1 (setsum (setsum (setsum 0 0) 0) (x10 (x2 (λ x13 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . 0)) 0))) = x7 (Inj1 (x1 (λ x9 : ι → ι . 0) (λ x9 : (ι → ι → ι) → ι → ι . x1 (λ x10 : ι → ι . x7 0) (λ x10 : (ι → ι → ι) → ι → ι . x0 (λ x11 : (ι → ι → ι → ι) → ι . 0) 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x2 (λ x9 . 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . x10 (x10 (setsum (setsum 0 0) (setsum 0 0)) (x2 (λ x13 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . x14 0 0))) 0) = setsum (x3 (λ x9 . x5 (Inj1 0) (λ x10 : ι → ι . x10 0)) (x2 (setsum (setsum 0 0)) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . 0)) (setsum (x3 (λ x9 . x9) (x0 (λ x9 : (ι → ι → ι → ι) → ι . 0) 0) (x2 (λ x9 . 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . 0))) 0)) (x6 (λ x9 . 0) (x6 (λ x9 . x6 (λ x10 . x3 (λ x11 . 0) 0 0) (x3 (λ x10 . 0) 0 0)) (x5 (x0 (λ x9 : (ι → ι → ι → ι) → ι . 0) 0) (λ x9 : ι → ι . setsum 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x7 . x1 (λ x9 : ι → ι . setsum (x9 (x6 (λ x10 . x0 (λ x11 : (ι → ι → ι → ι) → ι . 0) 0) (λ x10 x11 . x0 (λ x12 : (ι → ι → ι → ι) → ι . 0) 0) (λ x10 . 0))) (x6 (λ x10 . x9 0) (λ x10 x11 . 0) (λ x10 . x10))) (λ x9 : (ι → ι → ι) → ι → ι . x2 (λ x10 . x9 (λ x11 x12 . setsum 0 0) 0) (λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . Inj1 (x0 (λ x14 : (ι → ι → ι → ι) → ι . 0) (x11 0 0)))) = x2 (λ x9 . x5) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . x10 (x0 (λ x13 : (ι → ι → ι → ι) → ι . Inj1 (x2 (λ x14 . 0) (λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . 0))) x12) 0)) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : ι → ι . setsum 0 0) (λ x9 : (ι → ι → ι) → ι → ι . x5) = x5) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : (ι → ι → ι → ι) → ι . setsum x5 (Inj0 0)) x7 = x7) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 : (ι → ι → ι → ι) → ι . x7) x5 = x5) ⟶ False (proof)
Theorem 6fc01.. : ∀ x0 : (ι → ι → ((ι → ι) → ι) → ι) → ι → ι → ι . ∀ x1 : (ι → (ι → ι) → ι) → ι → ι . ∀ x2 : (((ι → ι) → (ι → ι → ι) → ι) → (ι → (ι → ι) → ι) → ι → ι) → (ι → ι) → ι . ∀ x3 : ((ι → (ι → ι → ι) → ι → ι) → ι) → ι → (ι → ι → ι → ι) → ι → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι) → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . x1 (λ x10 . λ x11 : ι → ι . setsum 0 x10) 0) 0 (λ x9 x10 x11 . 0) (x1 (λ x9 . λ x10 : ι → ι . x6) (setsum (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum 0 0) 0 (x5 0)) (setsum (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . 0)) (x5 0)))) = setsum 0 x6) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . setsum (x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . λ x14 : ι → (ι → ι) → ι . λ x15 . x3 (λ x16 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x16 x17 x18 . 0) 0) (λ x13 . x12 (λ x14 . 0))) (x3 (λ x10 : ι → (ι → ι → ι) → ι → ι . x7 0 (λ x11 x12 . 0)) (Inj0 0) (λ x10 x11 x12 . 0) 0) 0) (x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) (setsum (x6 0) (Inj1 0)) (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . x11 0 (λ x13 . 0)) (λ x10 . x1 (λ x11 . λ x12 : ι → ι . 0) 0)))) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . x10) (setsum (x7 0 (λ x12 x13 . 0)) (x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x12 x13 x14 . 0) 0)) (λ x12 x13 x14 . 0) x9) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) x4 (x7 (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . 0)) (λ x9 x10 . x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . 0) (λ x11 . 0)))) (setsum (setsum (setsum 0 0) 0) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x9) (setsum 0 0) (x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x9 x10 x11 . 0) 0)))) (λ x9 x10 x11 . 0) 0 = x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum 0 (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . x3 (λ x15 : ι → (ι → ι → ι) → ι → ι . x1 (λ x16 . λ x17 : ι → ι . 0) 0) 0 (λ x15 x16 x17 . x3 (λ x18 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x18 x19 x20 . 0) 0) 0) (λ x12 . x3 (λ x13 : ι → (ι → ι → ι) → ι → ι . x10) (Inj0 0) (λ x13 x14 x15 . setsum 0 0) 0))) (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . setsum 0 0)) (x6 (x1 (λ x9 . λ x10 : ι → ι . 0) (Inj1 (x1 (λ x9 . λ x10 : ι → ι . 0) 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . x11) (λ x9 . 0) = x4 (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj0 (x9 (λ x11 . setsum (x1 (λ x12 . λ x13 : ι → ι . 0) 0) (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . 0) (λ x12 . 0))) (x7 (λ x11 . λ x12 : ι → ι . λ x13 . 0)))) 0) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . x1 (λ x12 . λ x13 : ι → ι . setsum (Inj1 (setsum 0 0)) (x13 (setsum 0 0))) 0) (λ x9 . 0) = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 x7 : ι → ι . x1 (λ x9 . λ x10 : ι → ι . x1 (λ x11 . λ x12 : ι → ι . 0) (setsum (Inj0 0) (x6 (x7 0)))) 0 = Inj0 (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum (x1 (λ x12 . λ x13 : ι → ι . 0) 0) (x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . 0) (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . 0) (λ x12 . 0)) (λ x12 x13 x14 . x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι . λ x16 : ι → (ι → ι) → ι . λ x17 . 0) (λ x15 . 0)) (x7 0))) x5 (x4 (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . setsum 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x1 (λ x9 . λ x10 : ι → ι . Inj1 (x7 (x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . x13) (λ x11 . 0)))) (setsum 0 (x4 0)) = x7 (Inj1 (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . x7 0) (λ x9 . x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) (x3 (λ x10 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x10 x11 x12 . 0) 0) (x1 (λ x10 . λ x11 : ι → ι . 0) 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . Inj0 (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . Inj0 (x11 (λ x15 . 0))) (λ x12 . Inj0 (setsum 0 0)))) (x7 (λ x9 . x1 (λ x10 . λ x11 : ι → ι . Inj0 (setsum 0 0)) (setsum (setsum 0 0) (Inj1 0))) x5 (λ x9 . 0)) (x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . x1 (λ x10 . λ x11 : ι → ι . x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . x11 0) 0 (λ x12 x13 x14 . 0) (x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 0)) x5) 0 (λ x9 x10 x11 . 0) x4) = x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . x3 (λ x10 : ι → (ι → ι → ι) → ι → ι . Inj0 (x9 0 (λ x11 x12 . Inj0 0) 0)) (x7 (λ x10 . x9 x10 (λ x11 x12 . setsum 0 0) (x3 (λ x11 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x11 x12 x13 . 0) 0)) (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . x9 0 (λ x13 x14 . 0) 0) (λ x10 . x10)) (λ x10 . x6)) (λ x10 x11 x12 . x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . 0) (x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . x15 (λ x16 . 0)) x10 x12) x12) x6) x6 (λ x9 x10 x11 . setsum (Inj0 (setsum 0 x11)) (x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . 0) (Inj0 (x7 (λ x12 . 0) 0 (λ x12 . 0))) (λ x12 x13 . x3 (λ x14 : ι → (ι → ι → ι) → ι → ι . setsum 0 0) 0 (λ x14 x15 x16 . x15)) (setsum (Inj0 0) (x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 0)))) (x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . 0) (setsum 0 (Inj0 (x1 (λ x9 . λ x10 : ι → ι . 0) 0))) (λ x9 x10 x11 . x7 (λ x12 . x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . λ x14 : ι → (ι → ι) → ι . λ x15 . 0) (λ x13 . x13)) 0 (λ x12 . x11)) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum 0 (x1 (λ x12 . λ x13 : ι → ι . 0) 0)) 0 0))) ⟶ (∀ x4 : (ι → ι → ι) → ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι) → ι . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x1 (λ x12 . λ x13 : ι → ι . Inj1 (setsum (setsum 0 0) (Inj0 0))) x9) (x4 (λ x9 x10 . x9) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum (Inj1 0) x10) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 0) (setsum 0 0) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) 0 0)) (x1 (λ x9 . λ x10 : ι → ι . 0) (setsum 0 0))) 0) (setsum (setsum 0 0) 0) = setsum (x5 (λ x9 : (ι → ι) → ι → ι . x6)) (Inj1 (Inj0 (x4 (λ x9 x10 . Inj1 0) (Inj1 0) x6)))) ⟶ False (proof)
Theorem f7d60.. : ∀ x0 : (ι → ι) → ι → ι → ι → ι → ι . ∀ x1 : (((ι → (ι → ι) → ι → ι) → ι → ι → ι) → ι → ι → ι → ι) → ((((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι → ι) → ι . ∀ x2 : (((ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι) → ι) → ι → ι . ∀ x3 : ((ι → ι) → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 : ι → ι . 0) 0 (setsum (setsum (x0 (λ x9 . 0) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . 0)) (setsum 0 0) (x0 (λ x9 . 0) 0 0 0 0) (Inj1 0)) (Inj1 (x0 (λ x9 . 0) 0 0 0 0))) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . x11))) = x4) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x3 (λ x9 : ι → ι . x2 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x0 (λ x11 . 0) (x2 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0) (x2 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . Inj0 0) (x9 0)) (setsum (setsum 0 0) 0) (setsum 0 (x2 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0))) (x3 (λ x10 : ι → ι . 0) (Inj1 (x5 0 (λ x10 : ι → ι . 0))) 0)) (setsum (Inj0 (x0 (λ x9 . 0) x4 0 (x3 (λ x9 : ι → ι . 0) 0 0) x4)) 0) (Inj1 (x3 (λ x9 : ι → ι . 0) (x5 0 (λ x9 : ι → ι . x5 0 (λ x10 : ι → ι . 0))) 0)) = setsum (x6 0 x4) 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . Inj0 0) 0 = x7 (λ x9 : (ι → ι) → ι . x2 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x9 (λ x11 . x7 (λ x12 : (ι → ι) → ι . 0))) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x6) (x4 (x7 (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . x0 (λ x14 . 0) 0 0 0 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 . 0)))) = x6) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . setsum (setsum (setsum 0 (x0 (λ x13 . 0) 0 0 0 0)) (x0 (λ x13 . x3 (λ x14 : ι → ι . 0) 0 0) x10 (x2 (λ x13 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0) (Inj1 0) (x3 (λ x13 : ι → ι . 0) 0 0))) (Inj1 (Inj1 0))) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . x10) = setsum 0 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . Inj1 (x0 (λ x12 . Inj0 x11) (x2 (λ x12 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x2 (λ x13 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0) 0) (x2 (λ x12 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x14 x15 x16 . 0) (λ x13 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x14 x15 . 0)) x7) x7 (x9 (λ x12 : ι → ι . λ x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x15 x16 x17 . 0) (λ x14 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x15 x16 . 0)) (setsum 0 0) (x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x13 x14 x15 . 0) (λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x13 x14 . 0))))) = Inj1 (x3 (λ x9 : ι → ι . 0) 0 (setsum (setsum (x5 (λ x9 . 0)) 0) (x5 (λ x9 . x3 (λ x10 : ι → ι . 0) 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι → ι) → ι . x0 (λ x9 . 0) 0 (x0 (λ x9 . x9) (setsum (x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x0 (λ x10 . 0) 0 0 0 0) x5) 0) (x7 (λ x9 x10 . x7 (λ x11 x12 . x12))) (x3 (λ x9 : ι → ι . x5) x5 0) 0) x4 (setsum x6 (x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x3 (λ x10 : ι → ι . x3 (λ x11 : ι → ι . 0) 0 0) (Inj1 0) (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 . 0))) (Inj0 x5))) = x0 (λ x9 . Inj1 (Inj0 (Inj1 (setsum 0 0)))) (Inj1 x6) (x0 (λ x9 . 0) 0 0 0 (x0 (λ x9 . x0 (λ x10 . 0) (x7 (λ x10 x11 . 0)) (x7 (λ x10 x11 . 0)) (x0 (λ x10 . 0) 0 0 0 0) (Inj1 0)) 0 x4 x6 x4)) x6 (Inj0 x6)) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → ι → ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . x0 (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . x11) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 . Inj0 (x10 (λ x13 : ι → ι . λ x14 . Inj0 0) x9 0))) 0 (setsum (x3 (λ x9 : ι → ι . x2 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) (Inj1 0)) (x6 (x0 (λ x9 . 0) 0 0 0 0) (λ x9 . x7 (λ x10 : (ι → ι) → ι → ι . 0) 0 (λ x10 . 0)) (x3 (λ x9 : ι → ι . 0) 0 0) (setsum 0 0)) x4) (Inj1 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . 0)))) 0 (Inj1 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . x9 (λ x13 . λ x14 : ι → ι . λ x15 . Inj1 0) 0 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . 0))) = Inj1 0) ⟶ False (proof)
Theorem fa49b.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : ((ι → ((ι → ι) → ι → ι) → ι) → ι) → (ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x2 : (ι → ι) → (((ι → ι → ι) → ι) → ι) → ι → ((ι → ι) → ι) → ι . ∀ x3 : (ι → (ι → ι → ι) → ι) → (ι → ι → ι → ι) → (ι → ι → ι) → ι . (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 x6 x7 . x3 (λ x9 . λ x10 : ι → ι → ι . Inj0 (x3 (λ x11 . λ x12 : ι → ι → ι . x3 (λ x13 . λ x14 : ι → ι → ι . x1 (λ x15 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . λ x18 . 0) 0) (λ x13 x14 x15 . 0) (λ x13 x14 . x11)) (λ x11 x12 x13 . x11) (λ x11 x12 . 0))) (λ x9 x10 x11 . 0) (λ x9 x10 . 0) = x5) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 . λ x10 : ι → ι → ι . Inj0 (setsum x9 x9)) (λ x9 x10 x11 . 0) (λ x9 x10 . x0 (λ x11 . x0 (λ x12 . Inj0 0) (x3 (λ x12 . λ x13 : ι → ι → ι . 0) (λ x12 x13 x14 . 0) (λ x12 x13 . x2 (λ x14 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 (λ x14 : ι → ι . 0)))) (setsum x7 (Inj1 (setsum 0 0)))) = Inj1 x6) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x2 (λ x9 . x5 (λ x10 . x10) (x2 (λ x10 . Inj0 (x7 0 (λ x11 : ι → ι . 0))) (λ x10 : (ι → ι → ι) → ι . x6 (x6 0)) (x5 (λ x10 . x3 (λ x11 . λ x12 : ι → ι → ι . 0) (λ x11 x12 x13 . 0) (λ x11 x12 . 0)) (x7 0 (λ x10 : ι → ι . 0)) (λ x10 . Inj1 0) (x5 (λ x10 . 0) 0 (λ x10 . 0) 0)) (λ x10 : ι → ι . x10 x9)) (x0 (λ x10 . 0)) 0) (λ x9 : (ι → ι → ι) → ι . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . x0 (λ x11 . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) (Inj0 0)) (x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0) (λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . x0 (λ x15 . 0) 0) (x7 0 (λ x11 : ι → ι . 0)))) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) (setsum 0 (setsum (x3 (λ x10 . λ x11 : ι → ι → ι . 0) (λ x10 x11 x12 . 0) (λ x10 x11 . 0)) 0))) 0 (λ x9 : ι → ι . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . x7 (x7 (x3 (λ x11 . λ x12 : ι → ι → ι . 0) (λ x11 x12 x13 . 0) (λ x11 x12 . 0)) (λ x11 : ι → ι . Inj0 0)) (λ x11 : ι → ι . 0)) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x13) 0) = x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . setsum (x9 0 (λ x10 : ι → ι . λ x11 . Inj1 (x0 (λ x12 . 0) 0))) (Inj1 0)) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x11 0) (x0 (λ x9 . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . setsum (x11 (λ x14 . 0) 0) 0) (x6 (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0))) (x4 0))) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x2 (λ x9 . 0) (λ x9 : (ι → ι → ι) → ι . x7 (x0 (λ x10 . x3 (λ x11 . λ x12 : ι → ι → ι . x0 (λ x13 . 0) 0) (λ x11 x12 x13 . Inj0 0) (λ x11 x12 . 0)) (x9 (λ x10 x11 . x2 (λ x12 . 0) (λ x12 : (ι → ι → ι) → ι . 0) 0 (λ x12 : ι → ι . 0)))) 0 (λ x10 . Inj1 0) 0) 0 (λ x9 : ι → ι . 0) = setsum (x3 (λ x9 . λ x10 : ι → ι → ι . 0) (λ x9 x10 x11 . setsum x11 (setsum (Inj0 0) (x7 0 0 (λ x12 . 0) 0))) (λ x9 x10 . x9)) (x0 (λ x9 . 0) (x0 (λ x9 . Inj1 (x6 0 (λ x10 . 0) (λ x10 . 0))) 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x7) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x2 (λ x13 . x11 (Inj0 0)) (λ x13 : (ι → ι → ι) → ι . setsum x12 (setsum (x10 (λ x14 . 0) 0) (x10 (λ x14 . 0) 0))) 0 (λ x13 : ι → ι . setsum 0 0)) 0 = Inj0 (Inj0 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x6) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . setsum (x0 (λ x13 . 0) 0) (setsum 0 0)) (Inj1 (Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x7 (λ x10 . x7 (λ x11 . 0))) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x2 (λ x13 . 0) (λ x13 : (ι → ι → ι) → ι . 0) (setsum (Inj0 x9) (setsum x12 (x2 (λ x13 . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 (λ x13 : ι → ι . 0)))) (λ x13 : ι → ι . Inj0 (setsum (x3 (λ x14 . λ x15 : ι → ι → ι . 0) (λ x14 x15 x16 . 0) (λ x14 x15 . 0)) 0))) (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x7 (λ x10 . Inj1 0)) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . setsum (Inj1 (x10 (λ x13 . 0) 0)) (Inj0 0)) (x7 (λ x9 . 0))) = x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . Inj0 0) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . setsum (x2 (λ x13 . setsum (x0 (λ x14 . 0) 0) (x2 (λ x14 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 (λ x14 : ι → ι . 0))) (λ x13 : (ι → ι → ι) → ι . x3 (λ x14 . λ x15 : ι → ι → ι . Inj0 0) (λ x14 x15 x16 . x16) (λ x14 x15 . x1 (λ x16 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x16 . λ x17 : (ι → ι) → ι → ι . λ x18 : ι → ι . λ x19 . 0) 0)) 0 (λ x13 : ι → ι . Inj0 (Inj0 0))) (x2 (λ x13 . setsum (x11 0) (x11 0)) (λ x13 : (ι → ι → ι) → ι . Inj1 (Inj1 0)) x9 (λ x13 : ι → ι . Inj0 x12))) (Inj0 0)) ⟶ (∀ x4 : ι → (ι → ι) → ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x0 (λ x9 . 0) (Inj0 0) = Inj1 (x2 (λ x9 . 0) (λ x9 : (ι → ι → ι) → ι . setsum (x9 (λ x10 x11 . x0 (λ x12 . 0) 0)) 0) (x3 (λ x9 . λ x10 : ι → ι → ι . 0) (λ x9 x10 x11 . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0) (λ x9 x10 . x10)) (λ x9 : ι → ι . x2 (λ x10 . x9 (setsum 0 0)) (λ x10 : (ι → ι → ι) → ι . Inj0 (setsum 0 0)) (x7 0) (λ x10 : ι → ι . 0)))) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x0 (λ x9 . setsum (Inj0 (x2 (λ x10 . x6) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . 0)) (Inj1 0) (λ x10 : ι → ι . x2 (λ x11 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 : ι → ι . 0)))) (setsum (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . λ x17 . 0) 0) 0) (x0 (λ x10 . x0 (λ x11 . 0) 0) 0))) (x7 (λ x9 . x3 (λ x10 . λ x11 : ι → ι → ι . 0) (λ x10 x11 x12 . 0) (λ x10 x11 . x7 (λ x12 . x10)))) = setsum 0 (Inj1 (x5 (x0 (λ x9 . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0) (setsum 0 0))))) ⟶ False (proof)
Theorem 001c8.. : ∀ x0 : ((ι → ι) → ι) → ι → ι . ∀ x1 : ((((ι → ι) → ι) → ι) → ι) → ι → ι . ∀ x2 : (ι → ι) → ((ι → ι → ι → ι) → ι) → ι → ι . ∀ x3 : (ι → ι → ι → ι) → ι → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 x10 x11 . x1 (λ x12 : ((ι → ι) → ι) → ι . x2 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . setsum x11 (Inj0 0)) 0) (x1 (λ x12 : ((ι → ι) → ι) → ι . x3 (λ x13 x14 x15 . 0) 0) 0)) 0 = setsum x4 x6) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 x10 x11 . 0) x6 = Inj1 (Inj0 (x1 (λ x9 : ((ι → ι) → ι) → ι . Inj1 0) (setsum 0 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 . 0) (λ x9 : ι → ι → ι → ι . x9 0 (x1 (λ x10 : ((ι → ι) → ι) → ι . 0) 0) (x3 (λ x10 x11 x12 . x0 (λ x13 : ι → ι . x0 (λ x14 : ι → ι . 0) 0) 0) x5)) 0 = x7) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι → ι . x2 (λ x9 . 0) (λ x9 : ι → ι → ι → ι . 0) (x7 (λ x9 : (ι → ι) → ι . x2 (setsum (x9 (λ x10 . 0))) (λ x10 : ι → ι → ι → ι . 0) (x0 (λ x10 : ι → ι . x0 (λ x11 : ι → ι . 0) 0) 0)) (λ x9 x10 . x6 (λ x11 . x9) (λ x11 : ι → ι . x10) (λ x11 . 0) (setsum (x0 (λ x11 : ι → ι . 0) 0) 0)) 0) = x7 (λ x9 : (ι → ι) → ι . Inj1 (Inj0 (x5 (λ x10 . setsum 0 0)))) (λ x9 x10 . x6 (λ x11 . setsum x11 x10) (λ x11 : ι → ι . x1 (λ x12 : ((ι → ι) → ι) → ι . Inj0 (x1 (λ x13 : ((ι → ι) → ι) → ι . 0) 0)) (x3 (λ x12 x13 x14 . setsum 0 0) (x2 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . 0) 0))) (λ x11 . setsum (x2 (λ x12 . x0 (λ x13 : ι → ι . 0) 0) (λ x12 : ι → ι → ι → ι . x0 (λ x13 : ι → ι . 0) 0) x11) 0) 0) (Inj0 (setsum 0 (setsum (x6 (λ x9 . 0) (λ x9 : ι → ι . 0) (λ x9 . 0) 0) (Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x6 x7 . x1 (λ x9 : ((ι → ι) → ι) → ι . x6) 0 = x6) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 x7 . x1 (λ x9 : ((ι → ι) → ι) → ι . x0 (λ x10 : ι → ι . x2 (λ x11 . x3 (λ x12 x13 x14 . 0) (Inj0 0)) (λ x11 : ι → ι → ι → ι . x0 (λ x12 : ι → ι . Inj1 0) (Inj1 0)) (setsum (Inj0 0) (x2 (λ x11 . 0) (λ x11 : ι → ι → ι → ι . 0) 0))) (x9 (λ x10 : ι → ι . Inj0 0))) (x1 (λ x9 : ((ι → ι) → ι) → ι . x0 (λ x10 : ι → ι . x9 (λ x11 : ι → ι . x11 0)) (x9 (λ x10 : ι → ι . x1 (λ x11 : ((ι → ι) → ι) → ι . 0) 0))) x6) = setsum x7 (Inj0 x6)) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x0 (λ x9 : ι → ι . setsum (setsum 0 0) (x0 (λ x10 : ι → ι . x3 (λ x11 x12 x13 . x11) 0) (x5 x7 0))) (x2 Inj0 (λ x9 : ι → ι → ι → ι . x3 (λ x10 x11 x12 . x3 (λ x13 x14 x15 . x0 (λ x16 : ι → ι . 0) 0) (Inj1 0)) (x5 0 (setsum 0 0))) 0) = x2 (λ x9 . setsum (x0 (λ x10 : ι → ι . x9) (x3 (λ x10 x11 x12 . 0) (setsum 0 0))) (x1 (λ x10 : ((ι → ι) → ι) → ι . setsum (x3 (λ x11 x12 x13 . 0) 0) 0) 0)) (λ x9 : ι → ι → ι → ι . setsum (x0 (λ x10 : ι → ι . setsum x7 (setsum 0 0)) (x5 x7 (x5 0 0))) x7) (x0 (λ x9 : ι → ι . 0) x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → ι → ι → ι) → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 : ι → ι . 0) x5 = setsum 0 (x4 0)) ⟶ False (proof)
Theorem 9f7c7.. : ∀ x0 : (ι → (ι → ι) → (ι → ι) → ι → ι → ι) → ι → ι → ((ι → ι) → ι → ι) → ι . ∀ x1 : (((ι → (ι → ι) → ι → ι) → ι) → (ι → ι) → (ι → ι → ι) → (ι → ι) → ι) → ι → ι → ι → (ι → ι) → ι → ι . ∀ x2 : ((ι → (ι → ι → ι) → ι) → ι) → ι → ι . ∀ x3 : (ι → ι) → ι → (((ι → ι) → ι) → (ι → ι) → ι) → ι . (∀ x4 x5 . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . x3 (λ x9 . setsum 0 x5) (setsum x5 (x6 (λ x9 . 0) (setsum x5 (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . 0) 0 0 (λ x9 : ι → ι . λ x10 . 0))) (λ x9 . setsum (Inj1 0) (x6 (λ x10 . 0) 0 (λ x10 . 0) 0)) 0)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) = x4) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → (ι → ι) → ι . x3 (λ x9 . 0) (setsum (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . setsum (Inj1 0) (x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . 0) 0 0 0 (λ x14 . 0) 0)) 0 0 (λ x9 : ι → ι . λ x10 . 0)) (x2 (λ x9 : ι → (ι → ι → ι) → ι . setsum (Inj0 0) (setsum 0 0)) x4)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) = setsum 0 x4) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 : ι → (ι → ι → ι) → ι . x2 (λ x10 : ι → (ι → ι → ι) → ι . 0) 0) 0 = Inj0 (setsum x7 (x5 (λ x9 : ι → ι . x6 0 (λ x10 : ι → ι . 0) (λ x10 . Inj0 0) 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → (ι → ι → ι) → ι . 0) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x3 (λ x13 . x2 (λ x14 : ι → (ι → ι → ι) → ι . 0) (Inj1 0)) 0 (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . x13 (λ x15 . x15))) (setsum 0 (x6 0)) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x12 (x9 (λ x13 . λ x14 : ι → ι . λ x15 . 0))) (x6 (Inj1 0)) 0 (setsum (x2 (λ x9 : ι → (ι → ι → ι) → ι . 0) 0) (x3 (λ x9 . 0) 0 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0))) (λ x9 . x9) 0) (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x11 x12) (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . setsum 0 0) 0 x7 (λ x9 : ι → ι . λ x10 . x0 (λ x11 . λ x12 x13 : ι → ι . λ x14 x15 . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0))) 0 (λ x9 : ι → ι . λ x10 . 0)) (λ x9 . x7) (x5 (λ x9 : ι → ι . λ x10 . x9 0))) = setsum (x4 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (x2 (λ x9 : ι → (ι → ι → ι) → ι . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . 0) 0 0 0 (λ x10 . 0) 0) (x3 (λ x9 . 0) 0 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0))) (x5 (λ x9 : ι → ι . λ x10 . 0)) (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . 0) 0 0 0 (λ x14 . 0) 0) (Inj1 0) (setsum 0 0) (λ x9 : ι → ι . λ x10 . x6 0)) (λ x9 . 0) (Inj0 0))) 0) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x2 (λ x13 : ι → (ι → ι → ι) → ι . 0) (x9 (λ x13 . λ x14 : ι → ι . λ x15 . x15))) (x7 (λ x9 . 0)) (Inj0 (x7 (λ x9 . Inj0 0))) 0 (λ x9 . x3 (λ x10 . x7 (λ x11 . setsum (x2 (λ x12 : ι → (ι → ι → ι) → ι . 0) 0) (x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) 0 0 0 (λ x12 . 0) 0))) (setsum x5 (Inj1 (setsum 0 0))) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (setsum 0 (x10 (λ x12 . 0))) (x0 (λ x12 . λ x13 x14 : ι → ι . λ x15 x16 . x13 0) (x2 (λ x12 : ι → (ι → ι → ι) → ι . 0) 0) (x0 (λ x12 . λ x13 x14 : ι → ι . λ x15 x16 . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0)) (λ x12 : ι → ι . λ x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . 0) 0 0 0 (λ x14 . 0) 0)))) (x2 (λ x9 : ι → (ι → ι → ι) → ι . 0) x6) = x2 (λ x9 : ι → (ι → ι → ι) → ι . setsum (x0 (λ x10 . λ x11 x12 : ι → ι . λ x13 x14 . x2 (λ x15 : ι → (ι → ι → ι) → ι . 0) (Inj0 0)) (x2 (λ x10 : ι → (ι → ι → ι) → ι . x6) x6) (x7 (λ x10 . 0)) (λ x10 : ι → ι . λ x11 . setsum (x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) 0 0 0 (λ x12 . 0) 0) (Inj1 0))) (setsum (Inj1 (x9 0 (λ x10 x11 . 0))) (setsum (setsum 0 0) (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . 0) 0 0 0 (λ x10 . 0) 0)))) x6) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x11 (Inj1 (x10 (x12 0))) (setsum (x10 0) (Inj1 0))) x4 0 x7 (λ x9 . setsum x7 (x2 (λ x10 : ι → (ι → ι → ι) → ι . x9) (setsum (x2 (λ x10 : ι → (ι → ι → ι) → ι . 0) 0) (x0 (λ x10 . λ x11 x12 : ι → ι . λ x13 x14 . 0) 0 0 (λ x10 : ι → ι . λ x11 . 0))))) (Inj0 (Inj1 x4)) = setsum (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x11 0) (Inj0 0) (x3 (λ x9 . x7) (x2 (λ x9 : ι → (ι → ι → ι) → ι . x2 (λ x10 : ι → (ι → ι → ι) → ι . 0) 0) 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . Inj1 (Inj0 0))) (λ x9 : ι → ι . λ x10 . Inj0 0)) x4) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x3 (λ x14 . setsum 0 0) (x0 (λ x14 . λ x15 x16 : ι → ι . λ x17 x18 . 0) 0 (setsum (x11 0) 0) (λ x14 : ι → ι . λ x15 . x13)) (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0)) (Inj1 (x3 (λ x9 . Inj1 (x3 (λ x10 . 0) 0 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0))) (setsum 0 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . x2 (λ x15 : ι → (ι → ι → ι) → ι . 0) 0) (x3 (λ x11 . 0) 0 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0)) 0 (Inj1 0) (λ x11 . 0) 0))) 0 (λ x9 : ι → ι . λ x10 . Inj1 0) = x3 (λ x9 . setsum (x3 (λ x10 . setsum (setsum 0 0) (Inj1 0)) (x0 (λ x10 . λ x11 x12 : ι → ι . λ x13 x14 . x1 (λ x15 : (ι → (ι → ι) → ι → ι) → ι . λ x16 : ι → ι . λ x17 : ι → ι → ι . λ x18 : ι → ι . 0) 0 0 0 (λ x15 . 0) 0) (Inj0 0) (Inj1 0) (λ x10 : ι → ι . λ x11 . x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) 0 0 0 (λ x12 . 0) 0)) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x2 (λ x12 : ι → (ι → ι → ι) → ι . x10 (λ x13 . 0)) 0)) x6) x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum 0 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι) → ι → ι → ι → ι . x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x0 (λ x14 . λ x15 x16 : ι → ι . λ x17 x18 . x16 0) (Inj1 (setsum x12 (x11 0))) (x11 x12) (λ x14 : ι → ι . λ x15 . Inj1 (x0 (λ x16 . λ x17 x18 : ι → ι . λ x19 x20 . x20) (x1 (λ x16 : (ι → (ι → ι) → ι → ι) → ι . λ x17 : ι → ι . λ x18 : ι → ι → ι . λ x19 : ι → ι . 0) 0 0 0 (λ x16 . 0) 0) (setsum 0 0) (λ x16 : ι → ι . λ x17 . x0 (λ x18 . λ x19 x20 : ι → ι . λ x21 x22 . 0) 0 0 (λ x18 : ι → ι . λ x19 . 0))))) 0 (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . setsum (Inj1 (x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . 0) 0 0 0 (λ x14 . 0) 0)) (setsum (x0 (λ x14 . λ x15 x16 : ι → ι . λ x17 x18 . 0) 0 0 (λ x14 : ι → ι . λ x15 . 0)) x13)) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x11 (Inj0 0) (x2 (λ x13 : ι → (ι → ι → ι) → ι . 0) 0)) 0 0 (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x3 (λ x14 . 0) 0 (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0)) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) 0 0 0 (λ x9 . 0) 0) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) 0 0 0 (λ x9 . 0) 0) (λ x9 : ι → ι . λ x10 . x6 (λ x11 . 0))) (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . x0 (λ x14 . λ x15 x16 : ι → ι . λ x17 x18 . 0) 0 0 (λ x14 : ι → ι . λ x15 . 0)) (setsum 0 0) 0 (Inj1 0) (λ x10 . 0) 0) (x3 (λ x9 . setsum 0 0) (x6 (λ x9 . 0)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x9 (λ x11 . 0)))) (setsum (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x3 (λ x13 . 0) 0 (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0)) (Inj0 0) (x3 (λ x9 . 0) 0 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0)) (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . 0) 0 0 (λ x9 : ι → ι . λ x10 . 0)) (λ x9 . x0 (λ x10 . λ x11 x12 : ι → ι . λ x13 x14 . 0) 0 0 (λ x10 : ι → ι . λ x11 . 0)) (x5 0)) (x2 (λ x9 : ι → (ι → ι → ι) → ι . x5 0) (setsum 0 0))) (λ x9 : ι → ι . λ x10 . x9 0)) (λ x9 : ι → ι . λ x10 . x10) = setsum (Inj1 x4) 0) ⟶ False (proof)
Theorem 3165c.. : ∀ x0 : (ι → ι) → (ι → (ι → ι) → ι) → ι . ∀ x1 : ((ι → ι) → ι → ι) → (ι → ι) → (ι → (ι → ι) → ι) → ι → ι . ∀ x2 : ((ι → ι) → ι → (ι → ι → ι) → ι) → ι → ι → ι → (ι → ι) → ι . ∀ x3 : ((ι → (ι → ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι . x3 (λ x10 : ι → (ι → ι → ι) → ι . x9 (x9 (x7 (λ x11 . 0) 0 (λ x11 . 0) 0) (λ x11 x12 . x9 0 (λ x13 x14 . 0))) (λ x11 x12 . 0)) (λ x10 : ι → ι . 0)) (λ x9 : ι → ι . 0) = x3 (λ x9 : ι → (ι → ι → ι) → ι . x3 (λ x10 : ι → (ι → ι → ι) → ι . setsum (x1 (λ x11 : ι → ι . λ x12 . Inj0 0) (λ x11 . setsum 0 0) (λ x11 . λ x12 : ι → ι . Inj0 0) 0) (setsum 0 0)) (λ x10 : ι → ι . setsum (setsum (x6 0) (x9 0 (λ x11 x12 . 0))) (x1 (λ x11 : ι → ι . λ x12 . setsum 0 0) (λ x11 . setsum 0 0) (λ x11 . λ x12 : ι → ι . x2 (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι → ι . 0) 0 0 0 (λ x13 . 0)) (setsum 0 0)))) (λ x9 : ι → ι . x0 (λ x10 . Inj0 0) (λ x10 . λ x11 : ι → ι . x7 (λ x12 . Inj1 0) 0 (λ x12 . x12) (x7 (λ x12 . x11 0) (x11 0) (λ x12 . x2 (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι → ι . 0) 0 0 0 (λ x13 . 0)) (setsum 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι . x9 0 (λ x10 x11 . Inj1 (x7 (λ x12 . λ x13 : ι → ι . x1 (λ x14 : ι → ι . λ x15 . 0) (λ x14 . 0) (λ x14 . λ x15 : ι → ι . 0) 0) (λ x12 : ι → ι . x1 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) (λ x13 . λ x14 : ι → ι . 0) 0) 0 (x7 (λ x12 . λ x13 : ι → ι . 0) (λ x12 : ι → ι . 0) 0 0)))) (λ x9 : ι → ι . 0) = x6) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x2 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . setsum (Inj1 (setsum (x11 0 0) 0)) (x3 (λ x12 : ι → (ι → ι → ι) → ι . 0) (λ x12 : ι → ι . Inj1 (x1 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) (λ x13 . λ x14 : ι → ι . 0) 0)))) (Inj0 (x4 (x0 (λ x9 . 0) (λ x9 . λ x10 : ι → ι . x6)) 0 (λ x9 . x6) 0)) (x3 (λ x9 : ι → (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . x6)) (x7 (x7 (x2 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . 0) (x1 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) (λ x9 . λ x10 : ι → ι . 0) 0) 0 0 (λ x9 . x0 (λ x10 . 0) (λ x10 . λ x11 : ι → ι . 0))))) (λ x9 . setsum (Inj1 x9) (Inj0 (setsum 0 (x7 0)))) = Inj0 0) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 : ι → ι → ι . ∀ x7 . x2 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . 0) (x1 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . x1 (λ x10 : ι → ι . λ x11 . setsum (Inj0 0) (Inj0 0)) (λ x10 . 0) (λ x10 . λ x11 : ι → ι . 0) (x1 (λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x10 . x6 0 0) (λ x10 . λ x11 : ι → ι . 0) 0)) (λ x9 . λ x10 : ι → ι . setsum (x6 (x10 0) (setsum 0 0)) 0) (Inj1 (Inj1 x7))) (Inj0 0) (Inj0 (x0 (λ x9 . setsum (x5 0 0) (setsum 0 0)) (λ x9 . λ x10 : ι → ι . 0))) (λ x9 . 0) = x1 (λ x9 : ι → ι . λ x10 . setsum 0 x7) (λ x9 . x0 (λ x10 . x10) (λ x10 . λ x11 : ι → ι . 0)) (λ x9 . λ x10 : ι → ι . Inj0 (x2 (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι → ι . x1 (λ x14 : ι → ι . λ x15 . 0) (λ x14 . x12) (λ x14 . λ x15 : ι → ι . Inj0 0) 0) (setsum 0 0) (setsum (x2 (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι → ι . 0) 0 0 0 (λ x11 . 0)) (x10 0)) (setsum 0 (x1 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . 0) 0)) (λ x11 . x7))) x7) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι) → (ι → ι → ι) → ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x1 (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ι → (ι → ι → ι) → ι . x9 (x9 (x7 0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0)))) (λ x11 : ι → ι . x9 0)) (λ x9 . x5 (λ x10 . λ x11 : ι → ι . Inj1 (setsum (Inj0 0) (x3 (λ x12 : ι → (ι → ι → ι) → ι . 0) (λ x12 : ι → ι . 0)))) (λ x10 x11 . 0) (x5 (λ x10 . λ x11 : ι → ι . Inj1 (Inj0 0)) (λ x10 x11 . 0) (Inj0 0))) (λ x9 . λ x10 : ι → ι . 0) (x3 (λ x9 : ι → (ι → ι → ι) → ι . x2 (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι → ι . setsum 0 (x12 0 0)) (x0 (λ x10 . x2 (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι → ι . 0) 0 0 0 (λ x11 . 0)) (λ x10 . λ x11 : ι → ι . 0)) (Inj0 0) (setsum (x7 0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0)) (x9 0 (λ x10 x11 . 0))) (λ x10 . 0)) (λ x9 : ι → ι . x2 (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι → ι . x3 (λ x13 : ι → (ι → ι → ι) → ι . setsum 0 0) (λ x13 : ι → ι . x3 (λ x14 : ι → (ι → ι → ι) → ι . 0) (λ x14 : ι → ι . 0))) (setsum (x7 0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0)) (x7 0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0))) 0 0 (λ x10 . x9 0))) = Inj1 (setsum (setsum (x6 (x3 (λ x9 : ι → (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . 0)) (x6 0 0)) (Inj1 (x0 (λ x9 . 0) (λ x9 . λ x10 : ι → ι . 0)))) 0)) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : ι → ι . λ x10 . Inj1 (setsum x6 (x1 (λ x11 : ι → ι . λ x12 . setsum 0 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . x3 (λ x13 : ι → (ι → ι → ι) → ι . 0) (λ x13 : ι → ι . 0)) (Inj1 0)))) (λ x9 . x5) (λ x9 . λ x10 : ι → ι . x2 (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι → ι . x3 (λ x14 : ι → (ι → ι → ι) → ι . 0) (λ x14 : ι → ι . Inj1 (x1 (λ x15 : ι → ι . λ x16 . 0) (λ x15 . 0) (λ x15 . λ x16 : ι → ι . 0) 0))) (x3 (λ x11 : ι → (ι → ι → ι) → ι . setsum (x2 (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι → ι . 0) 0 0 0 (λ x12 . 0)) (x2 (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι → ι . 0) 0 0 0 (λ x12 . 0))) (λ x11 : ι → ι . x3 (λ x12 : ι → (ι → ι → ι) → ι . x9) (λ x12 : ι → ι . 0))) 0 0 (λ x11 . Inj0 x7)) x4 = x2 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . Inj1 x10) (x3 (λ x9 : ι → (ι → ι → ι) → ι . x7) (λ x9 : ι → ι . x0 (λ x10 . 0) (λ x10 . λ x11 : ι → ι . setsum 0 (x3 (λ x12 : ι → (ι → ι → ι) → ι . 0) (λ x12 : ι → ι . 0))))) x7 x7 (λ x9 . x7)) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι . x0 (λ x9 . x3 (λ x10 : ι → (ι → ι → ι) → ι . x6) (λ x10 : ι → ι . Inj0 (setsum 0 (x1 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . 0) 0)))) (λ x9 . λ x10 : ι → ι . 0) = setsum 0 (setsum x5 (x2 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . x10) (x7 (λ x9 . 0) (setsum 0 0) (λ x9 . x5)) (Inj0 (x3 (λ x9 : ι → (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . 0))) (x1 (λ x9 : ι → ι . λ x10 . x10) (λ x9 . x6) (λ x9 . λ x10 : ι → ι . x9) (setsum 0 0)) (λ x9 . 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . x0 (λ x9 . x9) (λ x9 . λ x10 : ι → ι . x10 (x0 (λ x11 . 0) (λ x11 . λ x12 : ι → ι . x0 (λ x13 . 0) (λ x13 . λ x14 : ι → ι . x14 0)))) = Inj0 (x1 (λ x9 : ι → ι . λ x10 . x1 (λ x11 : ι → ι . λ x12 . x3 (λ x13 : ι → (ι → ι → ι) → ι . 0) (λ x13 : ι → ι . setsum 0 0)) (λ x11 . x0 (λ x12 . x2 (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι → ι . 0) 0 0 0 (λ x13 . 0)) (λ x12 . λ x13 : ι → ι . Inj0 0)) (λ x11 . λ x12 : ι → ι . x1 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) (λ x13 . λ x14 : ι → ι . setsum 0 0) (x3 (λ x13 : ι → (ι → ι → ι) → ι . 0) (λ x13 : ι → ι . 0))) (setsum (setsum 0 0) (Inj0 0))) (λ x9 . x9) (λ x9 . λ x10 : ι → ι . x3 (λ x11 : ι → (ι → ι → ι) → ι . Inj1 (x2 (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι → ι . 0) 0 0 0 (λ x12 . 0))) (λ x11 : ι → ι . 0)) (setsum (x0 (λ x9 . x6 (λ x10 x11 x12 . 0)) (λ x9 . λ x10 : ι → ι . setsum 0 0)) (x5 (x5 0))))) ⟶ False (proof)
Theorem 2625c.. : ∀ x0 : (ι → ι) → ι → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x1 : ((ι → ι → ι) → (ι → (ι → ι) → ι) → ι → (ι → ι) → ι) → ι → (((ι → ι) → ι → ι) → ι → ι → ι) → ι . ∀ x2 : (ι → ((ι → ι) → ι → ι → ι) → ι) → (((ι → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x3 : (ι → (ι → (ι → ι) → ι) → ι → (ι → ι) → ι) → (ι → ι) → ι → ι . (∀ x4 : ι → ι . ∀ x5 . ∀ x6 x7 : ι → ι . x3 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . x10 (Inj0 0) (λ x13 . Inj1 (setsum x13 (setsum 0 0)))) (λ x9 . x7 (x7 (x2 (λ x10 . λ x11 : (ι → ι) → ι → ι → ι . x10) (λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x10 (λ x13 x14 . 0))))) (x7 (x6 x5)) = x7 (x0 (λ x9 . x3 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) (λ x10 . setsum (x2 (λ x11 . λ x12 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0)) (x6 0)) (setsum 0 x5)) (x0 (λ x9 . x5) (x2 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . x10 (λ x11 . 0) 0 0) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x7 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x7 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . setsum (x0 (λ x11 . x11) (x7 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)) (setsum (Inj0 0) (x7 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x3 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) (λ x9 . x7 (x6 (setsum x9 x9) (x0 (λ x10 . Inj1 0) (x6 0 0) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . Inj1 0)))) (x1 (λ x9 : ι → ι → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . x3 (λ x13 . λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . Inj1 (setsum 0 0)) (λ x13 . x10 (Inj0 0) (λ x14 . x1 (λ x15 : ι → ι → ι . λ x16 : ι → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . 0) 0 (λ x15 : (ι → ι) → ι → ι . λ x16 x17 . 0))) 0) (setsum (x3 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) (λ x9 . x1 (λ x10 : ι → ι → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) 0 (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . 0)) (setsum 0 0)) (setsum x4 (setsum 0 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x2 (λ x12 . λ x13 : (ι → ι) → ι → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0))) = setsum (x6 (x7 x5) (x3 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . x0 (λ x13 . Inj0 0) (x3 (λ x13 . λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . 0) (λ x13 . 0) 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . x14 0)) (λ x9 . x2 (λ x10 . λ x11 : (ι → ι) → ι → ι → ι . Inj0 0) (λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x12 0)) (setsum 0 0))) x4) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x2 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . x1 (λ x11 : ι → ι → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . x2 (λ x15 . λ x16 : (ι → ι) → ι → ι → ι . 0) (λ x15 : (ι → ι → ι) → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . x15 (λ x18 x19 . 0))) (x10 (λ x11 . x7) (Inj1 (setsum 0 0)) (x2 (λ x11 . λ x12 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x11 (λ x14 x15 . 0)))) (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . x10 (λ x14 . Inj1 0) 0 (Inj1 0))) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) = x1 (λ x9 : ι → ι → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . setsum 0 0) x4 (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . setsum x7 x10)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ((ι → ι) → ι → ι → ι) → (ι → ι → ι) → ι . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 . x2 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum 0 (Inj1 (x11 x7))) = x5 (λ x9 : ι → ι . λ x10 x11 . setsum (Inj1 (Inj0 (x3 (λ x12 . λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . 0) (λ x12 . 0) 0))) (Inj0 (Inj1 (x9 0)))) (λ x9 x10 . setsum 0 x9)) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x9 : ι → ι → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . setsum x11 x11) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . 0) = setsum (x6 (x4 (λ x9 x10 : ι → ι . 0))) 0) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 : ι → ι → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . x9 (x12 (x9 0 (setsum 0 0))) (x0 (λ x13 . x12 x11) (Inj1 (x10 0 (λ x13 . 0))) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . x0 (λ x15 . x1 (λ x16 : ι → ι → ι . λ x17 : ι → (ι → ι) → ι . λ x18 . λ x19 : ι → ι . 0) 0 (λ x16 : (ι → ι) → ι → ι . λ x17 x18 . 0)) (x0 (λ x15 . 0) 0 (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0)) (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . x16 0)))) (setsum (x2 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . x9) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0)) (x0 (λ x9 . x6) (setsum (x2 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0)) x5) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . 0) = x6) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 . x0 (λ x10 . x3 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) (λ x11 . x11) (x7 (x1 (λ x11 : ι → ι → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) 0 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . 0)))) 0 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0)) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0) = Inj0 0) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 x7 : (ι → ι) → ι . x0 (λ x9 . x0 (λ x10 . 0) 0 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . setsum x9 (x10 (λ x12 . x12) (x2 (λ x12 . λ x13 : (ι → ι) → ι → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0))))) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0) = Inj0 (Inj0 (Inj0 (x4 (λ x9 : ι → ι → ι . λ x10 . 0))))) ⟶ False (proof)
Theorem b4a18.. : ∀ x0 : (ι → ι) → ι → ι → (ι → ι → ι) → (ι → ι) → ι . ∀ x1 : ((ι → ((ι → ι) → ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x2 : ((((ι → ι → ι) → ι → ι) → ι → ι → ι) → ι) → (ι → ι) → ι . ∀ x3 : (ι → ((ι → ι) → ι) → ι) → ((ι → ι) → (ι → ι → ι) → ι) → ι . (∀ x4 . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x3 (λ x9 . λ x10 : (ι → ι) → ι . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . Inj1 x6) = x4) ⟶ (∀ x4 : (ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 . λ x10 : (ι → ι) → ι . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . 0) = x4 (λ x9 . setsum (x0 (λ x10 . Inj0 (Inj0 0)) x6 (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . λ x11 x12 . 0) (λ x10 : ι → ι . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . λ x12 x13 . 0) (λ x11 : ι → ι . 0))) (λ x10 x11 . setsum x9 (Inj1 0)) (λ x10 . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . λ x12 x13 . 0) (λ x11 : ι → ι . x9))) 0) (λ x9 . setsum 0 x7)) ⟶ (∀ x4 : ((ι → ι) → ι) → ((ι → ι) → ι) → ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι → ι . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 . x2 (λ x9 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x9 . x6 (λ x10 x11 . Inj1 x7)) = Inj0 0) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x2 (λ x9 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . x7 (x0 (λ x10 . x2 (λ x11 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . x9 (λ x12 : ι → ι → ι . λ x13 . 0) 0 0) (λ x11 . setsum 0 0)) 0 0 (λ x10 x11 . x11) (λ x10 . setsum 0 0))) (λ x9 . setsum (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . λ x11 x12 . x11) (λ x10 : ι → ι . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . λ x12 x13 . x12) (λ x11 : ι → ι . x10 0))) 0) = setsum (x6 0) (x7 (Inj1 (setsum (x0 (λ x9 . 0) 0 0 (λ x9 x10 . 0) (λ x9 . 0)) 0)))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . x9 0 (λ x12 : ι → ι . λ x13 . x12 (x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . λ x15 x16 . x15) (λ x14 : ι → ι . x0 (λ x15 . 0) 0 0 (λ x15 x16 . 0) (λ x15 . 0))))) (λ x9 : ι → ι . x6 0 0) = x6 (x5 0 (λ x9 . 0) (λ x9 . x5 (x7 (x2 (λ x10 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x10 . 0)) (x2 (λ x10 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x10 . 0)) (λ x10 . setsum 0 0)) (λ x10 . 0) (λ x10 . 0) (setsum x9 (x6 0 0))) 0) (x7 (Inj0 (setsum (Inj1 0) 0)) (Inj1 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . 0) (λ x9 : ι → ι . Inj0 0))) (λ x9 . setsum 0 (x6 (Inj0 0) (Inj0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : ι → ι → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . x0 (λ x12 . setsum (x0 (λ x13 . setsum 0 0) x12 (x2 (λ x13 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x13 . 0)) (λ x13 x14 . 0) (λ x13 . 0)) 0) 0 (x0 (λ x12 . x10) (Inj0 (x7 0 0)) 0 (λ x12 x13 . x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . λ x15 x16 . setsum 0 0) (λ x14 : ι → ι . 0)) (λ x12 . 0)) (λ x12 x13 . setsum (x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . λ x15 x16 . x15) (λ x14 : ι → ι . Inj1 0)) (Inj1 0)) (λ x12 . x2 (λ x13 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . Inj1 x10) (λ x13 . x2 (λ x14 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . x11) (λ x14 . setsum 0 0)))) (λ x9 : ι → ι . Inj1 (setsum (setsum (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . λ x11 x12 . 0) (λ x10 : ι → ι . 0)) (setsum 0 0)) 0)) = setsum 0 x4) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : ((ι → ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 . x7 (Inj1 0)) 0 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . 0) (λ x9 : ι → ι . x0 (λ x10 . x9 (x6 (λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (λ x11 : ι → ι . λ x12 . 0))) (x7 (x9 0)) (setsum (setsum 0 0) 0) (λ x10 x11 . x7 x10) (λ x10 . 0))) (λ x9 x10 . x10) Inj1 = x7 (x5 (x5 0 (λ x9 : ι → ι . λ x10 . 0)) (λ x9 : ι → ι . λ x10 . Inj0 (x9 (setsum 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 . x0 (λ x9 . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . λ x11 x12 . 0) (λ x10 : ι → ι . Inj1 (x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . λ x12 x13 . setsum 0 0) (λ x11 : ι → ι . x11 0)))) (Inj1 (Inj1 (Inj1 (setsum 0 0)))) (setsum (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . setsum (setsum 0 0) x10) (λ x9 : ι → ι . x7)) (setsum 0 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι . λ x13 x14 . 0) (λ x12 : ι → ι . 0)) (λ x9 : ι → ι . Inj1 0)))) (λ x9 . Inj0) (λ x9 . x5) = Inj0 x4) ⟶ False (proof)
Theorem 50893.. : ∀ x0 : (((ι → ι → ι) → ((ι → ι) → ι → ι) → ι) → ι) → (((ι → ι → ι) → ι → ι → ι) → ι) → ι . ∀ x1 : (ι → (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι) → (ι → ι) → ι → ι . ∀ x2 : ((ι → (ι → ι) → ι → ι → ι) → ι → ((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x3 : (((((ι → ι) → ι) → ι) → ι) → (((ι → ι) → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → (ι → ι → ι → ι) → ι . (∀ x4 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x7 : (ι → ι → ι) → (ι → ι) → ι . x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 x12 : ι → ι . λ x13 . setsum x13 0) (λ x9 . x0 (λ x10 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι → ι . Inj0 (setsum (x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 : (ι → ι → ι) → ι → ι → ι . 0)) (Inj1 0)))) (λ x9 x10 x11 . x7 (λ x12 x13 . setsum (x2 (λ x14 : ι → (ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . x3 (λ x18 : (((ι → ι) → ι) → ι) → ι . λ x19 : ((ι → ι) → ι) → ι → ι . λ x20 x21 : ι → ι . λ x22 . 0) (λ x18 . 0) (λ x18 x19 x20 . 0)) 0) 0) (λ x12 . x2 (λ x13 : ι → (ι → ι) → ι → ι → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . Inj0 (x16 0)) (x1 (λ x13 . λ x14 : ι → (ι → ι) → ι . λ x15 : (ι → ι) → ι . 0) (λ x13 . setsum 0 0) (x1 (λ x13 . λ x14 : ι → (ι → ι) → ι . λ x15 : (ι → ι) → ι . 0) (λ x13 . 0) 0)))) = x0 (λ x9 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x10 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 : (ι → ι → ι) → ι → ι → ι . 0)) (λ x10 : (ι → ι → ι) → ι → ι → ι . 0)) (λ x9 : (ι → ι → ι) → ι → ι → ι . x1 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 : (ι → ι) → ι . x12 (λ x13 . setsum 0 (x2 (λ x14 : ι → (ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . 0) 0))) (λ x10 . setsum (x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x10) (λ x11 : (ι → ι → ι) → ι → ι → ι . x2 (λ x12 : ι → (ι → ι) → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0) 0)) (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . x0 (λ x14 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x14 : (ι → ι → ι) → ι → ι → ι . 0)) (λ x11 . x1 (λ x12 . λ x13 : ι → (ι → ι) → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 . 0) 0) (x3 (λ x11 : (((ι → ι) → ι) → ι) → ι . λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 x14 : ι → ι . λ x15 . 0) (λ x11 . 0) (λ x11 x12 x13 . 0)))) (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 : (ι → ι) → ι . 0) (λ x10 . Inj1 (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . 0) (λ x11 . 0) 0)) (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 : (ι → ι) → ι . setsum 0 0) (λ x10 . x7 (λ x11 x12 . 0) (λ x11 . 0)) 0)))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0) (λ x9 . setsum 0 0) (λ x9 x10 x11 . x9) = x5 (λ x9 . λ x10 : ι → ι . setsum (x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . setsum (setsum 0 0) 0) (λ x11 : (ι → ι → ι) → ι → ι → ι . 0)) 0)) ⟶ (∀ x4 : ((ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι) → ι . x2 (λ x9 : ι → (ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x3 (λ x13 : (((ι → ι) → ι) → ι) → ι . λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 x16 : ι → ι . λ x17 . Inj1 (x15 (setsum 0 0))) (λ x13 . setsum x13 (x1 (λ x14 . λ x15 : ι → (ι → ι) → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 . 0) (setsum 0 0))) (λ x13 x14 x15 . x2 (λ x16 : ι → (ι → ι) → ι → ι → ι . λ x17 . λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . x16 (Inj0 0) (λ x20 . x2 (λ x21 : ι → (ι → ι) → ι → ι → ι . λ x22 . λ x23 : (ι → ι) → ι → ι . λ x24 : ι → ι . 0) 0) (x0 (λ x20 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x20 : (ι → ι → ι) → ι → ι → ι . 0)) (Inj0 0)) 0)) (setsum (x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 x12 : ι → ι . λ x13 . x12 (x10 (λ x14 : ι → ι . 0) 0)) (λ x9 . Inj1 (setsum 0 0)) (λ x9 x10 x11 . setsum (setsum 0 0) (setsum 0 0))) (setsum 0 x5)) = x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 x12 : ι → ι . λ x13 . x13) (λ x9 . x2 (λ x10 : ι → (ι → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . x10 0 (λ x14 . x1 (λ x15 . λ x16 : ι → (ι → ι) → ι . λ x17 : (ι → ι) → ι . x17 (λ x18 . 0)) (λ x15 . x3 (λ x16 : (((ι → ι) → ι) → ι) → ι . λ x17 : ((ι → ι) → ι) → ι → ι . λ x18 x19 : ι → ι . λ x20 . 0) (λ x16 . 0) (λ x16 x17 x18 . 0)) x11) (x1 (λ x14 . λ x15 : ι → (ι → ι) → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 . x11) (x3 (λ x14 : (((ι → ι) → ι) → ι) → ι . λ x15 : ((ι → ι) → ι) → ι → ι . λ x16 x17 : ι → ι . λ x18 . 0) (λ x14 . 0) (λ x14 x15 x16 . 0))) x11) (Inj1 0)) (λ x9 x10 x11 . setsum (setsum 0 0) (x3 (λ x12 : (((ι → ι) → ι) → ι) → ι . λ x13 : ((ι → ι) → ι) → ι → ι . λ x14 x15 : ι → ι . λ x16 . 0) (λ x12 . x11) (λ x12 x13 x14 . 0)))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x2 (λ x9 : ι → (ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x10) 0 = x7) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 : (ι → ι) → ι . x9) (λ x9 . x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 : ((ι → ι) → ι) → ι → ι . λ x12 x13 : ι → ι . λ x14 . x1 (λ x15 . λ x16 : ι → (ι → ι) → ι . λ x17 : (ι → ι) → ι . x17 (λ x18 . Inj1 0)) (λ x15 . x13 0) (x3 (λ x15 : (((ι → ι) → ι) → ι) → ι . λ x16 : ((ι → ι) → ι) → ι → ι . λ x17 x18 : ι → ι . λ x19 . setsum 0 0) (λ x15 . x3 (λ x16 : (((ι → ι) → ι) → ι) → ι . λ x17 : ((ι → ι) → ι) → ι → ι . λ x18 x19 : ι → ι . λ x20 . 0) (λ x16 . 0) (λ x16 x17 x18 . 0)) (λ x15 x16 x17 . Inj1 0))) (λ x10 . x10) (λ x10 x11 x12 . x3 (λ x13 : (((ι → ι) → ι) → ι) → ι . λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 x16 : ι → ι . λ x17 . x2 (λ x18 : ι → (ι → ι) → ι → ι → ι . λ x19 . λ x20 : (ι → ι) → ι → ι . λ x21 : ι → ι . setsum 0 0) (Inj0 0)) (λ x13 . 0) (λ x13 x14 x15 . Inj0 x13))) (Inj1 x6) = Inj0 0) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : ((ι → ι) → ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 : (ι → ι) → ι . setsum 0 (x2 (λ x12 : ι → (ι → ι) → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0) (x2 (λ x12 : ι → (ι → ι) → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . x0 (λ x16 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x16 : (ι → ι → ι) → ι → ι → ι . 0)) (Inj1 0)))) (λ x9 . Inj0 (x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 : ((ι → ι) → ι) → ι → ι . λ x12 x13 : ι → ι . λ x14 . setsum (x0 (λ x15 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x15 : (ι → ι → ι) → ι → ι → ι . 0)) (x11 (λ x15 : ι → ι . 0) 0)) (λ x10 . setsum (setsum 0 0) (x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 : (ι → ι → ι) → ι → ι → ι . 0))) (λ x10 x11 x12 . 0))) (x5 (λ x9 : ι → ι . λ x10 . x6) (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 : (ι → ι) → ι . Inj1 (x0 (λ x12 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x12 : (ι → ι → ι) → ι → ι → ι . 0))) (λ x9 . x2 (λ x10 : ι → (ι → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . x1 (λ x14 . λ x15 : ι → (ι → ι) → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 . 0) 0) 0) 0)) = x5 (λ x9 : ι → ι . λ x10 . Inj0 x6) (Inj0 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x0 (λ x9 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x10 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι → ι . Inj0 (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . Inj0 0) (λ x11 . 0) (Inj0 0)))) (λ x9 : (ι → ι → ι) → ι → ι → ι . x0 (λ x10 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι → ι . setsum (x3 (λ x11 : (((ι → ι) → ι) → ι) → ι . λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 x14 : ι → ι . λ x15 . x2 (λ x16 : ι → (ι → ι) → ι → ι → ι . λ x17 . λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . 0) 0) (λ x11 . x7 (λ x12 : (ι → ι) → ι . 0)) (λ x11 x12 x13 . setsum 0 0)) (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . x1 (λ x14 . λ x15 : ι → (ι → ι) → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 . 0) 0) (λ x11 . x11) (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . 0) (λ x11 . 0) 0)))) = x0 (λ x9 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . setsum (Inj1 (x6 (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 : (ι → ι) → ι . 0) (λ x10 . 0) 0) (λ x10 : ι → ι . λ x11 . x9 (λ x12 x13 . 0) (λ x12 : ι → ι . λ x13 . 0)) (λ x10 . x6 0 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0)))) (x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 : ((ι → ι) → ι) → ι → ι . λ x12 x13 : ι → ι . λ x14 . setsum (x13 0) (setsum 0 0)) (λ x10 . x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . Inj0 0) (λ x11 . x2 (λ x12 : ι → (ι → ι) → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0) 0) (x9 (λ x11 x12 . 0) (λ x11 : ι → ι . λ x12 . 0))) (λ x10 x11 x12 . setsum (x0 (λ x13 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x13 : (ι → ι → ι) → ι → ι → ι . 0)) (setsum 0 0)))) (λ x9 : (ι → ι → ι) → ι → ι → ι . x7 (λ x10 : (ι → ι) → ι . x9 (λ x11 x12 . setsum (x9 (λ x13 x14 . 0) 0 0) 0) (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . setsum 0 0) (λ x11 . x10 (λ x12 . 0)) 0) (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . x2 (λ x14 : ι → (ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . 0) 0) (λ x11 . 0) (x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 : (ι → ι → ι) → ι → ι → ι . 0)))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x7 0) (λ x9 : (ι → ι → ι) → ι → ι → ι . 0) = setsum (x7 (x6 (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (x7 0) 0))) (x0 (λ x9 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x10 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . setsum 0 0) (λ x11 . x1 (λ x12 . λ x13 : ι → (ι → ι) → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 . 0) 0) (x9 (λ x11 x12 . 0) (λ x11 : ι → ι . λ x12 . 0))) (λ x10 : (ι → ι → ι) → ι → ι → ι . Inj1 (setsum 0 0))) (λ x9 : (ι → ι → ι) → ι → ι → ι . Inj0 (x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 : ((ι → ι) → ι) → ι → ι . λ x12 x13 : ι → ι . λ x14 . x12 0) (λ x10 . 0) (λ x10 x11 x12 . x11))))) ⟶ False (proof)
Theorem 4873e.. : ∀ x0 : ((ι → ι) → ι) → ((ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι) → ι → ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x2 : (ι → ι → ι → ι) → (((ι → ι → ι) → ι) → ι) → ι . ∀ x3 : ((((ι → ι → ι) → ι) → ι → ι → ι) → ι) → ((ι → ι) → ι → (ι → ι) → ι → ι) → ι . (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x11 (x11 (x2 (λ x13 x14 x15 . x3 (λ x16 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x16 : ι → ι . λ x17 . λ x18 : ι → ι . λ x19 . 0)) (λ x13 : (ι → ι → ι) → ι . 0)))) = x4) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ι → ι . ∀ x6 x7 . x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . x0 (λ x10 : ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x1 (λ x14 . x12 (x12 0)) (x2 (λ x14 x15 x16 . 0) (λ x14 : (ι → ι → ι) → ι . Inj1 0)) (setsum (x0 (λ x14 : ι → ι . 0) (λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0)) (x3 (λ x14 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x14 : ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0))) (λ x14 : ι → ι . λ x15 . x13) (λ x14 . 0) x11)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x9 (Inj1 (x1 (λ x13 . 0) (x0 (λ x13 : ι → ι . 0) (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0)) (setsum 0 0) (λ x13 : ι → ι . λ x14 . x12) (λ x13 . Inj1 0) (x2 (λ x13 x14 x15 . 0) (λ x13 : (ι → ι → ι) → ι . 0))))) = setsum (setsum (x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . x9 (λ x10 : ι → ι → ι . x10 0 0) (x0 (λ x10 : ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x5 (λ x10 : ι → ι . 0) 0)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) x7) 0) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 x10 x11 . Inj1 (Inj1 (x2 (λ x12 x13 x14 . 0) (λ x12 : (ι → ι → ι) → ι . 0)))) (λ x9 : (ι → ι → ι) → ι . x6) = x6) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 x10 x11 . x7) (λ x9 : (ι → ι → ι) → ι . 0) = x7) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 . Inj0 (x1 (λ x10 . 0) (x1 (λ x10 . Inj0 0) x7 0 (λ x10 : ι → ι . λ x11 . x1 (λ x12 . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0) 0) (λ x10 . x7) (x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0))) x6 (λ x10 : ι → ι . λ x11 . x3 (λ x12 : ((ι → ι → ι) → ι) → ι → ι → ι . x1 (λ x13 . 0) 0 0 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . Inj1 0)) (λ x10 . 0) x6)) x5 (x0 (λ x9 : ι → ι . x6) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) (λ x9 : ι → ι . λ x10 . Inj1 (x2 (λ x11 x12 x13 . 0) (λ x11 : (ι → ι → ι) → ι . x0 (λ x12 : ι → ι . setsum 0 0) (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . setsum 0 0)))) (λ x9 . 0) x4 = setsum 0 (x2 (λ x9 x10 x11 . x11) (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . x10 (λ x11 : ι → ι → ι . setsum 0 0) x6 (Inj1 0)) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x11)))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 . x9) (x0 (λ x9 : ι → ι . setsum (x2 (λ x10 x11 x12 . Inj0 0) (λ x10 : (ι → ι → ι) → ι . x0 (λ x11 : ι → ι . 0) (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0))) 0) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) 0 (λ x9 : ι → ι . λ x10 . x1 (λ x11 . setsum (Inj0 x7) (x0 (λ x12 : ι → ι . x11) (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . Inj1 0))) x10 (setsum (x3 (λ x11 : ((ι → ι → ι) → ι) → ι → ι → ι . x3 (λ x12 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . setsum 0 0)) 0) (λ x11 : ι → ι . λ x12 . Inj1 (x1 (λ x13 . setsum 0 0) (setsum 0 0) (setsum 0 0) (λ x13 : ι → ι . λ x14 . Inj0 0) (λ x13 . x10) 0)) (λ x11 . x7) 0) (λ x9 . setsum (x2 (λ x10 x11 x12 . x12) (λ x10 : (ι → ι → ι) → ι . x6)) (setsum (Inj1 x9) x5)) (Inj1 0) = x0 (λ x9 : ι → ι . setsum (x9 (x1 (λ x10 . x6) (Inj1 0) x6 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . Inj1 0) (x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)))) (x0 (λ x10 : ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj1 x11))) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum (Inj0 (x9 (x11 0) (λ x13 . setsum 0 0))) (x0 (λ x13 : ι → ι . Inj1 0) (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . setsum (x1 (λ x17 . 0) 0 0 (λ x17 : ι → ι . λ x18 . 0) (λ x17 . 0) 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ι → (ι → ι) → (ι → ι) → ι → ι . x0 (λ x9 : ι → ι . setsum (x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . setsum (x10 (λ x11 : ι → ι → ι . 0) 0 0) (x6 (λ x11 . 0) (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0) 0)) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x2 (λ x10 x11 x12 . x10) (λ x10 : (ι → ι → ι) → ι . x1 (λ x11 . x11) (setsum 0 0) (setsum 0 0) (λ x11 : ι → ι . λ x12 . x0 (λ x13 : ι → ι . 0) (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0)) (λ x11 . 0) (x10 (λ x11 x12 . 0))))) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . Inj1 (Inj1 (Inj0 (setsum 0 0)))) = x6 (λ x9 . x9) (λ x9 : ι → ι . λ x10 . x2 (λ x11 x12 x13 . x3 (λ x14 : ((ι → ι → ι) → ι) → ι → ι → ι . x11) (λ x14 : ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . x1 (λ x18 . x17) (x0 (λ x18 : ι → ι . 0) (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 . 0)) (x16 0) (λ x18 : ι → ι . λ x19 . setsum 0 0) (λ x18 . x0 (λ x19 : ι → ι . 0) (λ x19 : ι → (ι → ι) → ι . λ x20 . λ x21 : ι → ι . λ x22 . 0)) x17)) (λ x11 : (ι → ι → ι) → ι . x2 (λ x12 x13 x14 . x3 (λ x15 : ((ι → ι → ι) → ι) → ι → ι → ι . x0 (λ x16 : ι → ι . 0) (λ x16 : ι → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . λ x19 . 0)) (λ x15 : ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . x16)) (λ x12 : (ι → ι → ι) → ι . 0))) (λ x9 . 0) (x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . x0 (λ x11 : ι → ι . x10 (λ x12 : ι → ι → ι . 0) 0 0) (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 . 0) 0 0 (λ x15 : ι → ι . λ x16 . 0) (λ x15 . 0) 0)) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x0 (λ x13 : ι → ι . x12) (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 : (ι → ι → ι) → (ι → ι → ι) → ι . x0 (λ x9 : ι → ι . x9 0) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . x3 (λ x13 : ((ι → ι → ι) → ι) → ι → ι → ι . Inj1 (x13 (λ x14 : ι → ι → ι . setsum 0 0) (x11 0) 0)) (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x16)) = x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . Inj0 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x12 (setsum (setsum 0 0) (Inj0 0)))) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x1 (λ x13 . Inj1 x10) 0 (setsum (setsum (Inj1 0) (x1 (λ x13 . 0) 0 0 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) 0)) 0) (λ x13 : ι → ι . λ x14 . x3 (λ x15 : ((ι → ι → ι) → ι) → ι → ι → ι . setsum (x2 (λ x16 x17 x18 . 0) (λ x16 : (ι → ι → ι) → ι . 0)) (x2 (λ x16 x17 x18 . 0) (λ x16 : (ι → ι → ι) → ι . 0))) (λ x15 : ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . x3 (λ x19 : ((ι → ι → ι) → ι) → ι → ι → ι . x18) (λ x19 : ι → ι . λ x20 . λ x21 : ι → ι . λ x22 . Inj0 0))) (λ x13 . setsum 0 x10) (Inj1 0))) ⟶ False (proof)
Theorem 07659.. : ∀ x0 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι → ι → ι) → ι → ι . ∀ x1 : ((((ι → ι) → ι → ι → ι) → ι → ι → ι → ι) → ι) → (ι → ι) → ι . ∀ x2 : (ι → ι) → ι → ((ι → ι → ι) → ι) → ι . ∀ x3 : (ι → (((ι → ι) → ι) → (ι → ι) → ι) → ι) → (ι → (ι → ι) → ι) → ((ι → ι → ι) → ι → ι → ι) → ι → ι . (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x9 . λ x10 : ι → ι . 0) (λ x9 : ι → ι → ι . λ x10 x11 . 0) (Inj1 (x7 (x0 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 x11 x12 . x0 (λ x13 : (ι → ι) → ι → ι . 0) (λ x13 : ι → ι . λ x14 x15 x16 . 0) 0) 0) (λ x9 : ι → ι . λ x10 . 0))) = setsum 0 (x2 (λ x9 . setsum x5 (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x10 . λ x11 : ι → ι . Inj0 0) (λ x10 : ι → ι → ι . λ x11 x12 . x1 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x13 . 0)) (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x10 . λ x11 : ι → ι . 0) (λ x10 : ι → ι → ι . λ x11 x12 . 0) 0))) x4 (λ x9 : ι → ι → ι . setsum 0 (x9 (x2 (λ x10 . 0) 0 (λ x10 : ι → ι → ι . 0)) (setsum 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x9 . λ x10 : ι → ι . x2 (λ x11 . x11) 0 (λ x11 : ι → ι → ι . setsum x7 x9)) (λ x9 : ι → ι → ι . λ x10 x11 . x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι . x0 (λ x14 : (ι → ι) → ι → ι . x0 (λ x15 : (ι → ι) → ι → ι . x13 (λ x16 : ι → ι . 0) (λ x16 . 0)) (λ x15 : ι → ι . λ x16 x17 x18 . 0) (x13 (λ x15 : ι → ι . 0) (λ x15 . 0))) (λ x14 : ι → ι . λ x15 x16 x17 . x3 (λ x18 . λ x19 : ((ι → ι) → ι) → (ι → ι) → ι . x17) (λ x18 . λ x19 : ι → ι . 0) (λ x18 : ι → ι → ι . λ x19 x20 . setsum 0 0) x15) x12) (λ x12 . λ x13 : ι → ι . setsum (x0 (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . λ x15 x16 x17 . setsum 0 0) (setsum 0 0)) x10) (λ x12 : ι → ι → ι . λ x13 x14 . Inj1 (setsum (x1 (λ x15 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x15 . 0)) (Inj1 0))) (setsum 0 (x9 0 x7))) (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . x11) (λ x11 . λ x12 : ι → ι . x9) (λ x11 : ι → ι → ι . λ x12 x13 . x1 (λ x14 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x14 . x12)) (setsum (setsum 0 0) 0)) (λ x9 . λ x10 : ι → ι . x0 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . λ x12 x13 x14 . x1 (λ x15 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x12) (λ x15 . 0)) (x10 (setsum 0 0))) (λ x9 : ι → ι → ι . λ x10 x11 . Inj1 (x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι . setsum 0 0) (λ x12 . λ x13 : ι → ι . x0 (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . λ x15 x16 x17 . 0) 0) (λ x12 : ι → ι → ι . λ x13 x14 . 0) 0)) x7) = x2 (λ x9 . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x9)) x5 (λ x9 : ι → ι → ι . setsum (setsum 0 (setsum x5 (setsum 0 0))) 0)) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 . setsum (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . x11 (λ x12 : ι → ι . 0) (λ x12 . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 . λ x14 : ι → ι . 0) (λ x13 : ι → ι → ι . λ x14 x15 . 0) 0)) (λ x10 . λ x11 : ι → ι . x9) (λ x10 : ι → ι → ι . λ x11 x12 . 0) (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . x10) (λ x10 . λ x11 : ι → ι . x9) (λ x10 : ι → ι → ι . λ x11 x12 . x1 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x13 . 0)) (Inj1 0))) 0) (Inj0 (x5 (λ x9 : ι → ι → ι . 0) (λ x9 . x0 (λ x10 : (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . λ x11 x12 x13 . x2 (λ x14 . 0) 0 (λ x14 : ι → ι → ι . 0))))) (λ x9 : ι → ι → ι . x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x10 . λ x11 : ι → ι . x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι . setsum x10 (x0 (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . λ x15 x16 x17 . 0) 0)) (λ x12 . λ x13 : ι → ι . x1 (λ x14 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . Inj1 0) (λ x14 . x11 0)) (λ x12 : ι → ι → ι . λ x13 x14 . 0) (x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 . λ x14 : ι → ι . 0) (λ x13 : ι → ι → ι . λ x14 x15 . 0) 0) (λ x12 . 0))) (λ x10 : ι → ι → ι . λ x11 x12 . x11) x7) = x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . Inj1 0) (λ x9 . λ x10 : ι → ι . setsum (setsum (x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x12 . 0)) (λ x11 . x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x12 . λ x13 : ι → ι . 0) (λ x12 : ι → ι → ι . λ x13 x14 . 0) 0)) (x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . x1 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x13 . 0)) (λ x11 . λ x12 : ι → ι . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 . λ x14 : ι → ι . 0) (λ x13 : ι → ι → ι . λ x14 x15 . 0) 0) (λ x11 : ι → ι → ι . λ x12 x13 . Inj1 0) 0)) 0) (λ x9 : ι → ι → ι . λ x10 x11 . x9 (x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . x11) (λ x13 . λ x14 : ι → ι . setsum 0 0) (λ x13 : ι → ι → ι . λ x14 x15 . x1 (λ x16 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x16 . 0)) x11) (λ x12 . setsum (Inj1 0) (setsum 0 0))) (Inj0 (setsum 0 0))) (setsum (x4 (λ x9 : (ι → ι) → ι . x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . Inj0 0) (λ x10 . λ x11 : ι → ι . x7) (λ x10 : ι → ι → ι . λ x11 x12 . x10 0 0) 0)) (setsum x7 0))) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x7 . x2 (λ x9 . x2 (λ x10 . x10) (Inj1 (x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x10 . 0))) (λ x10 : ι → ι → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 . λ x12 : ι → ι . x0 (λ x13 : (ι → ι) → ι → ι . setsum 0 0) (λ x13 : ι → ι . λ x14 x15 x16 . Inj1 0) (x1 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x13 . 0))) (λ x11 : ι → ι → ι . λ x12 x13 . x13) x7)) 0 (λ x9 : ι → ι → ι . 0) = x2 (λ x9 . Inj1 (x2 (λ x10 . 0) 0 (λ x10 : ι → ι → ι . Inj1 (x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 . λ x12 : ι → ι . 0) (λ x11 : ι → ι → ι . λ x12 x13 . 0) 0)))) (Inj1 (x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x6 (x6 0 (λ x10 : ι → ι . 0) 0 0) (λ x10 : ι → ι . 0) 0 (x6 0 (λ x10 : ι → ι . 0) 0 0)) (λ x9 . Inj1 0))) (λ x9 : ι → ι → ι . x9 (Inj0 0) (x5 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι . x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) Inj1 = x7 (λ x9 . λ x10 : ι → ι . setsum 0 (x6 (λ x11 x12 . setsum 0 (Inj1 0))))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . setsum (x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x2 (λ x11 . x2 (λ x12 . 0) 0 (λ x12 : ι → ι → ι . 0)) (Inj1 0) (λ x11 : ι → ι → ι . x11 0 0)) (λ x10 . Inj1 x6)) (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . x2 (λ x12 . Inj0 0) x10 (λ x12 : ι → ι → ι . x10)) (λ x10 . λ x11 : ι → ι . 0) (λ x10 : ι → ι → ι . λ x11 x12 . 0) (Inj0 (x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x10 . 0))))) (λ x9 . 0) = x5) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 : (ι → ι) → ι → ι . Inj1 (x2 (λ x10 . x2 (λ x11 . setsum 0 0) (Inj1 0) (λ x11 : ι → ι → ι . 0)) (setsum (setsum 0 0) 0) (λ x10 : ι → ι → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . x9 (λ x13 . 0) 0) (λ x11 . λ x12 : ι → ι . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 . λ x14 : ι → ι . 0) (λ x13 : ι → ι → ι . λ x14 x15 . 0) 0) (λ x11 : ι → ι → ι . λ x12 x13 . x12) 0))) (λ x9 : ι → ι . λ x10 x11 x12 . x2 (λ x13 . x11) 0 (λ x13 : ι → ι → ι . x13 0 (Inj0 x12))) 0 = setsum (setsum (x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . setsum (x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x12 . 0)) (setsum 0 0)) 0 (λ x9 . x9)) (x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . setsum (x6 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . 0) (λ x10 : ι → ι . 0) 0 0) 0) (λ x9 . x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . Inj1 0) (λ x10 . 0)))) (setsum 0 (x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . setsum (Inj1 0) (setsum 0 0)) (x2 (λ x9 . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . 0) (λ x10 : ι → ι . 0) 0 0) (x0 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 x11 x12 . 0) 0) (λ x9 : ι → ι → ι . x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x10 . 0))) (λ x9 . x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x0 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . λ x12 x13 x14 . 0) 0) (λ x10 . 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x0 (λ x9 : (ι → ι) → ι → ι . Inj1 (Inj0 x6)) (λ x9 : ι → ι . λ x10 x11 x12 . setsum 0 0) (x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x9 . x9)) = Inj0 (Inj1 0)) ⟶ False (proof)
Theorem bd450.. : ∀ x0 : (((ι → (ι → ι) → ι → ι) → ι) → ι) → ι → (((ι → ι) → ι) → ι) → ι . ∀ x1 : ((ι → ι) → ι → ((ι → ι) → ι → ι) → ι) → (ι → ι) → (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x2 : (((ι → ι → ι) → ι) → ι) → ι → ι → ι → (ι → ι) → ι . ∀ x3 : (ι → ι → ((ι → ι) → ι → ι) → ι) → (((ι → ι → ι) → ι) → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . Inj0 (x7 (λ x10 : ι → ι → ι . λ x11 . setsum (x2 (λ x12 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x12 . 0)) (x9 (λ x12 x13 . 0))))) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . x1 (λ x15 : ι → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . x14 (λ x18 . 0) 0) (λ x15 . x13) (λ x15 . λ x16 : ι → ι . λ x17 . 0) x13) (λ x12 : (ι → ι → ι) → ι . 0) (x11 (λ x12 . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x13 : (ι → ι) → ι . 0)) (Inj1 0)) (x11 (λ x12 . x10) (x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0)))) (λ x9 : (ι → ι → ι) → ι . x7 (λ x10 : ι → ι → ι . λ x11 . x7 (λ x12 : ι → ι → ι . λ x13 . x2 (λ x14 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x14 . 0)))) (x7 (λ x9 : ι → ι → ι . λ x10 . 0)) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . Inj1 (x9 (λ x10 . λ x11 : ι → ι . λ x12 . 0))) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 0) (x5 (λ x9 : (ι → ι) → ι → ι . 0) 0 (λ x9 . 0)) (λ x9 : (ι → ι) → ι . Inj0 0)) (λ x9 : (ι → ι) → ι . Inj0 0))) (x2 (λ x9 : (ι → ι → ι) → ι . Inj0 (setsum (x7 (λ x10 : ι → ι → ι . λ x11 . 0)) (setsum 0 0))) (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . x2 (λ x13 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x13 . 0)) (x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0)) (λ x9 . x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . setsum 0 0) (λ x10 . x2 (λ x11 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x11 . 0)) (λ x10 . λ x11 : ι → ι . λ x12 . x9) (x7 (λ x10 : ι → ι → ι . λ x11 . 0))) (λ x9 . λ x10 : ι → ι . λ x11 . x7 (λ x12 : ι → ι → ι . λ x13 . 0)) x4) (Inj0 x6) 0 (λ x9 . Inj0 (setsum x6 (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0))))) = x2 (λ x9 : (ι → ι → ι) → ι . setsum (x7 (λ x10 : ι → ι → ι . λ x11 . x11)) x6) (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . Inj1 (x1 (λ x13 : ι → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . 0) (λ x13 . 0) (λ x13 . λ x14 : ι → ι . λ x15 . 0) 0)) (λ x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 : ι → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . setsum 0 0) (λ x15 . Inj0 0) (λ x15 . λ x16 : ι → ι . λ x17 . setsum 0 0) (x2 (λ x15 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x15 . 0))) 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . Inj1 (x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0))) (λ x9 : (ι → ι → ι) → ι . setsum (setsum 0 0) (x9 (λ x10 x11 . 0))) 0 (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι . 0)) (λ x9 : (ι → ι) → ι . setsum 0 0)))) (Inj0 0) (Inj0 (x2 (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x11 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x11 . 0)) 0 (λ x10 : (ι → ι) → ι . x9 (λ x11 x12 . 0))) 0 x4 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x2 (λ x12 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x12 . 0)) (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0)) (Inj1 0) 0) (λ x9 . setsum (Inj0 0) x6))) (λ x9 . setsum 0 x6)) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → ι → ι → ι . ∀ x7 : (ι → ι) → ι . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . setsum x9 (setsum (setsum 0 0) (Inj1 0))) 0) (λ x9 : (ι → ι → ι) → ι . 0) (x7 (λ x9 . x9)) (Inj1 (Inj0 (x7 (λ x9 . 0)))) = x7 (λ x9 . x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 . x1 (λ x11 : ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . Inj1 (x1 (λ x14 : ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . λ x15 : ι → ι . λ x16 . 0) 0)) (λ x11 . Inj1 (x7 (λ x12 . 0))) (λ x11 . λ x12 : ι → ι . λ x13 . 0) (Inj1 0)) (λ x10 . λ x11 : ι → ι . λ x12 . 0) (setsum (x7 (λ x10 . 0)) 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι → ι → ι → ι . ∀ x7 : ι → ι . x2 (λ x9 : (ι → ι → ι) → ι . 0) 0 (x2 (λ x9 : (ι → ι → ι) → ι . Inj1 0) (x4 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x13 : (ι → ι) → ι . 0)) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . 0)) (x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 . 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0) 0) 0)) (x2 (λ x9 : (ι → ι → ι) → ι . x7 0) 0 0 0 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x3 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 0) (λ x10 : (ι → ι → ι) → ι . Inj1 0) (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0)) (x2 (λ x10 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x10 . 0)))) (x2 (λ x9 : (ι → ι → ι) → ι . 0) 0 (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0) (λ x9 . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0)) (λ x9 . λ x10 : ι → ι . λ x11 . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0)) 0) (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . 0) 0 0)) (λ x9 . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) (x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 . 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0) 0) (λ x10 : (ι → ι) → ι . x9))) (λ x9 . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0))) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x2 (λ x12 : (ι → ι → ι) → ι . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . Inj1 0) 0 (λ x13 : (ι → ι) → ι . Inj0 0)) (Inj1 (Inj1 0)) (x2 (λ x12 : (ι → ι → ι) → ι . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x13 : (ι → ι) → ι . 0)) x10 0 (x7 0) (λ x12 . x11 (λ x13 . 0) 0)) 0 (λ x12 . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) (x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x13 : (ι → ι) → ι . 0)) (λ x13 : (ι → ι) → ι . x2 (λ x14 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x14 . 0)))) (λ x9 : (ι → ι → ι) → ι . x5 (λ x10 . λ x11 : ι → ι . λ x12 . Inj0 (setsum 0 0))) (Inj1 (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0)))) (x6 (λ x9 : ι → ι → ι . 0) (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . 0) 0) (λ x9 . x6 (λ x10 : ι → ι → ι . 0) 0 0 0) (λ x9 . λ x10 : ι → ι . λ x11 . Inj0 0) (setsum 0 0)) 0 (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 0) (x6 (λ x9 : ι → ι → ι . 0) 0 0 0) (λ x9 : (ι → ι) → ι . setsum 0 0)))) (λ x9 . 0) = x2 (λ x9 : (ι → ι → ι) → ι . x7 0) (setsum (Inj1 (setsum (Inj0 0) 0)) (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . Inj0 0) (Inj0 0) (λ x12 : (ι → ι) → ι . x11 (λ x13 . 0) 0)) (λ x9 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . x12) (λ x12 : (ι → ι → ι) → ι . setsum 0 0) 0 (x10 0)) (x6 (λ x9 : ι → ι → ι . 0) (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0) 0) 0 (x7 0)))) (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x7 (x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . x1 (λ x15 : ι → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . 0) (λ x15 . 0) (λ x15 . λ x16 : ι → ι . λ x17 . 0) 0) (λ x12 . x10 0) (λ x12 . λ x13 : ι → ι . λ x14 . x13 0) (x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0))))) (setsum (x7 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0) 0 0)) (x2 (λ x9 : (ι → ι → ι) → ι . 0) 0 (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x9)) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) (Inj1 0) (λ x9 : (ι → ι) → ι . 0)) (λ x9 . x7 (Inj1 0)))) (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . x9) (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . x13 (λ x14 . 0) 0) (λ x11 : (ι → ι → ι) → ι . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0)) (x1 (λ x11 : ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . λ x13 . 0) 0) (Inj0 0)) 0 (λ x10 : (ι → ι) → ι . x10 (λ x11 . x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0))) (x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . x12 (λ x13 . x10 0) (x12 (λ x13 . 0) 0)) (λ x10 . x9) (λ x10 . λ x11 : ι → ι . λ x12 . 0) (x5 (λ x10 . λ x11 : ι → ι . λ x12 . Inj1 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι . x2 (λ x9 : (ι → ι → ι) → ι . Inj0 (x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x10) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x13 : (ι → ι) → ι . 0))) (Inj0 (Inj1 0)) x5)) (x2 (λ x9 : (ι → ι → ι) → ι . x9 (λ x10 x11 . 0)) (x6 0) (x6 (setsum x4 x5)) (Inj0 x4) (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x3 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . x2 (λ x16 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x16 . 0)) (λ x13 : (ι → ι → ι) → ι . x1 (λ x14 : ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . λ x15 : ι → ι . λ x16 . 0) 0) (setsum 0 0) 0) (λ x10 : (ι → ι → ι) → ι . x9) (setsum (x2 (λ x10 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x10 . 0)) (x7 0 0 (λ x10 . 0))) 0)) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x7 (setsum 0 (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0))) 0 (λ x10 . x1 (λ x11 : ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . x0 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x14 : (ι → ι) → ι . 0)) (λ x11 . Inj0 0) (λ x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x14 . 0)) (x0 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x11 : (ι → ι) → ι . 0)))) x5 (λ x9 : (ι → ι) → ι . x6 (Inj0 x5))) (setsum (Inj0 0) (x2 (λ x9 : (ι → ι → ι) → ι . setsum 0 (x9 (λ x10 x11 . 0))) (x6 (setsum 0 0)) 0 (x7 x5 0 (λ x9 . setsum 0 0)) (λ x9 . x7 (Inj1 0) x5 (λ x10 . x9)))) (λ x9 . x7 (x6 0) 0 (λ x10 . x7 (x7 (setsum 0 0) 0 (λ x11 . Inj1 0)) (setsum x9 (setsum 0 0)) (λ x11 . x9))) = setsum (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x10) (λ x9 : (ι → ι → ι) → ι . x7 (setsum (Inj1 0) 0) (x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x9 (λ x13 x14 . 0)) (λ x10 : (ι → ι → ι) → ι . setsum 0 0) 0 (x2 (λ x10 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x10 . 0))) (λ x10 . Inj1 (setsum 0 0))) (setsum 0 (x6 0)) (x6 0)) (Inj0 x4)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x10) (λ x9 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0) (Inj1 0) = setsum (setsum (Inj0 (x6 0)) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . Inj0 0) (λ x10 . x7 (λ x11 . 0)) (λ x10 . λ x11 : ι → ι . λ x12 . x10) 0) 0 (λ x9 : (ι → ι) → ι . x5))) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x10 : (ι → ι → ι) → ι . x7 (λ x11 . x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0)) (Inj0 0) (setsum x5 (setsum 0 0)) (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x9 (λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x6 0) (λ x10 : (ι → ι) → ι . 0)) (λ x10 . 0)) (x2 (λ x9 : (ι → ι → ι) → ι . 0) 0 0 (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x10 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x10 . 0)) 0 (λ x9 : (ι → ι) → ι . 0)) (λ x9 . setsum (Inj0 0) 0)) (λ x9 : (ι → ι) → ι . setsum (x7 (λ x10 . 0)) (Inj0 0)))) ⟶ (∀ x4 x5 x6 : ι → ι . ∀ x7 . x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x2 (λ x12 : (ι → ι → ι) → ι . 0) 0 (x11 (λ x12 . 0) (Inj1 (x11 (λ x12 . 0) 0))) 0 (λ x12 . x10)) (λ x9 . x6 (Inj0 0)) (λ x9 . λ x10 : ι → ι . λ x11 . 0) 0 = x2 (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . Inj1 (x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0)) (x1 (λ x11 : ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . Inj0 0) (λ x11 . x7) (λ x11 . λ x12 : ι → ι . λ x13 . 0) x7) 0) 0 (λ x10 : (ι → ι) → ι . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . x12) (λ x11 : (ι → ι → ι) → ι . x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . x13) (λ x12 . x11 (λ x13 x14 . 0)) (λ x12 . λ x13 : ι → ι . λ x14 . x14) (x9 (λ x12 x13 . 0))) (x10 (λ x11 . Inj1 0)) (setsum (x0 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x11 : (ι → ι) → ι . 0)) (x3 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 0)))) (x6 0) x7 (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι . setsum (Inj0 0) (setsum 0 0))) (λ x9 : (ι → ι) → ι . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x3 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . 0) (λ x13 : (ι → ι → ι) → ι . x1 (λ x14 : ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . λ x15 : ι → ι . λ x16 . 0) 0) (Inj0 0) (x1 (λ x13 : ι → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . 0) (λ x13 . 0) (λ x13 . λ x14 : ι → ι . λ x15 . 0) 0)) (λ x10 : (ι → ι → ι) → ι . x9 (λ x11 . x9 (λ x12 . 0))) x7 (setsum 0 (x9 (λ x10 . 0))))) (λ x9 . x5 (Inj0 (x6 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι . x5) = x5) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . setsum (x9 (λ x10 . λ x11 : ι → ι . λ x12 . 0)) (setsum (Inj0 (x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 . 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0) 0)) (x9 (λ x10 . λ x11 : ι → ι . λ x12 . 0)))) 0 (λ x9 : (ι → ι) → ι . Inj0 (setsum (Inj1 0) (Inj1 x5))) = x7) ⟶ False (proof)
Theorem 3677d.. : ∀ x0 : ((((ι → ι → ι) → ι → ι) → ι) → (ι → ι) → ι → ι → ι → ι) → (ι → (ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι → (ι → ι) → ι) → (ι → ι) → (ι → ι) → ι . ∀ x2 : (ι → ι → ι → ι → ι) → ι → ι . ∀ x3 : (((((ι → ι) → ι) → ι) → ι) → ι → ι) → ((ι → ι → ι → ι) → ι) → ι . (∀ x4 : ι → (ι → ι) → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 . setsum (Inj0 0) (x3 (λ x11 : (((ι → ι) → ι) → ι) → ι . λ x12 . x12) (λ x11 : ι → ι → ι → ι . x7 (x2 (λ x12 x13 x14 x15 . 0) 0)))) (λ x9 : ι → ι → ι → ι . x6) = x6) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 . x1 (λ x11 x12 . λ x13 : ι → ι . x0 (λ x14 : ((ι → ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 x17 x18 . x17) (λ x14 . λ x15 : ι → ι . λ x16 . x13 (x15 0))) (λ x11 . x1 (λ x12 x13 . λ x14 : ι → ι . x12) (λ x12 . setsum 0 (x3 (λ x13 : (((ι → ι) → ι) → ι) → ι . λ x14 . 0) (λ x13 : ι → ι → ι → ι . 0))) (λ x12 . x9 (λ x13 : (ι → ι) → ι . x0 (λ x14 : ((ι → ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 x17 x18 . 0) (λ x14 . λ x15 : ι → ι . λ x16 . 0)))) (λ x11 . x2 (λ x12 x13 x14 x15 . 0) (x0 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 x15 x16 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 x16 . λ x17 : ι → ι . 0) (λ x15 . 0) (λ x15 . 0))))) (λ x9 : ι → ι → ι → ι . 0) = Inj1 (x2 (λ x9 x10 x11 x12 . 0) (setsum (x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 . setsum 0 0) (λ x9 : ι → ι → ι → ι . x2 (λ x10 x11 x12 x13 . 0) 0)) 0))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 x10 x11 x12 . x9) (Inj1 x7) = x5 (λ x9 : ι → ι → ι . Inj0 (setsum (x0 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 x14 . x0 (λ x15 : ((ι → ι → ι) → ι → ι) → ι . λ x16 : ι → ι . λ x17 x18 x19 . 0) (λ x15 . λ x16 : ι → ι . λ x17 . 0)) (λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 0)) (setsum (Inj0 0) (Inj0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x5 : ((ι → ι) → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x2 (λ x9 x10 x11 x12 . 0) 0 = setsum (Inj0 0) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x1 (λ x9 x10 . λ x11 : ι → ι . setsum 0 (Inj1 (x3 (λ x12 : (((ι → ι) → ι) → ι) → ι . λ x13 . x2 (λ x14 x15 x16 x17 . 0) 0) (λ x12 : ι → ι → ι → ι . x9)))) (λ x9 . setsum x7 (x1 (λ x10 x11 . λ x12 : ι → ι . 0) (λ x10 . x10) (λ x10 . setsum (setsum 0 0) x9))) (λ x9 . x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 . 0) (λ x10 : ι → ι → ι → ι . x6)) = x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 . Inj1 (x2 (λ x11 x12 x13 x14 . x1 (λ x15 x16 . λ x17 : ι → ι . Inj0 0) (λ x15 . x12) (λ x15 . Inj0 0)) x6)) (λ x9 : ι → ι → ι → ι . x2 (λ x10 x11 x12 x13 . Inj0 (setsum x11 (x1 (λ x14 x15 . λ x16 : ι → ι . 0) (λ x14 . 0) (λ x14 . 0)))) (x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 . 0) (λ x10 : ι → ι → ι → ι . x9 0 (x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . λ x12 : ι → ι . λ x13 x14 x15 . 0) (λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x3 (λ x11 : (((ι → ι) → ι) → ι) → ι . λ x12 . 0) (λ x11 : ι → ι → ι → ι . 0)))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x1 (λ x9 x10 . λ x11 : ι → ι . 0) (setsum (Inj0 0)) (λ x9 . Inj1 (setsum (Inj0 (x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 . 0) (λ x10 : ι → ι → ι → ι . 0))) (x1 (λ x10 x11 . λ x12 : ι → ι . x11) (λ x10 . x9) (λ x10 . x9)))) = x7 (x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 . 0) (λ x9 : ι → ι → ι → ι . 0)) (λ x9 : ι → ι . λ x10 . x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . λ x12 : ι → ι . λ x13 x14 x15 . x0 (λ x16 : ((ι → ι → ι) → ι → ι) → ι . λ x17 : ι → ι . λ x18 x19 x20 . 0) (λ x16 . λ x17 : ι → ι . λ x18 . x17 (x1 (λ x19 x20 . λ x21 : ι → ι . 0) (λ x19 . 0) (λ x19 . 0)))) (λ x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 x15 x16 x17 . x1 (λ x18 x19 . λ x20 : ι → ι . setsum 0 0) (λ x18 . Inj0 0) (λ x18 . Inj1 0)) 0)) (x4 (λ x9 . λ x10 : ι → ι . λ x11 . x2 (λ x12 x13 x14 x15 . 0) (x10 0))) (x7 (x2 (λ x9 x10 x11 x12 . Inj1 (Inj0 0)) (setsum x5 (x1 (λ x9 x10 . λ x11 : ι → ι . 0) (λ x9 . 0) (λ x9 . 0)))) (λ x9 : ι → ι . λ x10 . 0) (Inj1 0) x6)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 x12 x13 . Inj0 (x2 (λ x14 x15 x16 x17 . x1 (λ x18 x19 . λ x20 : ι → ι . x19) (λ x18 . x15) (λ x18 . 0)) x13)) (λ x9 . λ x10 : ι → ι . setsum (x1 (λ x11 x12 . λ x13 : ι → ι . 0) (λ x11 . 0) (λ x11 . x3 (λ x12 : (((ι → ι) → ι) → ι) → ι . λ x13 . x13) (λ x12 : ι → ι → ι → ι . x0 (λ x13 : ((ι → ι → ι) → ι → ι) → ι . λ x14 : ι → ι . λ x15 x16 x17 . 0) (λ x13 . λ x14 : ι → ι . λ x15 . 0))))) = x5) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 x12 x13 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0) = x5) ⟶ False (proof)
Theorem 4bada.. : ∀ x0 : (ι → ι → ((ι → ι) → ι) → (ι → ι) → ι → ι) → (((ι → ι → ι) → ι) → ι) → (ι → ι → ι) → ι . ∀ x1 : (ι → ι) → ι → (ι → ι) → ι . ∀ x2 : (ι → ι) → (ι → ι → ι) → ((ι → ι → ι) → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι → ι) → ι . x3 (λ x9 . x9) 0 0 = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x9 . Inj1 x6) (x3 (λ x9 . x9) x6 (x3 (λ x9 . Inj1 x6) (x4 (x4 0)) (x2 (λ x9 . x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 x11 . 0)) (λ x9 x10 . 0) (λ x9 : ι → ι → ι . x2 (λ x10 . 0) (λ x10 x11 . 0) (λ x10 : ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0)) (λ x9 : ι → ι . λ x10 . x1 (λ x11 . 0) 0 (λ x11 . 0)) (λ x9 . x5 (λ x10 : (ι → ι) → ι → ι . 0))))) x7 = setsum (setsum (x5 (λ x9 : (ι → ι) → ι → ι . x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x3 (λ x15 . 0) 0 0) (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 x11 . setsum 0 0))) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 : (ι → ι → ι) → ι . x2 (λ x10 . Inj1 0) (λ x10 x11 . x10) (λ x10 : ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x10 . 0)) (λ x9 x10 . x2 (λ x11 . Inj0 0) (λ x11 x12 . x11) (λ x11 : ι → ι → ι . Inj0 0) (λ x11 : ι → ι . λ x12 . x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 : (ι → ι → ι) → ι . 0) (λ x13 x14 . 0)) (λ x11 . x7)))) (x3 (λ x9 . Inj1 0) 0 (x1 (λ x9 . Inj1 (Inj1 0)) (x3 (λ x9 . 0) 0 x7) (λ x9 . 0)))) ⟶ (∀ x4 : ι → (ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x2 (λ x9 . x1 (λ x10 . 0) 0 (λ x10 . x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . x14) (λ x11 : (ι → ι → ι) → ι . x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . Inj1 0) (λ x12 : (ι → ι → ι) → ι . x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 : (ι → ι → ι) → ι . 0) (λ x13 x14 . 0)) (λ x12 x13 . x10)) (λ x11 x12 . 0))) (λ x9 x10 . x10) (λ x9 : ι → ι → ι . setsum x7 (setsum (x9 (Inj0 0) 0) (setsum (setsum 0 0) (x5 0 0)))) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . x6 (x6 (x1 (λ x10 . 0) (x1 (λ x10 . 0) 0 (λ x10 . 0)) (λ x10 . x7)) (x3 (λ x10 . x6 0 0 0 0) 0 (x6 0 0 0 0)) (x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . Inj1 0) (λ x10 : (ι → ι → ι) → ι . x9) (λ x10 x11 . 0)) (x2 (λ x10 . Inj1 0) (λ x10 x11 . Inj1 0) (λ x10 : ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . 0) (λ x10 . setsum 0 0))) 0 (setsum (setsum 0 (setsum 0 0)) (x1 (λ x10 . x6 0 0 0 0) (x6 0 0 0 0) (λ x10 . x3 (λ x11 . 0) 0 0))) (setsum (setsum x7 0) 0)) = x6 (x1 (λ x9 . 0) (x4 0 (λ x9 . 0) (λ x9 . setsum 0 0)) (λ x9 . x1 (λ x10 . x2 (λ x11 . x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 x13 . 0)) (λ x11 x12 . x3 (λ x13 . 0) 0 0) (λ x11 : ι → ι → ι . Inj1 0) (λ x11 : ι → ι . λ x12 . x9) (λ x11 . setsum 0 0)) 0 (λ x10 . setsum x10 0))) (x1 (λ x9 . 0) (x5 x7 (x2 (λ x9 . 0) (λ x9 x10 . setsum 0 0) (λ x9 : ι → ι → ι . x7) (λ x9 : ι → ι . λ x10 . x3 (λ x11 . 0) 0 0) (λ x9 . x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 x11 . 0)))) (λ x9 . 0)) (setsum (x2 (λ x9 . x9) (λ x9 x10 . 0) (λ x9 : ι → ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . x7)) 0) (x4 (setsum (x3 (λ x9 . 0) (Inj1 0) (Inj0 0)) (x5 (setsum 0 0) (Inj1 0))) (λ x9 . 0) (λ x9 . 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x2 (λ x9 . setsum x9 (x7 (λ x10 . 0))) (λ x9 x10 . x7 (λ x11 . setsum (Inj0 0) (Inj1 0))) (λ x9 : ι → ι → ι . x1 (λ x10 . 0) (x3 (λ x10 . x6) 0 (x5 (λ x10 : (ι → ι) → ι . Inj0 0))) (λ x10 . x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 : (ι → ι → ι) → ι . x9 (x2 (λ x12 . 0) (λ x12 x13 . 0) (λ x12 : ι → ι → ι . 0) (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0)) (setsum 0 0)) (λ x11 x12 . 0))) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) = x7 (λ x9 . x7 (setsum (x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x12 (λ x15 . 0)) (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 x11 . x10))))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 . setsum x7 0) (Inj0 x7) (λ x9 . setsum x5 x5) = x6) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 x6 : ι → ι . ∀ x7 . x1 (λ x9 . setsum (setsum x9 (x6 (Inj0 0))) (x2 (λ x10 . setsum 0 0) (λ x10 x11 . x1 (λ x12 . 0) 0 (λ x12 . x2 (λ x13 . 0) (λ x13 x14 . 0) (λ x13 : ι → ι → ι . 0) (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0))) (λ x10 : ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . x11) Inj0)) (x3 (λ x9 . x6 (x1 (λ x10 . 0) (x1 (λ x10 . 0) 0 (λ x10 . 0)) (λ x10 . setsum 0 0))) (Inj0 (x6 (x4 0 (λ x9 : ι → ι . 0) (λ x9 . 0) 0))) x7) x6 = x6 (x2 (λ x9 . 0) (λ x9 x10 . x9) (λ x9 : ι → ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . setsum (setsum 0 0) 0) (λ x10 : (ι → ι → ι) → ι . Inj0 (x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 : (ι → ι → ι) → ι . 0) (λ x11 x12 . 0))) (λ x10 x11 . setsum 0 (setsum 0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . setsum 0 (setsum 0 (Inj1 0))) (λ x9 : (ι → ι → ι) → ι . x7 (λ x10 . x2 (λ x11 . 0) (λ x11 x12 . setsum 0 x10) (λ x11 : ι → ι → ι . Inj0 x10) (λ x11 : ι → ι . λ x12 . setsum 0 0) (λ x11 . 0))) (λ x9 x10 . setsum (setsum (x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x13 (λ x16 . 0)) (λ x11 : (ι → ι → ι) → ι . Inj1 0) (λ x11 x12 . 0)) (x7 (λ x11 . x2 (λ x12 . 0) (λ x12 x13 . 0) (λ x12 : ι → ι → ι . 0) (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0)))) (Inj0 0)) = x7 (λ x9 . Inj0 (x3 (λ x10 . x7 (λ x11 . x3 (λ x12 . 0) 0 0)) (setsum 0 (x7 (λ x10 . 0))) (x1 (λ x10 . x1 (λ x11 . 0) 0 (λ x11 . 0)) x9 (λ x10 . x2 (λ x11 . 0) (λ x11 x12 . 0) (λ x11 : ι → ι → ι . 0) (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0)))))) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι → ι . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . Inj0 0) (λ x9 : (ι → ι → ι) → ι . x6 (λ x10 . x10)) (λ x9 x10 . x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 : (ι → ι → ι) → ι . x11 (λ x12 x13 . Inj0 (x2 (λ x14 . 0) (λ x14 x15 . 0) (λ x14 : ι → ι → ι . 0) (λ x14 : ι → ι . λ x15 . 0) (λ x14 . 0)))) (λ x11 x12 . x2 (λ x13 . x11) (λ x13 x14 . setsum x13 0) (λ x13 : ι → ι → ι . 0) (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0))) = setsum (x3 (λ x9 . Inj1 (x2 (λ x10 . 0) (λ x10 x11 . 0) (λ x10 : ι → ι → ι . setsum 0 0) (λ x10 : ι → ι . λ x11 . Inj0 0) (λ x10 . x7 0 0))) (Inj0 (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x11 (λ x14 . 0)) (λ x9 : (ι → ι → ι) → ι . setsum 0 0) (λ x9 x10 . setsum 0 0))) 0) x5) ⟶ False (proof)
Theorem 15092.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : (ι → ι) → ι → ι → ((ι → ι) → ι) → ι . ∀ x2 : (ι → ι → ι) → (ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 : ι → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι → (ι → ι) → ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x3 (λ x9 . x9) 0 = x7 (x6 (x1 (λ x9 . x5 (λ x10 . λ x11 : ι → ι . λ x12 . x9)) (setsum (x6 0 0 (λ x9 . 0) 0) (Inj0 0)) (x7 (x7 0 (λ x9 : ι → ι . 0)) (λ x9 : ι → ι . 0)) (λ x9 : ι → ι . x3 (λ x10 . setsum 0 0) (x5 (λ x10 . λ x11 : ι → ι . λ x12 . 0)))) (x0 (λ x9 . x5 (λ x10 . λ x11 : ι → ι . λ x12 . 0)) (x1 (λ x9 . Inj0 0) (x0 (λ x9 . 0) 0) (Inj0 0) (λ x9 : ι → ι . 0))) (λ x9 . 0) (x5 (λ x9 . λ x10 : ι → ι . λ x11 . setsum (x1 (λ x12 . 0) 0 0 (λ x12 : ι → ι . 0)) (x1 (λ x12 . 0) 0 0 (λ x12 : ι → ι . 0))))) (λ x9 : ι → ι . x0 (λ x10 . x7 0 (λ x11 : ι → ι . Inj0 0)) 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x9 . 0) (setsum (x2 (λ x9 x10 . x2 (λ x11 x12 . Inj1 0) (λ x11 . x0 (λ x12 . 0) 0)) (λ x9 . 0)) (x1 (λ x9 . x5) x6 x6 (λ x9 : ι → ι . x3 (λ x10 . 0) (Inj0 0)))) = x6) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 x10 . 0) (λ x9 . Inj0 x5) = Inj1 (x0 (λ x9 . x9) x5)) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 x10 . x2 (λ x11 x12 . x10) (λ x11 . 0)) (λ x9 . 0) = x2 (λ x9 x10 . x7) (λ x9 . Inj1 x5)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → (ι → ι → ι) → ι . ∀ x7 . x1 (λ x9 . 0) 0 (x4 (x3 (λ x9 . 0) 0)) (λ x9 : ι → ι . setsum (x0 (λ x10 . x9 (setsum 0 0)) (x2 (λ x10 x11 . 0) (λ x10 . 0))) (x3 (λ x10 . 0) x7)) = setsum 0 (x2 (λ x9 . setsum (x1 (λ x10 . x7) 0 (setsum 0 0) (λ x10 : ι → ι . x0 (λ x11 . 0) 0))) (λ x9 . x3 (λ x10 . 0) 0))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x9 . x2 (λ x10 x11 . 0) (λ x10 . x1 (λ x11 . x9) x9 (x2 (λ x11 x12 . 0) (λ x11 . 0)) (λ x11 : ι → ι . 0))) (Inj1 (Inj0 0)) (setsum (x4 (λ x9 : (ι → ι) → ι . x2 (λ x10 x11 . setsum 0 0) (λ x10 . Inj1 0))) 0) (λ x9 : ι → ι . x7) = Inj0 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 . x6 0 (λ x10 : ι → ι . x2 (λ x11 x12 . Inj0 0) (λ x11 . x11))) (x0 (λ x9 . x1 (λ x10 . x10) (x3 (λ x10 . 0) (x0 (λ x10 . 0) 0)) (x5 (λ x10 x11 . Inj1 0)) (λ x10 : ι → ι . 0)) (setsum (x2 (λ x9 x10 . 0) (λ x9 . setsum 0 0)) (setsum 0 (Inj0 0)))) = x6 (x0 (λ x9 . 0) (setsum 0 (Inj1 0))) (λ x9 : ι → ι . x9 (x3 (λ x10 . x3 (λ x11 . x0 (λ x12 . 0) 0) (setsum 0 0)) (x1 (λ x10 . setsum 0 0) (Inj1 0) (x0 (λ x10 . 0) 0) (λ x10 : ι → ι . x2 (λ x11 x12 . 0) (λ x11 . 0)))))) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x9 . x6) x6 = Inj1 (setsum (x4 x7 (λ x9 . Inj0 (x1 (λ x10 . 0) 0 0 (λ x10 : ι → ι . 0)))) (x0 (λ x9 . 0) (x3 (λ x9 . x2 (λ x10 x11 . 0) (λ x10 . 0)) x6)))) ⟶ False (proof)
Theorem 9a10f.. : ∀ x0 : ((ι → ι) → ι) → ι → ι . ∀ x1 : (((ι → (ι → ι) → ι) → ι) → (ι → ι → ι) → (ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → (ι → ι) → ι . ∀ x2 : ((ι → ι) → (ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → (ι → ι) → ι → ι) → ι . ∀ x3 : (ι → ι → ι) → ι → ((ι → ι → ι) → (ι → ι) → ι) → ι → ι → ι . (∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x9 x10 . 0) (x4 (x4 x5)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . setsum x6 (Inj0 x7)) (setsum 0 (x0 (λ x9 : ι → ι . setsum 0 0) (x3 (λ x9 x10 . setsum 0 0) (setsum 0 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . x10 0) 0 0))) (x4 (x4 0)) = setsum (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (λ x9 x10 . x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 x13 : ι → ι → ι . λ x14 . 0) (λ x11 x12 . setsum 0 (x3 (λ x13 x14 . 0) 0 (λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) 0 0)) 0 x9 (λ x11 . 0)) x6 0 (λ x9 . setsum (x3 (λ x10 x11 . Inj1 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . x2 (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . 0)) (x2 (λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0)) 0) x7)) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x11 (setsum (setsum 0 0) 0) 0) (λ x9 x10 . 0) (Inj1 0) 0 (λ x9 . x7))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 x10 . x9) (x3 (λ x9 x10 . x9) (x3 (λ x9 x10 . x6 0) x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . Inj1 (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 x13 : ι → ι → ι . λ x14 . 0) (λ x11 x12 . 0) 0 0 (λ x11 . 0))) (setsum 0 0) x7) (λ x9 : ι → ι → ι . λ x10 : ι → ι . 0) x5 (setsum 0 (x3 (λ x9 x10 . x0 (λ x11 : ι → ι . 0) 0) (Inj1 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . Inj1 0) (setsum 0 0) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . 0) (λ x9 x10 . 0) 0 0 (λ x9 . 0))))) (λ x9 : ι → ι → ι . λ x10 : ι → ι . x7) 0 (setsum 0 (x0 (λ x9 : ι → ι . x0 (λ x10 : ι → ι . x2 (λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0)) (x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 x12 : ι → ι → ι . λ x13 . 0) (λ x10 x11 . 0) 0 0 (λ x10 . 0))) 0)) = x7) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ι → ι → ι . x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 : ι → ι . x3 (λ x15 x16 . setsum x13 (x0 (λ x17 : ι → ι . 0) 0)) 0 (λ x15 : ι → ι → ι . λ x16 : ι → ι . x14 0) (x14 (x3 (λ x15 x16 . 0) 0 (λ x15 : ι → ι → ι . λ x16 : ι → ι . 0) 0 0)) 0) 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x3 (λ x13 x14 . x1 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 x17 : ι → ι → ι . λ x18 . x0 (λ x19 : ι → ι . 0) (Inj0 0)) (λ x15 x16 . Inj0 (x3 (λ x17 x18 . 0) 0 (λ x17 : ι → ι → ι . λ x18 : ι → ι . 0) 0 0)) 0 (x0 (λ x15 : ι → ι . 0) (x0 (λ x15 : ι → ι . 0) 0)) (λ x15 . 0)) x12 (λ x13 : ι → ι → ι . λ x14 : ι → ι . Inj1 (x0 (λ x15 : ι → ι . x14 0) (setsum 0 0))) (x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . setsum (Inj1 0) 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . setsum (x3 (λ x17 x18 . 0) 0 (λ x17 : ι → ι → ι . λ x18 : ι → ι . 0) 0 0) x14)) 0) = setsum (Inj0 (setsum (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (λ x9 x10 . Inj0 0) 0 (x6 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) 0) (λ x9 . x0 (λ x10 : ι → ι . 0) 0)) (x6 (λ x9 : ι → ι . λ x10 . x10) (λ x9 . x6 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0) 0) (Inj1 0)))) (x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x11 (λ x14 . x13)) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x11 (Inj1 (x3 (λ x13 x14 . 0) 0 (λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x13) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) = x6) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . 0) (λ x9 x10 . Inj0 (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 x13 : ι → ι → ι . λ x14 . setsum (x13 0 0) (x1 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 x17 : ι → ι → ι . λ x18 . 0) (λ x15 x16 . 0) 0 0 (λ x15 . 0))) (λ x11 x12 . x10) x6 0 (λ x11 . x2 (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . x13 0 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . x3 (λ x16 x17 . 0) 0 (λ x16 : ι → ι → ι . λ x17 : ι → ι . 0) 0 0)))) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x12) (λ x9 x10 . Inj1 (Inj0 (Inj1 0))) (setsum (x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . 0)) (Inj1 (x7 (λ x9 . 0) 0 (λ x9 . 0) 0))) (Inj1 (x7 (λ x9 . x9) (Inj0 0) (λ x9 . x3 (λ x10 x11 . 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . 0) 0 0) 0)) (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 x12 : ι → ι → ι . λ x13 . x13) (λ x10 x11 . x10) 0 0 (λ x10 . 0))) (x0 (λ x9 : ι → ι . 0) (x7 (λ x9 . Inj1 (x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 x12 : ι → ι → ι . λ x13 . 0) (λ x10 x11 . 0) 0 0 (λ x10 . 0))) 0 (λ x9 . Inj0 (setsum 0 0)) x6)) (λ x9 . 0) = x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x11 0 (x10 0 (setsum 0 0))) (λ x9 x10 . x6) (Inj0 0) (x0 (λ x9 : ι → ι . x5 (λ x10 : ι → ι → ι . λ x11 : ι → ι . Inj0 0)) (x3 (λ x9 x10 . 0) (setsum 0 x6) (λ x9 : ι → ι → ι . λ x10 : ι → ι . x3 (λ x11 x12 . x9 0 0) (x3 (λ x11 x12 . 0) 0 (λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) 0 0) (λ x11 : ι → ι → ι . λ x12 : ι → ι . x12 0) (setsum 0 0) (Inj0 0)) (x7 (λ x9 . 0) (setsum 0 0) (λ x9 . setsum 0 0) (x0 (λ x9 : ι → ι . 0) 0)) (setsum 0 (x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0))))) (λ x9 . x9)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . setsum (Inj1 (x11 (x3 (λ x13 x14 . 0) 0 (λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) 0 0) (x1 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 x15 : ι → ι → ι . λ x16 . 0) (λ x13 x14 . 0) 0 0 (λ x13 . 0)))) (setsum (x1 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 x15 : ι → ι → ι . λ x16 . x0 (λ x17 : ι → ι . 0) 0) (λ x13 x14 . 0) 0 (x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (λ x13 . 0)) (x3 (λ x13 x14 . x13) (x1 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 x15 : ι → ι → ι . λ x16 . 0) (λ x13 x14 . 0) 0 0 (λ x13 . 0)) (λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) (setsum 0 0) (x11 0 0)))) (λ x9 x10 . setsum (x2 (λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x13 (λ x16 . 0)) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0)) 0) (x3 (λ x9 x10 . Inj1 (x0 (λ x11 : ι → ι . 0) (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 x13 : ι → ι → ι . λ x14 . 0) (λ x11 x12 . 0) 0 0 (λ x11 . 0)))) 0 (λ x9 : ι → ι → ι . λ x10 : ι → ι . Inj0 0) (setsum 0 0) (x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x1 (λ x14 : (ι → (ι → ι) → ι) → ι . λ x15 x16 : ι → ι → ι . λ x17 . Inj1 0) (λ x14 x15 . setsum 0 0) (x1 (λ x14 : (ι → (ι → ι) → ι) → ι . λ x15 x16 : ι → ι → ι . λ x17 . 0) (λ x14 x15 . 0) 0 0 (λ x14 . 0)) (x3 (λ x14 x15 . 0) 0 (λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) 0 0) (λ x14 . x11 (λ x15 . 0))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0))) (x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x11 (λ x14 . x3 (λ x15 x16 . Inj0 0) 0 (λ x15 : ι → ι → ι . λ x16 : ι → ι . x2 (λ x17 : ι → ι . λ x18 : ι → ι → ι . λ x19 : (ι → ι) → ι . λ x20 : ι → ι . λ x21 . 0) (λ x17 x18 . λ x19 : ι → ι . λ x20 . 0)) (x3 (λ x15 x16 . 0) 0 (λ x15 : ι → ι → ι . λ x16 : ι → ι . 0) 0 0) (x11 (λ x15 . 0)))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0)) (λ x9 . x2 (λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x1 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 x17 : ι → ι → ι . λ x18 . Inj0 (x0 (λ x19 : ι → ι . 0) 0)) (λ x15 x16 . setsum (setsum 0 0) (x2 (λ x17 : ι → ι . λ x18 : ι → ι → ι . λ x19 : (ι → ι) → ι . λ x20 : ι → ι . λ x21 . 0) (λ x17 x18 . λ x19 : ι → ι . λ x20 . 0))) (x11 (x3 (λ x15 x16 . 0) 0 (λ x15 : ι → ι → ι . λ x16 : ι → ι . 0) 0 0) 0) (x13 (Inj0 0)) (λ x15 . x0 (λ x16 : ι → ι . x14) (x1 (λ x16 : (ι → (ι → ι) → ι) → ι . λ x17 x18 : ι → ι → ι . λ x19 . 0) (λ x16 x17 . 0) 0 0 (λ x16 . 0)))) (λ x10 x11 . λ x12 : ι → ι . λ x13 . setsum x13 x13)) = x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . Inj1) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj1 (x11 0))) ⟶ (∀ x4 . ∀ x5 x6 x7 : ι → ι . x0 (λ x9 : ι → ι . x7 (Inj1 (setsum 0 (Inj0 0)))) (x7 0) = setsum x4 (x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 : ι → ι . 0) (x12 (x10 0 0))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . Inj1 0)))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 . x0 (λ x9 : ι → ι . x9 0) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x10 (x3 (λ x13 x14 . x2 (λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 : (ι → ι) → ι . λ x18 : ι → ι . λ x19 . 0) (λ x15 x16 . λ x17 : ι → ι . λ x18 . 0)) (x11 0 0) (λ x13 : ι → ι → ι . λ x14 : ι → ι . x14 0) x12 (x10 0 0)) (x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . x0 (λ x18 : ι → ι . 0) 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . x16))) (λ x9 x10 . x2 (λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 x17 : ι → ι → ι . λ x18 . x1 (λ x19 : (ι → (ι → ι) → ι) → ι . λ x20 x21 : ι → ι → ι . λ x22 . 0) (λ x19 x20 . 0) 0 0 (λ x19 . 0)) (λ x15 x16 . 0) x12 (x13 0) (λ x15 . 0))) 0 x4 (λ x9 . 0)) = Inj1 0) ⟶ False (proof)
Theorem dc9ca.. : ∀ x0 : (((((ι → ι) → ι) → ι) → ι) → ι → ι → (ι → ι) → ι → ι) → (ι → ι) → (((ι → ι) → ι → ι) → ι → ι → ι) → ι . ∀ x1 : (ι → (ι → (ι → ι) → ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x2 : (ι → ι → ι → ι) → (ι → (ι → ι → ι) → ι → ι) → ι . ∀ x3 : (ι → ι → ι) → ι → (ι → (ι → ι) → ι → ι) → ι . (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 . x3 (λ x9 x10 . x3 (λ x11 x12 . setsum (x2 (λ x13 x14 x15 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 . Inj0 0)) (setsum 0 x10)) (Inj1 (x6 (λ x11 : (ι → ι) → ι . setsum 0 0))) (λ x11 . λ x12 : ι → ι . λ x13 . setsum 0 x10)) (Inj0 (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . setsum 0 0) (λ x9 . Inj0 (x3 (λ x10 x11 . 0) 0 (λ x10 . λ x11 : ι → ι . λ x12 . 0))))) (λ x9 . λ x10 : ι → ι . λ x11 . setsum 0 (Inj1 (x2 (λ x12 x13 x14 . x0 (λ x15 : (((ι → ι) → ι) → ι) → ι . λ x16 x17 . λ x18 : ι → ι . λ x19 . 0) (λ x15 . 0) (λ x15 : (ι → ι) → ι → ι . λ x16 x17 . 0)) (λ x12 . λ x13 : ι → ι → ι . λ x14 . x1 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 . 0) (λ x15 . 0))))) = x3 (λ x9 x10 . setsum 0 (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 . x10) (λ x11 . x9))) (setsum (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . 0) (λ x9 . x7)) (setsum 0 (Inj0 (x6 (λ x9 : (ι → ι) → ι . 0))))) (λ x9 . λ x10 : ι → ι . λ x11 . x11)) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x3 (λ x9 x10 . x9) 0 (λ x9 . λ x10 : ι → ι . λ x11 . x1 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . λ x14 . x11) (λ x12 . setsum x12 (x2 (λ x13 x14 x15 . x12) (λ x13 . λ x14 : ι → ι → ι . λ x15 . 0)))) = x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . x3 (λ x12 x13 . x3 (λ x14 x15 . x15) x11 (λ x14 . λ x15 : ι → ι . λ x16 . Inj0 x14)) (x2 (λ x12 x13 x14 . 0) (λ x12 . λ x13 : ι → ι → ι . λ x14 . x2 (λ x15 x16 x17 . x17) (λ x15 . λ x16 : ι → ι → ι . λ x17 . x1 (λ x18 . λ x19 : ι → (ι → ι) → ι → ι . λ x20 . 0) (λ x18 . 0)))) (λ x12 . λ x13 : ι → ι . λ x14 . Inj0 0)) (λ x9 . x9)) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x9 x10 x11 . x7 x10 (λ x12 . Inj1 0)) (λ x9 . λ x10 : ι → ι → ι . λ x11 . x11) = x7 x5 (λ x9 . Inj1 (setsum (Inj0 (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 . 0) (λ x10 . 0))) (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 . 0) (λ x10 . 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x2 (λ x9 x10 x11 . Inj0 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) = x4) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . x2 (λ x12 x13 x14 . x1 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 . x16 (x2 (λ x18 x19 x20 . 0) (λ x18 . λ x19 : ι → ι → ι . λ x20 . 0)) (λ x18 . x17) (x16 0 (λ x18 . 0) 0)) (λ x15 . 0)) (λ x12 . λ x13 : ι → ι → ι . λ x14 . x3 (λ x15 x16 . Inj0 0) 0 (λ x15 . λ x16 : ι → ι . λ x17 . x1 (λ x18 . λ x19 : ι → (ι → ι) → ι → ι . λ x20 . x2 (λ x21 x22 x23 . 0) (λ x21 . λ x22 : ι → ι → ι . λ x23 . 0)) (λ x18 . Inj1 0)))) (λ x9 . x9) = x2 (λ x9 x10 x11 . x7) (λ x9 . λ x10 : ι → ι → ι . λ x11 . x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . x2 (λ x12 x13 x14 . x11) (λ x12 . λ x13 : ι → ι → ι . λ x14 . 0)) (λ x9 . x0 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . x2 (λ x15 x16 x17 . Inj1 0) (λ x15 . λ x16 : ι → ι → ι . λ x17 . setsum (x3 (λ x18 x19 . 0) 0 (λ x18 . λ x19 : ι → ι . λ x20 . 0)) (x3 (λ x18 x19 . 0) 0 (λ x18 . λ x19 : ι → ι . λ x20 . 0)))) (λ x10 . setsum (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 . x0 (λ x14 : (((ι → ι) → ι) → ι) → ι . λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 . 0) (λ x14 : (ι → ι) → ι → ι . λ x15 x16 . 0)) (λ x11 . x1 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . λ x14 . 0) (λ x12 . 0))) (x0 (λ x11 : (((ι → ι) → ι) → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . Inj1 0) (λ x11 . x9) (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . setsum 0 0))) (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . x10 (λ x13 . setsum (x1 (λ x14 . λ x15 : ι → (ι → ι) → ι → ι . λ x16 . 0) (λ x14 . 0)) (x3 (λ x14 x15 . 0) 0 (λ x14 . λ x15 : ι → ι . λ x16 . 0))) (setsum (x2 (λ x13 x14 x15 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 . 0)) (x3 (λ x13 x14 . 0) 0 (λ x13 . λ x14 : ι → ι . λ x15 . 0))))) = Inj0 x5) ⟶ (∀ x4 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . x0 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj0 (Inj1 x13)) (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x9 (λ x12 . x1 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . λ x15 . 0) (λ x13 . x13)) 0) = x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum (Inj1 (x0 (λ x12 : (((ι → ι) → ι) → ι) → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . x1 (λ x17 . λ x18 : ι → (ι → ι) → ι → ι . λ x19 . 0) (λ x17 . 0)) (λ x12 . x2 (λ x13 x14 x15 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 . 0)) (λ x12 : (ι → ι) → ι → ι . λ x13 x14 . setsum 0 0))) (setsum (setsum 0 (x9 (λ x12 . 0) 0)) (setsum (x7 (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0)) (setsum 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x0 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 x15 x16 . x3 (λ x17 x18 . x3 (λ x19 x20 . 0) x17 (λ x19 . λ x20 : ι → ι . λ x21 . x19)) (x3 (λ x17 x18 . Inj0 0) (setsum 0 0) (λ x17 . λ x18 : ι → ι . λ x19 . x18 0)) (λ x17 . λ x18 : ι → ι . Inj1)) (λ x14 . λ x15 : ι → ι → ι . λ x16 . x1 (λ x17 . λ x18 : ι → (ι → ι) → ι → ι . λ x19 . Inj0 (x2 (λ x20 x21 x22 . 0) (λ x20 . λ x21 : ι → ι → ι . λ x22 . 0))) (λ x17 . 0))) (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x9 (λ x12 . x0 (λ x13 : (((ι → ι) → ι) → ι) → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . x3 (λ x18 x19 . Inj0 0) (x1 (λ x18 . λ x19 : ι → (ι → ι) → ι → ι . λ x20 . 0) (λ x18 . 0)) (λ x18 . λ x19 : ι → ι . λ x20 . Inj1 0)) (λ x13 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 x15 . x1 (λ x16 . λ x17 : ι → (ι → ι) → ι → ι . λ x18 . setsum 0 0) (λ x16 . x3 (λ x17 x18 . 0) 0 (λ x17 . λ x18 : ι → ι . λ x19 . 0)))) x7) = Inj1 (x3 (λ x9 x10 . 0) 0 (λ x9 . λ x10 : ι → ι . λ x11 . x11))) ⟶ False (proof)
Theorem 2bfdd.. : ∀ x0 : (ι → ι → ι) → (ι → ι → (ι → ι) → ι → ι) → (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι → ι) → (((ι → ι → ι) → ι) → ι) → ι . ∀ x2 : (ι → ι) → (((ι → ι → ι) → ι → ι → ι) → (ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . setsum (x2 (λ x10 . 0) (λ x10 : (ι → ι → ι) → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0)) x6) (x2 (λ x9 . 0) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . x2 (λ x13 . x1 (λ x14 x15 . x0 (λ x16 x17 . 0) (λ x16 x17 . λ x18 : ι → ι . λ x19 . 0) (λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0)) (λ x14 : (ι → ι → ι) → ι . 0)) (λ x13 : (ι → ι → ι) → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . x14 (x15 0)))) = Inj1 (setsum x5 0)) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 . Inj1 (x2 (λ x10 . Inj0 (x0 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0))) (λ x10 : (ι → ι → ι) → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0))) (setsum (x1 (λ x9 . x3 (λ x10 . x7)) (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 x11 . setsum 0 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj1 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0))) x5) = x6) ⟶ (∀ x4 x5 : (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 . x2 (λ x9 . x3 (λ x10 . 0) (Inj1 0)) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . x3 (λ x13 . 0) (setsum (Inj0 (x3 (λ x13 . 0) 0)) 0)) = x3 (λ x9 . x0 (λ x10 x11 . setsum 0 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 . 0) (λ x14 : (ι → ι → ι) → ι → ι → ι . λ x15 x16 : ι → ι . λ x17 . 0)) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . Inj0 (x2 (λ x13 . 0) (λ x13 : (ι → ι → ι) → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . x13 (λ x17 x18 . 0) 0 0)))) (x2 (λ x9 . x9) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . x10 (x0 (λ x13 x14 . x11 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x2 (λ x16 . 0) (λ x16 : (ι → ι → ι) → ι → ι → ι . λ x17 x18 : ι → ι . λ x19 . 0)))))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι → ι → ι . ∀ x7 : (ι → ι) → ι → ι → ι . x2 (λ x9 . setsum (x0 (λ x10 x11 . x1 (λ x12 x13 . x13) (λ x12 : (ι → ι → ι) → ι . x11)) (λ x10 x11 . λ x12 : ι → ι . λ x13 . x13) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0)) (x5 (x6 (λ x10 . λ x11 : ι → ι . x0 (λ x12 x13 . 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0)) (x0 (λ x10 x11 . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0)) (setsum 0 0) (x6 (λ x10 . λ x11 : ι → ι . 0) 0 0 0)) (λ x10 : ι → ι . λ x11 . Inj1 (x2 (λ x12 . 0) (λ x12 : (ι → ι → ι) → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . 0))) (λ x10 . 0) (setsum x9 0))) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . 0) = x4) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x1 (λ x9 x10 . setsum (Inj0 x6) (x2 (λ x11 . x0 (λ x12 x13 . Inj1 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . x12) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0)) (λ x11 : (ι → ι → ι) → ι → ι → ι . λ x12 x13 : ι → ι . λ x14 . x1 (λ x15 x16 . setsum 0 0) (λ x15 : (ι → ι → ι) → ι . 0)))) (λ x9 : (ι → ι → ι) → ι . 0) = setsum (Inj1 (x7 (λ x9 : (ι → ι) → ι → ι . 0))) (x3 (λ x9 . 0) 0)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 x10 . x6) (λ x9 : (ι → ι → ι) → ι . Inj1 (x9 (λ x10 x11 . x9 (λ x12 x13 . Inj0 0)))) = Inj1 (x2 (λ x9 . setsum 0 (x0 (λ x10 x11 . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . x3 (λ x13 . 0) 0))) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . x10 (x0 (λ x13 x14 . x2 (λ x15 . 0) (λ x15 : (ι → ι → ι) → ι → ι → ι . λ x16 x17 : ι → ι . λ x18 . 0)) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x2 (λ x16 . 0) (λ x16 : (ι → ι → ι) → ι → ι → ι . λ x17 x18 : ι → ι . λ x19 . 0)))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → ι → ι → ι . x0 (λ x9 x10 . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj0 (setsum (setsum x12 (x1 (λ x13 x14 . 0) (λ x13 : (ι → ι → ι) → ι . 0))) (setsum 0 (x0 (λ x13 x14 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0))))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . 0) = setsum (x3 (λ x9 . x5) 0) (x0 (λ x9 x10 . x3 (λ x11 . Inj1 (Inj0 0)) (x0 (λ x11 x12 . x2 (λ x13 . 0) (λ x13 : (ι → ι → ι) → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . 0)) (λ x11 x12 . λ x13 : ι → ι . λ x14 . x14) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x10))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . Inj1 (x2 (λ x12 . Inj0 0) (λ x12 : (ι → ι → ι) → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x0 (λ x9 x10 . x1 (λ x11 x12 . x1 (λ x13 x14 . Inj1 x11) (λ x13 : (ι → ι → ι) → ι . Inj0 (x1 (λ x14 x15 . 0) (λ x14 : (ι → ι → ι) → ι . 0)))) (λ x11 : (ι → ι → ι) → ι . x10)) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj0 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . x2 (λ x12 . 0) (λ x12 : (ι → ι → ι) → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . 0)) = x1 (λ x9 x10 . x0 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x2 (λ x14 . x3 (λ x15 . x2 (λ x16 . 0) (λ x16 : (ι → ι → ι) → ι → ι → ι . λ x17 x18 : ι → ι . λ x19 . 0)) x13) (λ x14 : (ι → ι → ι) → ι → ι → ι . λ x15 x16 : ι → ι . λ x17 . x1 (λ x18 x19 . 0) (λ x18 : (ι → ι → ι) → ι . x1 (λ x19 x20 . 0) (λ x19 : (ι → ι → ι) → ι . 0))))) (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 x11 . x1 (λ x12 x13 . x0 (λ x14 x15 . x0 (λ x16 x17 . 0) (λ x16 x17 . λ x18 : ι → ι . λ x19 . 0) (λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0)) (λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . x3 (λ x17 . 0) 0)) (λ x12 : (ι → ι → ι) → ι . 0)) (λ x10 x11 . λ x12 : ι → ι . λ x13 . x12 (x12 (x12 0))) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0))) ⟶ False (proof)
Theorem ab27c.. : ∀ x0 : ((((ι → ι → ι) → ι → ι) → ι) → ι) → ι → ι . ∀ x1 : (((ι → (ι → ι) → ι) → ι) → ι → ι) → ((((ι → ι) → ι) → (ι → ι) → ι) → ι → ι) → ι . ∀ x2 : (ι → ι → ι) → ((ι → ι → ι) → ((ι → ι) → ι) → ι) → ι → ι → (ι → ι) → ι . ∀ x3 : ((ι → ι) → ι) → ι → ((ι → ι → ι) → ι) → ι . (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x3 (λ x9 : ι → ι . x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 . Inj1 0) (λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . λ x11 . setsum (Inj1 0) (x10 (λ x12 : ι → ι . x2 (λ x13 x14 . 0) (λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι . 0) 0 0 (λ x13 . 0)) (λ x12 . x11)))) (x2 (λ x9 x10 . setsum x6 (setsum (x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . 0) 0) 0)) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . 0) (setsum 0 (x3 (λ x9 : ι → ι . x2 (λ x10 x11 . 0) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) 0 0 (λ x10 . 0)) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . 0) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 . 0)) (λ x9 : ι → ι → ι . 0))) (Inj1 (x7 x6)) (λ x9 . setsum (Inj1 (x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . λ x11 . 0))) (x3 (λ x10 : ι → ι . x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . 0)) (setsum 0 0) (λ x10 : ι → ι → ι . x7 0)))) (λ x9 : ι → ι → ι . 0) = x2 (λ x9 x10 . Inj0 (setsum (x2 (λ x11 x12 . setsum 0 0) (λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι . x9) (Inj1 0) 0 (λ x11 . 0)) (setsum 0 (Inj1 0)))) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . Inj0 (Inj1 (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . x12) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . x3 (λ x13 : ι → ι . 0) 0 (λ x13 : ι → ι → ι . 0))))) (Inj0 (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) (setsum (x4 0) (setsum 0 0)))) (setsum (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . setsum (x9 (λ x11 . λ x12 : ι → ι . 0)) (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . 0))) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 . x6)) (x3 (λ x9 : ι → ι . 0) 0 (λ x9 : ι → ι → ι . x3 (λ x10 : ι → ι . 0) (x2 (λ x10 x11 . 0) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) 0 0 (λ x10 . 0)) (λ x10 : ι → ι → ι . x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)))) (λ x9 . setsum (x7 x5) (x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 . x11) (λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . λ x11 . Inj0 0)))) ⟶ (∀ x4 : ι → (ι → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι → ι → ι) → ι . ∀ x7 . x3 (λ x9 : ι → ι . 0) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . x9 (λ x10 : ι → ι → ι . λ x11 . setsum x7 (x9 (λ x12 : ι → ι → ι . λ x13 . 0)))) (setsum (setsum (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) 0) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . x5) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)))) (λ x9 : ι → ι → ι . x0 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x12 : (ι → (ι → ι) → ι) → ι . λ x13 . x0 (λ x14 : ((ι → ι → ι) → ι → ι) → ι . 0) 0) (λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . λ x13 . Inj0 0)) (Inj1 (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . 0)))) 0) = Inj1 0) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι → ι . ∀ x7 : ι → ι . x2 (λ x9 x10 . x6 x9 x9) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . x9 (x10 (λ x11 . Inj1 (x3 (λ x12 : ι → ι . 0) 0 (λ x12 : ι → ι → ι . 0)))) 0) 0 (setsum 0 0) (λ x9 . x0 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . setsum (x6 0 0) (x10 (λ x11 : ι → ι → ι . λ x12 . Inj1 0))) (x6 (x6 (x7 0) 0) 0)) = x6 (setsum 0 (setsum (Inj0 (Inj1 0)) (Inj1 (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)))) x4) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . x2 (λ x9 x10 . 0) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . x9 (x9 (x0 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . 0) 0) (x7 (λ x12 . 0) 0 (λ x12 . 0) 0)) (x0 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . x3 (λ x13 : ι → ι . 0) 0 (λ x13 : ι → ι → ι . 0)) 0)) 0) x6 (setsum (Inj0 0) (Inj0 (x2 (λ x9 x10 . x10) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . Inj0 0) x5 x5 (λ x9 . 0)))) (λ x9 . 0) = x6) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . setsum (Inj0 0) (x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . 0) (x6 (setsum 0 0) (λ x11 : ι → ι . λ x12 . x2 (λ x13 x14 . 0) (λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι . 0) 0 0 (λ x13 . 0)) (λ x11 . 0)))) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 . 0) = x6 (setsum (Inj0 0) x4) (λ x9 : ι → ι . λ x10 . Inj1 (x6 (x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x12 : (ι → (ι → ι) → ι) → ι . λ x13 . 0) (λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . λ x13 . 0)) 0) (λ x11 : ι → ι . λ x12 . x12) (λ x11 . 0))) (λ x9 . 0)) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . Inj0 0) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . Inj1) = x7 (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . Inj1 (x9 (λ x11 . λ x12 : ι → ι . 0))) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 . x2 (λ x11 x12 . 0) (λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι . x1 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 . x12 (λ x15 . 0)) (λ x13 : ((ι → ι) → ι) → (ι → ι) → ι . λ x14 . x11 0 0)) 0 x6 (λ x11 . Inj1 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . setsum (x0 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . x2 (λ x13 x14 . 0) (λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι . 0) 0 0 (λ x13 . 0)) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . x0 (λ x13 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)) 0) (setsum (setsum 0 (x3 (λ x10 : ι → ι . 0) 0 (λ x10 : ι → ι → ι . 0))) 0)) 0 = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . x9 (λ x10 : ι → ι → ι . λ x11 . Inj0 (x10 (x0 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . 0) 0) 0))) (x3 (λ x9 : ι → ι . x2 (λ x10 x11 . x3 (λ x12 : ι → ι . x3 (λ x13 : ι → ι . 0) 0 (λ x13 : ι → ι → ι . 0)) (Inj1 0) (λ x12 : ι → ι → ι . 0)) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) (Inj0 (x0 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)) 0 (setsum (x7 0))) 0 (λ x9 : ι → ι → ι . x2 (λ x10 x11 . 0) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . setsum (x10 0 0) (x2 (λ x12 x13 . 0) (λ x12 : ι → ι → ι . λ x13 : (ι → ι) → ι . 0) 0 0 (λ x12 . 0))) x5 (Inj1 0) (λ x10 . Inj0 0))) = x3 (λ x9 : ι → ι . x7 (x7 (x9 (x7 0)))) (x6 (λ x9 . x2 (λ x10 x11 . x11) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) (setsum (x7 0) (x2 (λ x10 x11 . 0) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) 0 0 (λ x10 . 0))) 0 (λ x10 . x2 (λ x11 x12 . Inj0 0) (λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι . Inj1 0) (Inj0 0) 0 (λ x11 . setsum 0 0))) (x2 (λ x9 x10 . x10) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . x7 (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . 0))) (Inj0 0) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . x2 (λ x10 x11 . 0) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) 0 0 (λ x10 . 0)) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)) (λ x9 . Inj1 (setsum 0 0)))) (λ x9 : ι → ι → ι . Inj1 (setsum (x3 (λ x10 : ι → ι . setsum 0 0) (setsum 0 0) (λ x10 : ι → ι → ι . x3 (λ x11 : ι → ι . 0) 0 (λ x11 : ι → ι → ι . 0))) 0))) ⟶ False (proof)
Theorem f8888.. : ∀ x0 : (ι → ι → ι) → ι → ι → (ι → ι) → ι . ∀ x1 : (ι → (ι → ι → ι → ι) → ι → ι → ι → ι) → (ι → ι) → ι . ∀ x2 : ((ι → ι) → ι → ι) → (ι → (ι → ι → ι) → ι) → ι . ∀ x3 : ((ι → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι . (∀ x4 x5 x6 . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . setsum (x1 (λ x10 . λ x11 : ι → ι → ι → ι . λ x12 x13 x14 . setsum x12 (setsum 0 0)) (λ x10 . x6)) (x7 (λ x10 : ι → ι → ι . λ x11 : ι → ι . setsum (x11 0) (x3 (λ x12 : ι → ((ι → ι) → ι → ι) → ι . 0) 0)))) x4 = setsum (Inj0 0) (setsum (x7 (λ x9 : ι → ι → ι . λ x10 : ι → ι . x7 (λ x11 : ι → ι → ι . λ x12 : ι → ι . Inj0 0))) 0)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x9 (x7 (λ x10 x11 . setsum 0 0) (λ x10 : ι → ι . λ x11 . x1 (λ x12 . λ x13 : ι → ι → ι → ι . λ x14 x15 x16 . 0) (λ x12 . x11))) (λ x10 : ι → ι . x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . x11 (Inj0 0) (λ x12 : ι → ι . λ x13 . x1 (λ x14 . λ x15 : ι → ι → ι → ι . λ x16 x17 x18 . 0) (λ x14 . 0))))) (setsum (x0 (λ x9 x10 . x7 (λ x11 x12 . 0) (λ x11 : ι → ι . λ x12 . setsum 0 0)) (setsum (setsum 0 0) 0) 0 (λ x9 . setsum 0 0)) (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x6 (λ x10 . 0)) (x7 (λ x9 x10 . setsum 0 0) (λ x9 : ι → ι . λ x10 . x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 x15 . 0) (λ x11 . 0))))) = setsum (x0 (λ x9 x10 . Inj0 (setsum x10 0)) (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x9 0 (λ x10 : ι → ι . λ x11 . 0)) 0) (Inj1 (x2 (λ x9 : ι → ι . λ x10 . x6 (λ x11 . 0)) (λ x9 . λ x10 : ι → ι → ι . x10 0 0))) (λ x9 . x7 (λ x10 x11 . x10) (λ x10 : ι → ι . setsum (Inj1 0)))) 0) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → ι . λ x10 . x9 0) (λ x9 . λ x10 : ι → ι → ι . x9) = x4) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : ((ι → ι) → ι → ι) → ι . x2 (λ x9 : ι → ι . λ x10 . x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 x15 . 0) (λ x11 . 0)) (λ x9 . λ x10 : ι → ι → ι . x6 (x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 x15 . x12 0 0 x14) (λ x11 . x9)) (x2 (λ x11 : ι → ι . λ x12 . Inj1 0) (λ x11 . λ x12 : ι → ι → ι . setsum x9 (x2 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . λ x14 : ι → ι → ι . 0)))) 0 (Inj0 (Inj0 (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . 0) 0)))) = x6 (x6 0 0 (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . Inj0 (setsum 0 0)) (λ x9 . 0)) (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . x1 (λ x14 . λ x15 : ι → ι → ι → ι . λ x16 x17 x18 . 0) (λ x14 . x2 (λ x15 : ι → ι . λ x16 . 0) (λ x15 . λ x16 : ι → ι → ι . 0))) (λ x9 . 0))) (x5 (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x6 0 (x7 (λ x10 : ι → ι . λ x11 . 0)) (Inj0 0) (x5 0 0 0)) 0) x4 0) (Inj1 0) (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . 0) (x6 (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . setsum 0 0) (λ x9 . x5 0 0 0)) (setsum (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . 0) 0) (x7 (λ x9 : ι → ι . λ x10 . 0))) (setsum (x6 0 0 0 0) (x5 0 0 0)) 0))) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . setsum (x3 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . x3 (λ x15 : ι → ((ι → ι) → ι → ι) → ι . x0 (λ x16 x17 . 0) 0 0 (λ x16 . 0)) 0) (setsum (setsum 0 0) x12)) (x0 (λ x14 x15 . x3 (λ x16 : ι → ((ι → ι) → ι → ι) → ι . x15) (Inj0 0)) 0 0 (λ x14 . x2 (λ x15 : ι → ι . λ x16 . x3 (λ x17 : ι → ((ι → ι) → ι → ι) → ι . 0) 0) (λ x15 . λ x16 : ι → ι → ι . x3 (λ x17 : ι → ((ι → ι) → ι → ι) → ι . 0) 0)))) (λ x9 . 0) = Inj0 (x4 (λ x9 . λ x10 : ι → ι . Inj1 0) (λ x9 : ι → ι . λ x10 . x6 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι . ∀ x7 . x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . Inj0 (Inj1 (x3 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . x11) (x0 (λ x14 x15 . 0) 0 0 (λ x14 . 0))))) (λ x9 . x1 (λ x10 . λ x11 : ι → ι → ι → ι . λ x12 x13 x14 . setsum (x11 0 0 (Inj1 0)) x12) (setsum (Inj1 (x1 (λ x10 . λ x11 : ι → ι → ι → ι . λ x12 x13 x14 . 0) (λ x10 . 0))))) = setsum 0 0) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x6 : (ι → ι) → (ι → ι → ι) → ι . ∀ x7 . x0 (λ x9 x10 . x10) (Inj1 (x2 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . λ x10 : ι → ι → ι . Inj1 (x2 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . λ x12 : ι → ι → ι . 0))))) (x0 (λ x9 x10 . 0) (Inj1 (setsum 0 (x0 (λ x9 x10 . 0) 0 0 (λ x9 . 0)))) x4 (λ x9 . x3 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (x0 (λ x10 x11 . 0) (x0 (λ x10 x11 . 0) 0 0 (λ x10 . 0)) (setsum 0 0) (λ x10 . x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 x15 . 0) (λ x11 . 0))))) (λ x9 . x9) = Inj0 (x0 (λ x9 x10 . x7) (setsum (setsum (x0 (λ x9 x10 . 0) 0 0 (λ x9 . 0)) (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . 0) (λ x9 . 0))) 0) (setsum (setsum (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0)) 0) (setsum x4 0)) (λ x9 . x6 (λ x10 . 0) (λ x10 x11 . x10)))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 x10 . x10) 0 (x0 (λ x9 x10 . x9) x5 (Inj0 x7) (λ x9 . x7)) (λ x9 . x7) = Inj0 (x2 (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . x10) x7) (λ x9 . λ x10 : ι → ι → ι . 0))) ⟶ False (proof)
Theorem cd8e8.. : ∀ x0 : (ι → (ι → ι) → ι) → ι → ι → (ι → ι) → ι . ∀ x1 : (ι → ι) → ((ι → ι → ι) → ι) → ι . ∀ x2 : (ι → ι → (ι → ι → ι) → (ι → ι) → ι) → (ι → ι) → ((ι → ι) → ι) → ι . ∀ x3 : (ι → ι) → ((ι → ι) → (ι → ι → ι) → ι) → ι → ι . (∀ x4 : (ι → ι) → ι → ι → ι → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . 0) (x7 (λ x9 : ι → ι → ι . setsum (x9 0 (x7 (λ x10 : ι → ι → ι . 0))) (x7 (λ x10 : ι → ι → ι . x2 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) (λ x11 . 0) (λ x11 : ι → ι . 0))))) = x7 (λ x9 : ι → ι → ι . setsum (Inj0 (x7 (λ x10 : ι → ι → ι . setsum 0 0))) (x3 (λ x10 . x7 (λ x11 : ι → ι → ι . 0)) (λ x10 : ι → ι . λ x11 : ι → ι → ι . 0) (x9 (Inj0 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 . x7) (λ x9 : ι → ι . λ x10 : ι → ι → ι . x9 x6) x7 = x7) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (λ x9 . x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 : ι → ι → ι . x9) x9) (λ x9 : ι → ι . setsum (x0 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . x0 (λ x13 . λ x14 : ι → ι . 0) 0 0 (λ x13 . 0)) (λ x12 : ι → ι . λ x13 : ι → ι → ι . setsum 0 0) (Inj0 0)) (x0 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . 0) 0) 0 (Inj1 0) (λ x10 . Inj1 0)) (Inj1 (setsum 0 0)) (λ x10 . x10)) 0) = setsum x5 0) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x7 . x2 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (λ x9 . x1 (λ x10 . x10) (λ x10 : ι → ι → ι . x10 0 (x10 (x1 (λ x11 . 0) (λ x11 : ι → ι → ι . 0)) x7))) (λ x9 : ι → ι . x9 (x1 (λ x10 . 0) (λ x10 : ι → ι → ι . x6 (λ x11 : (ι → ι) → ι → ι . λ x12 . x1 (λ x13 . 0) (λ x13 : ι → ι → ι . 0))))) = setsum (x2 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . setsum 0 (setsum (x11 0 0) x9)) (λ x9 . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 . setsum (x10 (λ x12 . 0) 0) 0)) (λ x9 : ι → ι . x7)) (x1 (λ x9 . setsum x7 0) (λ x9 : ι → ι → ι . x9 (x9 (Inj1 0) 0) (x1 (λ x10 . x7) (λ x10 : ι → ι → ι . x10 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 . setsum 0 (Inj0 (x6 (λ x10 : ι → ι . x6 (λ x11 : ι → ι . 0) 0 (λ x11 . 0) 0) (Inj1 0) (λ x10 . x10) x7))) (λ x9 : ι → ι → ι . 0) = x4 (x6 (λ x9 : ι → ι . x9 (setsum 0 0)) x5 (λ x9 . x2 (λ x10 x11 . λ x12 : ι → ι → ι . λ x13 : ι → ι . 0) (λ x10 . x2 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) (λ x11 . x2 (λ x12 x13 . λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) (λ x12 . 0) (λ x12 : ι → ι . 0)) (λ x11 : ι → ι . setsum 0 0)) (λ x10 : ι → ι . x0 (λ x11 . λ x12 : ι → ι . x0 (λ x13 . λ x14 : ι → ι . 0) 0 0 (λ x13 . 0)) 0 (x2 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) (λ x11 . 0) (λ x11 : ι → ι . 0)) (λ x11 . x9))) (x4 (Inj1 (setsum 0 0))))) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x5 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x1 (λ x9 . Inj0 0) (λ x9 : ι → ι → ι . Inj0 (Inj0 (x5 (λ x10 x11 x12 . x11) (λ x10 : ι → ι . x10 0) (Inj0 0)))) = Inj1 (Inj1 (x2 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . x9) (λ x9 . Inj1 (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 : ι → ι → ι . 0) 0)) (λ x9 : ι → ι . x6 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 x7 . x0 (λ x9 . λ x10 : ι → ι . x9) 0 0 (λ x9 . x6) = x6) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 . λ x10 : ι → ι . setsum (x2 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) x10 (λ x11 : ι → ι . x1 (λ x12 . x12) (λ x12 : ι → ι → ι . x2 (λ x13 x14 . λ x15 : ι → ι → ι . λ x16 : ι → ι . 0) (λ x13 . 0) (λ x13 : ι → ι . 0)))) 0) (Inj0 (x1 (λ x9 . x6) (λ x9 : ι → ι → ι . x0 (λ x10 . λ x11 : ι → ι . x7) (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 : ι → ι → ι . 0) 0) (Inj0 0) (λ x10 . 0)))) 0 (λ x9 . setsum x9 x6) = setsum (x4 (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . 0) (setsum 0 (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . 0) 0)))) (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . x1 (λ x11 . x1 (λ x12 . x11) (λ x12 : ι → ι → ι . x11)) (λ x11 : ι → ι → ι . x2 (λ x12 x13 . λ x14 : ι → ι → ι . λ x15 : ι → ι . x0 (λ x16 . λ x17 : ι → ι . 0) 0 0 (λ x16 . 0)) (λ x12 . x12) (λ x12 : ι → ι . 0))) 0)) ⟶ False (proof)
Theorem cd23f.. : ∀ x0 : (ι → ι) → ι → (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x1 : ((((ι → ι) → ι) → ι) → ι) → (ι → ι) → ι . ∀ x2 : ((((ι → ι) → ι → ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x3 (λ x9 . x1 (λ x10 : ((ι → ι) → ι) → ι . 0) (λ x10 . x0 (λ x11 . x2 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x13 . Inj1 0) (setsum 0 0)) x10 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 x12 . 0))) (Inj1 (setsum 0 (x0 (λ x9 . x2 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . 0) 0) x6 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0)))) = Inj0 (setsum (setsum (x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . x2 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . 0) 0) (Inj1 0)) x6) (x3 (λ x9 . x2 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . 0) x6) (x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x6 : (ι → ι → ι → ι) → ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x9 . Inj0 (x2 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . x1 (λ x12 : ((ι → ι) → ι) → ι . 0) (λ x12 . x0 (λ x13 . 0) 0 (λ x13 : (ι → ι) → ι → ι . 0) (λ x13 x14 . 0))) x9)) 0 = x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . setsum 0 0) x4) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . ∀ x7 . x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . 0) (Inj0 (x6 (λ x9 : (ι → ι) → ι . setsum (Inj1 0) x7) (λ x9 . x9))) = x6 (λ x9 : (ι → ι) → ι . setsum 0 0) (λ x9 . 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . 0) 0 = Inj1 0) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x1 (λ x9 : ((ι → ι) → ι) → ι . 0) (λ x9 . 0) = setsum (x0 (λ x9 . Inj0 0) (setsum 0 x6) (λ x9 : (ι → ι) → ι → ι . x7 (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . x12)) (λ x9 x10 . Inj1 (x7 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . x0 (λ x14 . 0) 0 (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 x15 . 0))))) (x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . x10) 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x1 (λ x9 : ((ι → ι) → ι) → ι . Inj0 (Inj1 0)) (λ x9 . x3 (λ x10 . x0 (λ x11 . 0) (Inj0 (x0 (λ x11 . 0) 0 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 x12 . 0))) (λ x11 : (ι → ι) → ι → ι . Inj1 0) (λ x11 x12 . x2 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x14 . x13 (λ x15 : ι → ι . λ x16 x17 . 0) 0) x9)) (setsum (Inj0 x9) (setsum (setsum 0 0) (Inj0 0)))) = setsum (x1 (λ x9 : ((ι → ι) → ι) → ι . setsum (Inj0 0) 0) (λ x9 . x7 (x0 (λ x10 . x7 0 0) (setsum 0 0) (λ x10 : (ι → ι) → ι → ι . x0 (λ x11 . 0) 0 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 x12 . 0)) (λ x10 x11 . Inj1 0)) (setsum (setsum 0 0) (Inj0 0)))) (x1 (λ x9 : ((ι → ι) → ι) → ι . 0) (λ x9 . 0))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x0 (x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . x3 (λ x11 . x9 (λ x12 : ι → ι . λ x13 x14 . setsum 0 0) 0) (Inj1 0))) 0 (λ x9 : (ι → ι) → ι → ι . x5) (λ x9 x10 . setsum (x0 (λ x11 . setsum (x1 (λ x12 : ((ι → ι) → ι) → ι . 0) (λ x12 . 0)) (x0 (λ x12 . 0) 0 (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 x13 . 0))) (x1 (λ x11 : ((ι → ι) → ι) → ι . x11 (λ x12 : ι → ι . 0)) (λ x11 . Inj1 0)) (λ x11 : (ι → ι) → ι → ι . setsum 0 (x7 0 (λ x12 : ι → ι . 0) (λ x12 . 0))) (λ x11 x12 . 0)) (x2 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . x12) (Inj1 (setsum 0 0)))) = Inj0 (Inj1 (x4 (x0 (λ x9 . x7 0 (λ x10 : ι → ι . 0) (λ x10 . 0)) 0 (λ x9 : (ι → ι) → ι → ι . Inj1 0) (λ x9 x10 . x9)) (Inj0 x5)))) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . x0 (λ x9 . setsum x7 0) (x3 (λ x9 . 0) x7) (λ x9 : (ι → ι) → ι → ι . x7) (λ x9 x10 . 0) = x3 (λ x9 . x1 (λ x10 : ((ι → ι) → ι) → ι . x10 (λ x11 : ι → ι . 0)) (λ x10 . x9)) (setsum (x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . setsum 0 (x2 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . 0) 0)) (Inj0 (setsum 0 0))) (setsum x5 (setsum (Inj0 0) 0)))) ⟶ False (proof)
Theorem 8c027.. : ∀ x0 : ((ι → ι → ι) → ι) → ι → ι . ∀ x1 : (ι → (ι → ι) → ι) → ι → ι . ∀ x2 : (ι → ι) → ι → ι . ∀ x3 : (ι → ι) → ((ι → ι) → ((ι → ι) → ι → ι) → ι) → ι . (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 : ι → ι . x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . Inj1 0) = x4) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x3 x7 (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . x0 (λ x12 : ι → ι → ι . 0) (x3 (λ x12 . x3 (λ x13 . 0) (λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . 0)) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . x13 (λ x14 . 0) 0))) (setsum (Inj0 (x1 (λ x11 . λ x12 : ι → ι . 0) 0)) (x3 (λ x11 . setsum 0 0) (λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . x1 (λ x13 . λ x14 : ι → ι . 0) 0)))) = x7 x4) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . x2 (λ x9 . setsum 0 0) x5 = x5) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : ((ι → ι) → ι) → ι → ι . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . x2 (λ x9 . setsum (x2 (λ x10 . x1 (λ x11 . λ x12 : ι → ι . 0) x9) (x2 (λ x10 . 0) 0)) (setsum (Inj0 x9) x9)) 0 = Inj1 x4) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 x7 . x1 (λ x9 . λ x10 : ι → ι . 0) (setsum (setsum 0 0) (x4 x7)) = setsum 0 (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . x7))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι . x1 (λ x9 . λ x10 : ι → ι . 0) (x7 (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . x0 (λ x11 : ι → ι → ι . 0) (x9 0))) (λ x9 : ι → ι . setsum (Inj1 (x7 0 (λ x10 : ι → ι . 0) 0)) (x1 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . 0)) x5)) x5) = setsum x4 0) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι → ι → ι . ∀ x7 : ι → ι → ι → ι → ι . x0 (λ x9 : ι → ι → ι . x3 (λ x10 . x1 (λ x11 . λ x12 : ι → ι . x0 (λ x13 : ι → ι → ι . 0) (Inj1 0)) 0) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . setsum (x7 (x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . 0)) (x10 0) (x10 0) (x2 (λ x12 . 0) 0)) (Inj0 (Inj0 0)))) 0 = Inj1 (x7 0 0 (Inj0 0) 0)) ⟶ (∀ x4 : (ι → ι) → ι → (ι → ι) → ι . ∀ x5 x6 x7 . x0 (λ x9 : ι → ι → ι . x3 (λ x10 . x9 (x2 (λ x11 . 0) (x0 (λ x11 : ι → ι → ι . 0) 0)) (Inj0 x10)) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . x2 (λ x12 . x2 (λ x13 . Inj1 0) 0) 0)) (x1 (λ x9 . λ x10 : ι → ι . x1 (λ x11 . λ x12 : ι → ι . 0) (x1 (λ x11 . λ x12 : ι → ι . x9) 0)) x7) = setsum (x4 (λ x9 . 0) x5 (λ x9 . 0)) x7) ⟶ False (proof)
Theorem 381ed.. : ∀ x0 : ((ι → ι) → (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι → ι) → ι → ι . ∀ x1 x2 : (ι → ι) → ι → ι . ∀ x3 : (ι → ι) → (ι → ι) → ι . (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x7 . x3 (λ x9 . x2 (λ x10 . x7) 0) (λ x9 . x7) = x2 (λ x9 . x5) (setsum (setsum (Inj0 0) 0) x4)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι . x3 (λ x9 . x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x3 (λ x15 . x15) (λ x15 . Inj1 (x1 (λ x16 . 0) 0))) 0) (λ x9 . x7 (λ x10 . λ x11 : ι → ι . 0)) = x7 (λ x9 . λ x10 : ι → ι . Inj0 (x6 x9))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x9 . x9) (setsum x6 (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . setsum 0 0) 0)) = x5 x4) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι → ι → ι) → ι → ι . x2 (λ x9 . 0) (Inj1 (x2 (λ x9 . x7 (λ x10 x11 x12 . setsum 0 0) (Inj1 0)) (x2 (λ x9 . x9) (Inj0 0)))) = x7 (λ x9 x10 . x0 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . Inj1 (Inj0 x15))) 0) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι → ι → ι) → ι → ι . x1 (λ x9 . x5) 0 = Inj1 x6) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . x1 (λ x9 . x3 (λ x10 . 0) (λ x10 . x9)) (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (x4 (setsum (x4 0 0) 0) (Inj1 x6))) = x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x12 (x3 (λ x14 . x0 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι) → ι . λ x17 . λ x18 : ι → ι . λ x19 . Inj0 0) (x12 0)) (λ x14 . 0))) (x3 (λ x9 . x9) (λ x9 . x9))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x13) 0 = Inj0 x6) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 . x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (setsum (setsum x5 (x4 (λ x9 : (ι → ι) → ι . x6 (λ x10 : (ι → ι) → ι . 0)))) (Inj0 0)) = x5) ⟶ False (proof)
Theorem f02bb.. : ∀ x0 : (ι → ι → (ι → ι → ι) → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x1 : ((ι → ((ι → ι) → ι → ι) → ι → ι) → ι) → ι → ((ι → ι) → ι → ι → ι) → ι . ∀ x2 : (ι → ι → ι) → ι → ι → ((ι → ι) → ι → ι) → ι . ∀ x3 : (ι → ι) → (ι → ι) → ι . (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 . 0) (λ x9 . setsum (Inj1 0) (Inj1 0)) = x4) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . x3 (λ x10 . x10) (λ x10 . 0)) (λ x9 . 0) = x3 (λ x9 . setsum 0 0) (λ x9 . Inj0 x7)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι . ∀ x7 . x2 (λ x9 x10 . x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 . x11) (λ x11 : ι → ι . x11 (Inj1 0)) (λ x11 . 0)) (Inj0 0) x4 (λ x9 : ι → ι . λ x10 . 0) = x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . Inj1 (x0 (λ x13 x14 . λ x15 : ι → ι → ι . λ x16 . setsum 0 (x1 (λ x17 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x17 : ι → ι . λ x18 x19 . 0))) (λ x13 : ι → ι . x11 (x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x14 : ι → ι . λ x15 x16 . 0)) (Inj0 0)) (λ x13 . Inj0 x12))) (λ x9 : ι → ι . x6 (setsum (x6 (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x10 : ι → ι . λ x11 x12 . 0)) (Inj1 0) x5) (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x10 : ι → ι . λ x11 x12 . x12))) 0 (x9 (Inj1 (Inj1 0)))) (λ x9 . Inj0 (x2 (λ x10 x11 . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) (x2 (λ x12 x13 . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0)) (λ x12 : ι → ι . λ x13 x14 . setsum 0 0)) x7 0 (λ x10 : ι → ι . λ x11 . x11)))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι → ι) → (ι → ι → ι) → (ι → ι) → ι . x2 (λ x9 . Inj1) x6 0 (λ x9 : ι → ι . Inj1) = setsum 0 x5) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . setsum (Inj1 (setsum x5 0)) x7) 0 (λ x9 : ι → ι . λ x10 x11 . x9 0) = x4) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . Inj0 0) (x2 (λ x9 x10 . setsum (x2 (λ x11 x12 . x10) (x2 (λ x11 x12 . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0)) (x7 (λ x11 : (ι → ι) → ι → ι . 0) 0 0) (λ x11 : ι → ι . λ x12 . x0 (λ x13 x14 . λ x15 : ι → ι → ι . λ x16 . 0) (λ x13 : ι → ι . 0) (λ x13 . 0))) (Inj1 (Inj0 0))) (x5 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . x7 (λ x11 : (ι → ι) → ι → ι . Inj1 0) (x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x11 : ι → ι . λ x12 x13 . 0)) 0)) x6 (λ x9 : ι → ι . λ x10 . 0)) (λ x9 : ι → ι . λ x10 x11 . x9 0) = setsum (Inj1 (x5 (λ x9 : ι → ι . x2 (λ x10 x11 . x11) (x0 (λ x10 x11 . λ x12 : ι → ι → ι . λ x13 . 0) (λ x10 : ι → ι . 0) (λ x10 . 0)) (x5 (λ x10 : ι → ι . 0) (λ x10 : ι → ι . λ x11 . 0)) (λ x10 : ι → ι . λ x11 . setsum 0 0)) (λ x9 : ι → ι . λ x10 . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . x10) (x3 (λ x11 . 0) (λ x11 . 0)) (λ x11 : ι → ι . λ x12 x13 . Inj0 0)))) 0) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . setsum 0 (x2 (λ x13 x14 . x14) x12 0 (λ x13 : ι → ι . λ x14 . Inj1 0))) (λ x9 : ι → ι . Inj0 x5) (λ x9 . 0) = Inj1 (x7 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . Inj1 (setsum x11 x11)))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι . x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . x11 (Inj1 (x2 (λ x13 x14 . setsum 0 0) (x3 (λ x13 . 0) (λ x13 . 0)) 0 (λ x13 : ι → ι . λ x14 . x2 (λ x15 x16 . 0) 0 0 (λ x15 : ι → ι . λ x16 . 0)))) (x2 (λ x13 x14 . x2 (λ x15 x16 . x0 (λ x17 x18 . λ x19 : ι → ι → ι . λ x20 . 0) (λ x17 : ι → ι . 0) (λ x17 . 0)) 0 0 (λ x15 : ι → ι . λ x16 . Inj1 0)) 0 (Inj0 (x1 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x13 : ι → ι . λ x14 x15 . 0))) (λ x13 : ι → ι . λ x14 . setsum x12 (setsum 0 0)))) (λ x9 : ι → ι . setsum (x2 (λ x10 x11 . x2 (λ x12 x13 . Inj0 0) x10 (x9 0) (λ x12 : ι → ι . λ x13 . Inj0 0)) x6 (Inj0 (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x10 : ι → ι . λ x11 x12 . 0))) (λ x10 : ι → ι . λ x11 . x9 (Inj0 0))) (x9 (setsum (x3 (λ x10 . 0) (λ x10 . 0)) (setsum 0 0)))) (λ x9 . Inj0 (x7 0 (λ x10 : ι → ι . x6))) = setsum (Inj0 (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x7 (x2 (λ x12 x13 . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0)) (λ x12 : ι → ι . x0 (λ x13 x14 . λ x15 : ι → ι → ι . λ x16 . 0) (λ x13 : ι → ι . 0) (λ x13 . 0))))) (setsum (x3 (λ x9 . 0) (λ x9 . setsum x6 (Inj1 0))) 0)) ⟶ False (proof)
Theorem 1cbc7.. : ∀ x0 : (((ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι → ι → ι → ι . ∀ x1 : (ι → ι → ι) → (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x2 : (ι → (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι → ι) → (ι → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x3 : ((ι → ι) → ι → ι) → ((ι → (ι → ι) → ι → ι) → ι) → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : (ι → ι) → ι . x3 (λ x9 : ι → ι . λ x10 . setsum (x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 . Inj1 (Inj0 0)) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0)) 0) (λ x9 : ι → (ι → ι) → ι → ι . 0) = Inj0 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x3 (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ι → ι . λ x12 . setsum (x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . x2 (λ x18 . λ x19 : ((ι → ι) → ι → ι) → ι . λ x20 . λ x21 : ι → ι . λ x22 . 0) (λ x18 . 0) (λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . λ x20 . 0)) (λ x13 . Inj1 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . setsum 0 0)) (x0 (λ x13 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x2 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 . 0) (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . 0)) (setsum 0 0) (x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0)) 0 0)) (λ x11 : ι → (ι → ι) → ι → ι . x9 (x0 (λ x12 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (x1 (λ x12 x13 . 0) (λ x12 : (ι → ι) → ι . λ x13 x14 . 0)) (x3 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . 0)) (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 . 0) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . 0)) (Inj1 0)))) (λ x9 : ι → (ι → ι) → ι → ι . 0) = setsum (Inj0 (Inj0 (setsum 0 x7))) (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . setsum (setsum x11 (setsum 0 0)) (x1 (λ x14 x15 . x15) (λ x14 : (ι → ι) → ι . λ x15 x16 . x14 (λ x17 . 0)))) (λ x9 . Inj0 (Inj0 x7)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x1 (λ x12 x13 . setsum (Inj1 0) (x0 (λ x14 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0)) (λ x12 : (ι → ι) → ι . λ x13 x14 . x14)))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι) → ι) → ι . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) (x0 (λ x14 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum 0 0) x11 x11 (setsum (setsum 0 0) 0)) (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . x15 (x14 (λ x17 . 0) 0))) (λ x9 . x6 (Inj0 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x10 (setsum 0 (x7 (λ x12 : ι → ι . Inj1 0)))) = x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj1 0) (λ x9 . setsum (x0 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum 0 (x3 (λ x11 : ι → ι . λ x12 . 0) (λ x11 : ι → (ι → ι) → ι → ι . 0))) 0 0 (x3 (λ x10 : ι → ι . λ x11 . x7 (λ x12 : ι → ι . 0)) (λ x10 : ι → (ι → ι) → ι → ι . x6 0)) (x6 0)) (x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (x0 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0) (x6 0) (setsum 0 0) (x6 0)) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x11))) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . Inj1)) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x9 . setsum 0 x6) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum 0 (setsum (x3 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . 0)) 0)) = setsum (x0 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x5 (x5 (x1 (λ x10 x11 . 0) (λ x10 : (ι → ι) → ι . λ x11 x12 . 0)))) 0 (Inj0 (x4 x6)) (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι) → ι . λ x10 x11 . x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . x15 0) (λ x12 . x1 (λ x13 x14 . 0) (λ x13 : (ι → ι) → ι . λ x14 x15 . 0)) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . x14))) (x5 0)) (Inj1 (x7 (λ x9 : (ι → ι) → ι . x1 (λ x10 x11 . x3 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . 0)) (λ x10 : (ι → ι) → ι . λ x11 x12 . x0 (λ x13 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0))))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 x10 . x10) (λ x9 : (ι → ι) → ι . λ x10 x11 . 0) = x5 (x1 (λ x9 x10 . x0 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x9) (Inj1 (Inj1 0)) (x1 (λ x11 x12 . x9) (λ x11 : (ι → ι) → ι . λ x12 x13 . Inj1 0)) (setsum (x0 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0) x7) (Inj1 0)) (λ x9 : (ι → ι) → ι . λ x10 x11 . Inj0 x7)) (λ x9 x10 . Inj0 (x0 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (x3 (λ x11 : ι → ι . λ x12 . x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0)) (λ x11 : ι → (ι → ι) → ι → ι . 0)) (x1 (λ x11 x12 . x11) (λ x11 : (ι → ι) → ι . λ x12 x13 . 0)) 0 (Inj1 0))) (λ x9 . Inj1 (setsum (Inj1 (x5 0 (λ x10 x11 . 0) (λ x10 . 0) 0)) x6)) (x4 (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x13) (λ x9 . x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 x16 . 0) (λ x15 : (ι → ι) → ι . λ x16 x17 . 0)) (λ x10 . x1 (λ x11 x12 . 0) (λ x11 : (ι → ι) → ι . λ x12 x13 . 0)) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x1 (λ x12 x13 . x13) (λ x12 : (ι → ι) → ι . λ x13 x14 . setsum 0 0))) (λ x9 x10 . x10))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι) → (ι → ι) → ι . x1 (λ x9 x10 . x6 (x7 (λ x11 x12 . 0) (λ x11 . x9)) (λ x11 : ι → ι . Inj0 (setsum x10 (x3 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . 0))))) (λ x9 : (ι → ι) → ι . λ x10 x11 . setsum (x9 (λ x12 . x9 (λ x13 . x1 (λ x14 x15 . 0) (λ x14 : (ι → ι) → ι . λ x15 x16 . 0)))) (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 . x3 (λ x13 : ι → ι . λ x14 . x13 0) (λ x13 : ι → (ι → ι) → ι → ι . x0 (λ x14 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0)) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . x1 (λ x15 x16 . setsum 0 0) (λ x15 : (ι → ι) → ι . λ x16 x17 . x17)))) = x6 (setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x3 (λ x14 : ι → ι . λ x15 . Inj1 0) (λ x14 : ι → (ι → ι) → ι → ι . x1 (λ x15 x16 . 0) (λ x15 : (ι → ι) → ι . λ x16 x17 . 0))) (λ x9 . Inj1 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x3 (λ x12 : ι → ι . λ x13 . x2 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 . 0) (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . 0)) (λ x12 : ι → (ι → ι) → ι → ι . setsum 0 0))) (Inj1 (setsum (setsum 0 0) (x5 (λ x9 . 0))))) (λ x9 : ι → ι . setsum (x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 x16 . Inj0 0) (λ x15 : (ι → ι) → ι . λ x16 x17 . setsum 0 0)) (λ x10 . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . x16 0) (λ x13 . x1 (λ x14 x15 . 0) (λ x14 : (ι → ι) → ι . λ x15 x16 . 0)) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0))) 0)) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 x5 = Inj0 x7) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι → ι) → ι . ∀ x7 . x0 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x13 (x13 (x3 (λ x15 : ι → ι . λ x16 . 0) (λ x15 : ι → (ι → ι) → ι → ι . 0)))) (λ x10 . setsum 0 0) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x3 (λ x13 : ι → ι . λ x14 . setsum x14 x14) (λ x13 : ι → (ι → ι) → ι → ι . x11 (setsum 0 0)))) 0 0 (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj1 0) (λ x9 . setsum (Inj0 (Inj0 0)) (x5 (λ x10 : (ι → ι) → ι . setsum 0 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x0 (λ x12 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . Inj0 0) (λ x13 . Inj0 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0)) 0 (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . x1 (λ x17 x18 . 0) (λ x17 : (ι → ι) → ι . λ x18 x19 . 0)) (λ x12 . x10 0) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . Inj1 0)) (x3 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . x10 0)) (x10 (setsum 0 0)))) (setsum (Inj1 (x5 (λ x9 : (ι → ι) → ι . x1 (λ x10 x11 . 0) (λ x10 : (ι → ι) → ι . λ x11 x12 . 0)))) (x1 (λ x9 x10 . setsum (x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0)) (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι) → ι . λ x12 x13 . 0))) (λ x9 : (ι → ι) → ι . λ x10 x11 . x1 (λ x12 x13 . x0 (λ x14 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0) (λ x12 : (ι → ι) → ι . λ x13 x14 . 0)))) = Inj0 (Inj0 (Inj0 0))) ⟶ False (proof)
Theorem aefa3.. : ∀ x0 : (ι → ι) → (ι → ι) → ι . ∀ x1 x2 : (ι → ι) → ι → ι . ∀ x3 : (((((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι . (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → (ι → ι) → ι → ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x3 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . x9 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0) (λ x10 : ι → ι . λ x11 . 0)) 0 = x5 (λ x9 x10 x11 . 0) (λ x9 . x3 (λ x10 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . Inj1 (setsum 0 (Inj0 0))) (x6 (x1 (λ x10 . x3 (λ x11 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) 0) (x1 (λ x10 . 0) 0)) (setsum (x3 (λ x10 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) 0) 0))) 0 (x3 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) 0)) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : ((ι → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 . x3 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . x1 (λ x10 . 0) (x1 (λ x10 . Inj0 0) x7)) (x5 (x6 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x7) (setsum 0))) = setsum (x4 (Inj0 (setsum (x6 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) (λ x9 . 0)) (x1 (λ x9 . 0) 0)))) (Inj1 (Inj0 (x4 (x6 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) (λ x9 . 0)))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → (ι → ι → ι) → ι . x2 (λ x9 . setsum (x0 (λ x10 . x3 (λ x11 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . x11 (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x12 : ι → ι . λ x13 . 0)) (Inj1 0)) (λ x10 . Inj1 0)) (x1 (λ x10 . x10) x9)) x4 = Inj1 (x3 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (setsum (x3 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (x1 (λ x9 . 0) 0)) x5))) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 . x2 (λ x10 . x7) (Inj0 (x1 (λ x10 . setsum 0 0) x9))) (setsum 0 0) = Inj1 x6) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 . x2 (λ x10 . x9) (Inj0 (x7 (λ x10 . setsum 0 0)))) 0 = x2 (λ x9 . x2 (λ x10 . x9) 0) x4) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 . x0 (λ x10 . x6 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x10) (λ x11 : ι → ι . x7 0) (λ x11 . setsum 0 (x3 (λ x12 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) 0))) (λ x10 . x2 (λ x11 . x7 0) (x2 (λ x11 . x11) (x0 (λ x11 . 0) (λ x11 . 0))))) 0 = setsum 0 0) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x0 (λ x9 . Inj1 (x3 (λ x10 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . x6) 0)) (λ x9 . setsum x6 (x2 (λ x10 . setsum 0 x9) 0)) = Inj1 0) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ((ι → ι) → (ι → ι) → ι → ι) → ι . x0 (λ x9 . x9) (λ x9 . x7 (λ x10 x11 : ι → ι . λ x12 . setsum x12 (x2 (λ x13 . x3 (λ x14 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) 0) (Inj0 0)))) = x7 (λ x9 x10 : ι → ι . λ x11 . x10 (x3 (λ x12 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (Inj0 (x7 (λ x12 x13 : ι → ι . λ x14 . 0)))))) ⟶ False (proof)
Theorem 22432.. : ∀ x0 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → (((ι → ι) → ι) → ι) → ι . ∀ x1 : (ι → ι) → (ι → ι) → ι → ι → (ι → ι) → ι . ∀ x2 : ((ι → (ι → ι) → ι) → (ι → ι) → ((ι → ι) → ι → ι) → ι) → ι → (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι . ∀ x3 : (((((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι) → ι) → (ι → ι → ι → ι → ι) → ι → ι . (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → (ι → ι → ι) → ι → ι . x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum 0 (setsum 0 0)) (λ x9 x10 x11 x12 . x0 (λ x13 : (ι → ι) → ι . x13 (λ x14 . 0)) (λ x13 : ι → ι . 0) (λ x13 : (ι → ι) → ι . x12)) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x9 x10 x11 x12 . x9) 0) = setsum (x5 (λ x9 . 0)) x4) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x9 x10 x11 x12 . x10) (setsum (Inj1 (x5 (λ x9 . x1 (λ x10 . 0) (λ x10 . 0) 0 0 (λ x10 . 0)) (x1 (λ x9 . 0) (λ x9 . 0) 0 0 (λ x9 . 0)) (λ x9 . 0))) (setsum (x6 (Inj1 0)) (x0 (λ x9 : (ι → ι) → ι . setsum 0 0) (λ x9 : ι → ι . 0) (λ x9 : (ι → ι) → ι . setsum 0 0)))) = setsum (setsum x4 (x6 (Inj0 (x5 (λ x9 . 0) 0 (λ x9 . 0))))) (Inj0 0)) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . Inj1 (setsum (x9 (x9 0 (λ x12 . 0)) (λ x12 . x9 0 (λ x13 . 0))) (Inj1 (x2 (λ x12 : ι → (ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x12 : ι → ι . λ x13 . 0) 0)))) 0 (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 : ι → ι . λ x10 . x2 (λ x11 : ι → (ι → ι) → ι . λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . 0) (Inj1 0) (λ x11 . λ x12 : ι → ι . λ x13 . setsum x11 (x12 x11)) (λ x11 : ι → ι . λ x12 . x2 (λ x13 : ι → (ι → ι) → ι . λ x14 : ι → ι . λ x15 : (ι → ι) → ι → ι . Inj1 (Inj1 0)) (x11 (setsum 0 0)) (λ x13 . λ x14 : ι → ι . λ x15 . x2 (λ x16 : ι → (ι → ι) → ι . λ x17 : ι → ι . λ x18 : (ι → ι) → ι → ι . x0 (λ x19 : (ι → ι) → ι . 0) (λ x19 : ι → ι . 0) (λ x19 : (ι → ι) → ι . 0)) (Inj0 0) (λ x16 . λ x17 : ι → ι . λ x18 . setsum 0 0) (λ x16 : ι → ι . λ x17 . x16 0) 0) (λ x13 : ι → ι . λ x14 . x12) 0) (Inj0 0)) x7 = Inj1 0) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 : ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . 0) (x4 (λ x9 : ι → ι → ι . x1 (λ x10 . x7) (λ x10 . x0 (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . Inj1 0) (λ x11 : (ι → ι) → ι . setsum 0 0)) (setsum 0 0) (x1 (λ x10 . x7) (λ x10 . x0 (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . 0) (λ x11 : (ι → ι) → ι . 0)) (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 x11 x12 x13 . 0) 0) (Inj0 0) (λ x10 . 0)) (λ x10 . x10))) (λ x9 . λ x10 : ι → ι . λ x11 . setsum 0 (x0 (λ x12 : (ι → ι) → ι . x12 (λ x13 . 0)) (λ x12 : ι → ι . setsum (setsum 0 0) (x12 0)) (λ x12 : (ι → ι) → ι . Inj1 x11))) (λ x9 : ι → ι . λ x10 . x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . Inj1 0) (λ x11 x12 x13 x14 . x14) (Inj0 x6)) (Inj0 (setsum x7 x5)) = setsum (Inj0 0) x6) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 : ι → ι . x1 (λ x9 . Inj1 0) (λ x9 . x0 (λ x10 : (ι → ι) → ι . 0) (λ x10 : ι → ι . setsum (x6 0) (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x7 0) (λ x11 x12 x13 x14 . 0) (Inj0 0))) (λ x10 : (ι → ι) → ι . x9)) (x6 0) 0 (λ x9 . x2 (λ x10 : ι → (ι → ι) → ι . λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . x1 (λ x13 . x1 (λ x14 . x14) (λ x14 . x2 (λ x15 : ι → (ι → ι) → ι . λ x16 : ι → ι . λ x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x15 : ι → ι . λ x16 . 0) 0) x13 (setsum 0 0) (λ x14 . x1 (λ x15 . 0) (λ x15 . 0) 0 0 (λ x15 . 0))) (λ x13 . x2 (λ x14 : ι → (ι → ι) → ι . λ x15 : ι → ι . λ x16 : (ι → ι) → ι → ι . 0) (x0 (λ x14 : (ι → ι) → ι . 0) (λ x14 : ι → ι . 0) (λ x14 : (ι → ι) → ι . 0)) (λ x14 . λ x15 : ι → ι . λ x16 . Inj0 0) (λ x14 : ι → ι . λ x15 . x12 (λ x16 . 0) 0) 0) (x0 (λ x13 : (ι → ι) → ι . x1 (λ x14 . 0) (λ x14 . 0) 0 0 (λ x14 . 0)) (λ x13 : ι → ι . x12 (λ x14 . 0) 0) (λ x13 : (ι → ι) → ι . x1 (λ x14 . 0) (λ x14 . 0) 0 0 (λ x14 . 0))) (setsum 0 0) (λ x13 . 0)) x9 (λ x10 . λ x11 : ι → ι . λ x12 . x9) (λ x10 : ι → ι . λ x11 . x2 (λ x12 : ι → (ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . x0 (λ x15 : (ι → ι) → ι . x2 (λ x16 : ι → (ι → ι) → ι . λ x17 : ι → ι . λ x18 : (ι → ι) → ι → ι . 0) 0 (λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x16 : ι → ι . λ x17 . 0) 0) (λ x15 : ι → ι . x2 (λ x16 : ι → (ι → ι) → ι . λ x17 : ι → ι . λ x18 : (ι → ι) → ι → ι . 0) 0 (λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x16 : ι → ι . λ x17 . 0) 0) (λ x15 : (ι → ι) → ι . 0)) 0 (λ x12 . λ x13 : ι → ι . λ x14 . setsum x14 (setsum 0 0)) (λ x12 : ι → ι . λ x13 . Inj1 (setsum 0 0)) (x10 0)) x9) = x6 (x1 (λ x9 . x0 (λ x10 : (ι → ι) → ι . x0 (λ x11 : (ι → ι) → ι . x1 (λ x12 . 0) (λ x12 . 0) 0 0 (λ x12 . 0)) (λ x11 : ι → ι . 0) (λ x11 : (ι → ι) → ι . Inj1 0)) (λ x10 : ι → ι . Inj1 (x7 0)) (λ x10 : (ι → ι) → ι . x10 (λ x11 . x2 (λ x12 : ι → (ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x12 : ι → ι . λ x13 . 0) 0))) (λ x9 . x0 (λ x10 : (ι → ι) → ι . Inj1 0) (λ x10 : ι → ι . x7 (setsum 0 0)) (λ x10 : (ι → ι) → ι . 0)) (x5 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 x11 x12 x13 . 0) (x5 (λ x10 . 0)))) (x4 0) (λ x9 . x5 (λ x10 . x9)))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x9 . setsum (x2 (λ x10 : ι → (ι → ι) → ι . λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . x12 (λ x13 . x12 (λ x14 . 0) 0) (Inj0 0)) 0 (λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x10 : ι → ι . λ x11 . 0) (x6 (setsum 0 0))) 0) (λ x9 . x9) (x2 (λ x9 : ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . 0) (x2 (λ x9 : ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . x0 (λ x13 : (ι → ι) → ι . 0) (λ x13 : ι → ι . 0) (λ x13 : (ι → ι) → ι . 0)) (x7 (λ x12 . 0))) (x7 (λ x9 . x0 (λ x10 : (ι → ι) → ι . 0) (λ x10 : ι → ι . 0) (λ x10 : (ι → ι) → ι . 0))) (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 : ι → ι . λ x10 . x9 (x9 0)) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . Inj1 0) (λ x9 x10 x11 x12 . 0) (x7 (λ x9 . 0)))) (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 : ι → ι . λ x10 . 0) x5) (setsum 0 x5) (λ x9 . x7 (λ x10 . x10)) = x7 (λ x9 . x7 (λ x10 . setsum 0 (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 x12 x13 x14 . 0) (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 x12 x13 x14 . 0) 0))))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 : (ι → ι) → ι . 0) (λ x9 : ι → ι . 0) (λ x9 : (ι → ι) → ι . Inj0 (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . x10 (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . λ x13 . 0)) (λ x11 : (ι → ι) → ι . Inj0 0)) (λ x10 x11 x12 x13 . x0 (λ x14 : (ι → ι) → ι . x12) (λ x14 : ι → ι . 0) (λ x14 : (ι → ι) → ι . x13)) (x1 (λ x10 . x9 (λ x11 . 0)) (λ x10 . 0) (x0 (λ x10 : (ι → ι) → ι . 0) (λ x10 : ι → ι . 0) (λ x10 : (ι → ι) → ι . 0)) 0 (λ x10 . x0 (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . 0) (λ x11 : (ι → ι) → ι . 0))))) = x4 (λ x9 : (ι → ι) → ι . 0) (x5 (x4 (λ x9 : (ι → ι) → ι . x1 (λ x10 . 0) (λ x10 . x10) (setsum 0 0) (x9 (λ x10 . 0)) (λ x10 . Inj0 0)) (Inj1 (x0 (λ x9 : (ι → ι) → ι . 0) (λ x9 : ι → ι . 0) (λ x9 : (ι → ι) → ι . 0)))) (λ x9 x10 . x10) (setsum 0) (x4 (λ x9 : (ι → ι) → ι . Inj1 (Inj1 0)) (setsum (x5 0 (λ x9 x10 . 0) (λ x9 . 0) 0) 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 : (ι → ι) → ι . x2 (λ x10 : ι → (ι → ι) → ι . λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x10 : ι → ι . λ x11 . x3 (λ x12 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x11) (λ x12 x13 x14 x15 . setsum x14 x14) (x10 (x2 (λ x12 : ι → (ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x12 : ι → ι . λ x13 . 0) 0))) 0) (λ x9 : ι → ι . x5 (setsum (x7 0 0) 0)) (λ x9 : (ι → ι) → ι . 0) = x5 (x1 (λ x9 . 0) (λ x9 . 0) (x0 (λ x9 : (ι → ι) → ι . 0) (λ x9 : ι → ι . x1 (λ x10 . 0) (λ x10 . x10) (Inj0 0) (Inj0 0) (λ x10 . x10)) (λ x9 : (ι → ι) → ι . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x9 (λ x11 . 0)) (λ x10 x11 x12 x13 . 0) (x1 (λ x10 . 0) (λ x10 . 0) 0 0 (λ x10 . 0)))) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x9 x10 x11 x12 . x9) (setsum (x1 (λ x9 . 0) (λ x9 . 0) 0 0 (λ x9 . 0)) (x5 0))) (λ x9 . 0))) ⟶ False (proof)
Theorem a9210.. : ∀ x0 : (ι → ι → ι) → (ι → ι → ι → ι) → ι . ∀ x1 : (ι → ι) → ι → ι → ι . ∀ x2 : (ι → ι → ι) → ι → ι . ∀ x3 : (((ι → (ι → ι) → ι → ι) → ι) → ι) → ι → ι . (∀ x4 . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x7) x4 = x7) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x0 (λ x10 x11 . x1 (λ x12 . x3 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) (setsum 0 0)) 0 (x9 (λ x12 . λ x13 : ι → ι . λ x14 . x13 0))) (λ x10 x11 x12 . x12)) (setsum 0 0) = setsum x7 (x1 (λ x9 . x0 (λ x10 x11 . x3 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) x7) (λ x10 x11 x12 . x10)) (x1 (λ x9 . x6) x5 (setsum (Inj1 0) x7)) (setsum x7 (x1 (λ x9 . 0) (x4 0) x7)))) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι) → ι . x2 (λ x9 x10 . x2 (λ x11 x12 . setsum (Inj0 0) 0) 0) 0 = x2 (λ x9 x10 . Inj1 0) (setsum x6 (x4 x6 0 (x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) x6)))) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x9 x10 . x3 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . 0) (x0 (λ x11 x12 . x0 (λ x13 x14 . x1 (λ x15 . 0) 0 0) (λ x13 x14 x15 . Inj1 0)) (λ x11 x12 x13 . setsum x10 x12))) (Inj0 0) = setsum 0 (setsum 0 0)) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ((ι → ι) → ι) → ι → ι → ι . x1 (λ x9 . x3 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) (Inj1 (x3 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x6) 0))) (x1 (λ x9 . Inj0 (setsum (Inj0 0) (x2 (λ x10 x11 . 0) 0))) x5 (Inj0 (Inj1 0))) (x0 (λ x9 x10 . 0) (λ x9 x10 x11 . x9)) = setsum x6 (setsum (x0 (λ x9 x10 . Inj0 (setsum 0 0)) (λ x9 x10 x11 . x7 (λ x12 . x10) (λ x12 : ι → ι . x9) x9 (x1 (λ x12 . 0) 0 0))) (x0 (λ x9 x10 . x3 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x12 x13 . 0) 0) (setsum 0 0)) (λ x9 x10 x11 . 0)))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι . x1 (λ x9 . 0) (x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) (setsum (x2 (λ x9 x10 . x9) 0) 0)) 0 = x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . setsum (Inj0 (setsum x6 x6)) (setsum (x5 (λ x10 x11 x12 . x0 (λ x13 x14 . 0) (λ x13 x14 x15 . 0))) (setsum (x5 (λ x10 x11 x12 . 0)) 0))) (x0 (λ x9 x10 . x0 (λ x11 x12 . setsum (x1 (λ x13 . 0) 0 0) 0) (λ x11 x12 x13 . x12)) (λ x9 x10 x11 . setsum x9 (Inj1 (x2 (λ x12 x13 . 0) 0))))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 x7 . x0 (λ x9 x10 . x3 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . 0) x9) (λ x9 x10 x11 . setsum 0 (Inj1 0)) = setsum 0 (Inj0 (x1 (x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0)) (x2 (λ x9 x10 . 0) x7) (x0 (λ x9 x10 . x1 (λ x11 . 0) 0 0) (λ x9 x10 x11 . x3 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 x10 . setsum x6 x9) (λ x9 x10 x11 . 0) = x7 (setsum (setsum (x0 (λ x9 x10 . x2 (λ x11 x12 . 0) 0) (λ x9 x10 x11 . 0)) (x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x10 x11 . 0) 0) (x0 (λ x9 x10 . 0) (λ x9 x10 x11 . 0)))) (x5 (x2 (λ x9 x10 . x6) (x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0)))) (x7 (Inj1 (setsum 0 0)) (x0 (λ x9 x10 . 0) (λ x9 x10 x11 . 0)))) ⟶ False (proof)
Theorem b4f37.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : (ι → ι) → (ι → ι → ι → ι → ι) → ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x2 : (ι → ι → ι) → ι → ι → ι → ι . ∀ x3 : ((ι → ι → ι) → ι) → (((ι → ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι) → ι . (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x3 (λ x9 : ι → ι → ι . x2 (λ x10 x11 . setsum 0 (x3 (λ x12 : ι → ι → ι . x12 0 0) (λ x12 : (ι → ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0))) (Inj1 (Inj0 x7)) 0 (x5 (Inj1 (x5 0)))) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . Inj1 (x3 (λ x13 : ι → ι → ι . x12) (λ x13 : (ι → ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x14))) = Inj0 (Inj0 (x2 (λ x9 x10 . x2 (λ x11 x12 . x1 (λ x13 . 0) (λ x13 x14 x15 x16 . 0) (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0 (λ x13 . 0)) 0 (x6 (λ x11 . 0)) 0) (setsum (x0 (λ x9 . 0) 0) (Inj1 0)) (setsum (setsum 0 0) x7) 0))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → (ι → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι → ι → ι . x3 (λ x9 : ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) = setsum 0 (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj0 (setsum (x9 (λ x11 . 0) 0) x6)) (x0 (λ x9 . 0) (x3 (λ x9 : ι → ι → ι . x2 (λ x10 x11 . 0) 0 0 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x0 (λ x13 . 0) 0))) (x4 0 (setsum 0 (setsum 0 0))) (Inj1 (x4 (x5 (λ x9 x10 x11 . 0) (λ x9 . 0) 0 0) (Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x2 (λ x9 x10 . 0) (x2 (λ x9 x10 . x0 (λ x11 . 0) x9) x6 (setsum 0 (x5 (λ x9 x10 x11 . 0))) (setsum x4 (Inj1 (setsum 0 0)))) (x3 (λ x9 : ι → ι → ι . x9 (x9 0 (x5 (λ x10 x11 x12 . 0))) (x2 (λ x10 x11 . setsum 0 0) 0 (Inj0 0) (Inj0 0))) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x12)) 0 = setsum (setsum 0 (setsum (x0 (λ x9 . x3 (λ x10 : ι → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) x6) 0)) 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 x10 . x1 Inj0 (λ x11 x12 x13 x14 . setsum x11 x13) (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 . 0) 0) (setsum (x2 (λ x11 x12 . 0) (x6 0) (setsum 0 0) x9) (setsum 0 (x2 (λ x11 x12 . 0) 0 0 0))) (λ x11 . setsum x10 (Inj0 (x0 (λ x12 . 0) 0)))) (Inj1 (Inj0 0)) (setsum (setsum (x6 (x3 (λ x9 : ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0))) 0) (setsum (setsum (setsum 0 0) (setsum 0 0)) (Inj0 (x2 (λ x9 x10 . 0) 0 0 0)))) (Inj0 (Inj0 (x2 (λ x9 x10 . 0) (x6 0) (setsum 0 0) 0))) = setsum (setsum (x2 (λ x9 x10 . 0) (x6 x4) (setsum (x2 (λ x9 x10 . 0) 0 0 0) (Inj0 0)) (setsum (x3 (λ x9 : ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) x7)) x4) (x6 x4)) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 . x7) (λ x9 x10 x11 x12 . x2 (λ x13 x14 . 0) (x3 (λ x13 : ι → ι → ι . 0) (λ x13 : (ι → ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . Inj1 (x1 (λ x17 . 0) (λ x17 x18 x19 x20 . 0) (λ x17 : ι → ι → ι . λ x18 : ι → ι . λ x19 . 0) 0 (λ x17 . 0)))) (Inj1 (x0 (λ x13 . x2 (λ x14 x15 . 0) 0 0 0) (x1 (λ x13 . 0) (λ x13 x14 x15 x16 . 0) (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0 (λ x13 . 0)))) x10) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x9 (Inj0 (x2 (λ x12 x13 . Inj1 0) (x0 (λ x12 . 0) 0) 0 0)) (x0 (λ x12 . setsum (x9 0 0) (x9 0 0)) (x1 (λ x12 . setsum 0 0) (λ x12 x13 x14 x15 . 0) (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . Inj0 0) 0 (λ x12 . 0)))) 0 (λ x9 . x6) = Inj1 (setsum 0 (Inj1 (Inj0 (setsum 0 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x1 (λ x9 . 0) (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) (setsum (Inj1 (x6 (x7 0) (x6 0 0))) 0) (λ x9 . setsum (x3 (λ x10 : ι → ι → ι . x3 (λ x11 : ι → ι → ι . x10 0 0) (λ x11 : (ι → ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0)) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj1 0)) (x3 (λ x10 : ι → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0))) = x4 (λ x9 . x7 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → (ι → ι) → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 . x6) (x4 0 (setsum 0 (x2 (λ x9 x10 . 0) (x2 (λ x9 x10 . 0) 0 0 0) (x1 (λ x9 . 0) (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) 0 (λ x9 . 0)) x6))) = x4 (x5 (λ x9 . λ x10 : ι → ι . x0 (λ x11 . Inj1 x9) x9) (Inj1 (x0 (λ x9 . x5 (λ x10 . λ x11 : ι → ι . 0) 0) (x2 (λ x9 x10 . 0) 0 0 0)))) (setsum x7 (x4 0 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 . x3 (λ x10 : ι → ι → ι . setsum (setsum (Inj0 0) (Inj0 0)) (x0 (λ x11 . x0 (λ x12 . 0) 0) (x0 (λ x11 . 0) 0))) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj0 (x0 (λ x14 . x13) 0))) (setsum (setsum (x0 (λ x9 . x1 (λ x10 . 0) (λ x10 x11 x12 x13 . 0) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 (λ x10 . 0)) 0) (x3 (λ x9 : ι → ι → ι . x5 0 0 (λ x10 . 0) 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 0))) (x2 (λ x9 x10 . x0 (λ x11 . x3 (λ x12 : ι → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) 0) 0 (Inj1 (x0 (λ x9 . 0) 0)) (Inj1 0))) = Inj0 0) ⟶ False (proof)
Theorem 36f64.. : ∀ x0 : (((ι → (ι → ι) → ι) → ι → ι) → ι) → ι → ι . ∀ x1 : (ι → ι → ι) → (ι → ((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x2 : (((ι → ι) → ι) → ι) → (((ι → ι) → ι → ι → ι) → ι) → (((ι → ι) → ι) → ι) → ι → ι → ι . ∀ x3 : (ι → ι) → ((ι → ι) → ι) → ι . (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 . x3 (λ x9 . x7) (λ x9 : ι → ι . 0) = x7) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 Inj0 (λ x9 : ι → ι . 0) = x7) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : (ι → ι) → (ι → ι) → ι . x2 (λ x9 : (ι → ι) → ι . setsum 0 0) (λ x9 : (ι → ι) → ι → ι → ι . x9 (λ x10 . x10) 0 x5) (λ x9 : (ι → ι) → ι . x2 (λ x10 : (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι → ι → ι . x9 (x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . setsum 0 0))) (λ x10 : (ι → ι) → ι . x6 (λ x11 . 0) (x1 (λ x11 x12 . x1 (λ x13 x14 . 0) (λ x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0)) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x11))) (setsum x5 (setsum (x6 (λ x10 . 0) 0) (x2 (λ x10 : (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι → ι → ι . 0) (λ x10 : (ι → ι) → ι . 0) 0 0))) (setsum (Inj0 (x1 (λ x10 x11 . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0))) (x9 (λ x10 . 0)))) x5 (setsum (setsum 0 0) (x7 (λ x9 . x7 (λ x10 . x6 (λ x11 . 0) 0) (λ x10 . x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . 0) 0)) (λ x9 . x7 (λ x10 . x9) (λ x10 . x3 (λ x11 . 0) (λ x11 : ι → ι . 0))))) = Inj0 (x2 (λ x9 : (ι → ι) → ι . Inj0 (Inj1 (x1 (λ x10 x11 . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0)))) (λ x9 : (ι → ι) → ι → ι → ι . x5) (λ x9 : (ι → ι) → ι . x9 (λ x10 . x2 (λ x11 : (ι → ι) → ι . x7 (λ x12 . 0) (λ x12 . 0)) (λ x11 : (ι → ι) → ι → ι → ι . x10) (λ x11 : (ι → ι) → ι . setsum 0 0) 0 (x9 (λ x11 . 0)))) (x1 (λ x9 x10 . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0)) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → (ι → ι) → ι → ι . x2 (λ x9 : (ι → ι) → ι . x2 (λ x10 : (ι → ι) → ι . setsum (x10 (λ x11 . setsum 0 0)) (x10 (λ x11 . x2 (λ x12 : (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι → ι → ι . 0) (λ x12 : (ι → ι) → ι . 0) 0 0))) (λ x10 : (ι → ι) → ι → ι → ι . Inj1 (x2 (λ x11 : (ι → ι) → ι . x9 (λ x12 . 0)) (λ x11 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι) → ι . Inj0 0) (setsum 0 0) (x10 (λ x11 . 0) 0 0))) (λ x10 : (ι → ι) → ι . x10 (λ x11 . x7 (x1 (λ x12 x13 . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0)) (λ x12 . x12) 0)) (x3 (λ x10 . setsum (Inj1 0) 0) (λ x10 : ι → ι . Inj1 0)) (Inj0 0)) (λ x9 : (ι → ι) → ι → ι → ι . x3 (λ x10 . x2 (λ x11 : (ι → ι) → ι . x9 (λ x12 . x0 (λ x13 : (ι → (ι → ι) → ι) → ι → ι . 0) 0) (x1 (λ x12 x13 . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0)) (Inj1 0)) (λ x11 : (ι → ι) → ι → ι → ι . x9 (λ x12 . 0) 0 (setsum 0 0)) (λ x11 : (ι → ι) → ι . x0 (λ x12 : (ι → (ι → ι) → ι) → ι → ι . setsum 0 0) (setsum 0 0)) (x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . 0) (x1 (λ x11 x12 . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0))) 0) (λ x10 : ι → ι . x10 (Inj1 (x7 0 (λ x11 . 0) 0)))) (λ x9 : (ι → ι) → ι . 0) (Inj0 (x2 (λ x9 : (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι → ι → ι . 0) (λ x9 : (ι → ι) → ι . x5 (λ x10 : (ι → ι) → ι → ι . x2 (λ x11 : (ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι) → ι . 0) 0 0) (x3 (λ x10 . 0) (λ x10 : ι → ι . 0)) (λ x10 . 0) (x5 (λ x10 : (ι → ι) → ι → ι . 0) 0 (λ x10 . 0) 0)) x6 (x7 (x7 0 (λ x9 . 0) 0) (λ x9 . x5 (λ x10 : (ι → ι) → ι → ι . 0) 0 (λ x10 . 0) 0) (x4 0)))) (Inj1 (setsum (x1 (λ x9 x10 . x1 (λ x11 x12 . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0)) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x7 0 (λ x12 . 0) 0)) x6)) = x2 (λ x9 : (ι → ι) → ι . x0 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . x10 (λ x11 . λ x12 : ι → ι . x0 (λ x13 : (ι → (ι → ι) → ι) → ι → ι . x0 (λ x14 : (ι → (ι → ι) → ι) → ι → ι . 0) 0) (setsum 0 0)) (Inj0 (x7 0 (λ x11 . 0) 0))) (setsum (x7 (x9 (λ x10 . 0)) (λ x10 . 0) (setsum 0 0)) (x2 (λ x10 : (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι → ι → ι . x3 (λ x11 . 0) (λ x11 : ι → ι . 0)) (λ x10 : (ι → ι) → ι . Inj0 0) (x2 (λ x10 : (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι → ι → ι . 0) (λ x10 : (ι → ι) → ι . 0) 0 0) (x7 0 (λ x10 . 0) 0)))) (λ x9 : (ι → ι) → ι → ι → ι . setsum (setsum (Inj1 (x2 (λ x10 : (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι → ι → ι . 0) (λ x10 : (ι → ι) → ι . 0) 0 0)) (x5 (λ x10 : (ι → ι) → ι → ι . x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . 0) 0) 0 (λ x10 . 0) (x1 (λ x10 x11 . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0)))) (x3 (λ x10 . 0) (λ x10 : ι → ι . x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . x0 (λ x12 : (ι → (ι → ι) → ι) → ι → ι . 0) 0) (x10 0)))) (λ x9 : (ι → ι) → ι . x1 (λ x10 x11 . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x9 (λ x13 . x13))) (x1 (λ x9 x10 . x9) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0)) (setsum (x4 (x5 (λ x9 : (ι → ι) → ι → ι . setsum 0 0) (Inj1 0) (λ x9 . 0) 0)) x6)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 x10 . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . Inj1 x9) = setsum (setsum (x0 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . x1 (λ x10 x11 . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . setsum 0 0)) (Inj0 (x3 (λ x9 . 0) (λ x9 : ι → ι . 0)))) x6) (x2 (λ x9 : (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι → ι → ι . 0) (λ x9 : (ι → ι) → ι . x9 x7) (x7 (x2 (λ x9 : (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι → ι → ι . 0) (λ x9 : (ι → ι) → ι . 0) (x3 (λ x9 . 0) (λ x9 : ι → ι . 0)) 0)) x6)) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 x10 . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) = x6 (λ x9 : (ι → ι) → ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x7 : ι → ι → ι → ι → ι . x0 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . 0) (x1 (λ x9 x10 . x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . x2 (λ x12 : (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι → ι → ι . x11 (λ x13 . λ x14 : ι → ι . 0) 0) (λ x12 : (ι → ι) → ι . 0) (setsum 0 0) (x1 (λ x12 x13 . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0))) (setsum 0 (x1 (λ x11 x12 . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0)))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x2 (λ x12 : (ι → ι) → ι . x3 (λ x13 . setsum 0 0) (λ x13 : ι → ι . Inj0 0)) (λ x12 : (ι → ι) → ι → ι → ι . setsum (x11 0) (Inj1 0)) (λ x12 : (ι → ι) → ι . setsum (Inj0 0) (x3 (λ x13 . 0) (λ x13 : ι → ι . 0))) (setsum (x10 (λ x12 . 0)) (setsum 0 0)) (Inj1 x9))) = x1 (λ x9 x10 . setsum 0 (x3 (λ x11 . setsum (setsum 0 0) 0) (λ x11 : ι → ι . 0))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x7 (x11 0) (x2 (λ x12 : (ι → ι) → ι . x2 (λ x13 : (ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι → ι → ι . 0) (λ x13 : (ι → ι) → ι . 0) (x12 (λ x13 . 0)) (x3 (λ x13 . 0) (λ x13 : ι → ι . 0))) (λ x12 : (ι → ι) → ι → ι → ι . setsum (x10 (λ x13 . 0)) (setsum 0 0)) (λ x12 : (ι → ι) → ι . x1 (λ x13 x14 . 0) (λ x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . x2 (λ x16 : (ι → ι) → ι . 0) (λ x16 : (ι → ι) → ι → ι → ι . 0) (λ x16 : (ι → ι) → ι . 0) 0 0)) 0 0) 0 (x11 (setsum (x11 0) (Inj0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . x0 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . x9 (λ x10 . λ x11 : ι → ι . x2 (λ x12 : (ι → ι) → ι . x9 (λ x13 . λ x14 : ι → ι . x13) (x2 (λ x13 : (ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι → ι → ι . 0) (λ x13 : (ι → ι) → ι . 0) 0 0)) (λ x12 : (ι → ι) → ι → ι → ι . setsum (x12 (λ x13 . 0) 0 0) (setsum 0 0)) (λ x12 : (ι → ι) → ι . 0) (setsum x7 (x9 (λ x12 . λ x13 : ι → ι . 0) 0)) x7) (x0 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . setsum (x1 (λ x11 x12 . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0)) (x1 (λ x11 x12 . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0))) (setsum 0 0))) (setsum (x1 (λ x9 x10 . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (Inj0 0) (x10 (λ x12 . 0)))) (Inj0 x5)) = x6 (λ x9 . λ x10 : ι → ι . λ x11 . 0)) ⟶ False (proof)
Theorem 2836d.. : ∀ x0 : ((ι → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x1 : (((ι → (ι → ι) → ι → ι) → ι) → ι) → ι → ι → ι . ∀ x2 : ((((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ((ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x3 : (((ι → ι) → ι) → ((ι → ι → ι) → ι) → (ι → ι → ι) → ι) → ι → ι . (∀ x4 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ι → ι → ι . x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . x2 (λ x12 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . λ x14 x15 . Inj1 0) (x2 (λ x12 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . λ x14 x15 . x13 (x2 (λ x16 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x17 : ι → ι → ι . λ x18 x19 . 0) 0 (λ x16 x17 : ι → ι . 0) 0) (x1 (λ x16 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0)) (x9 (λ x12 . setsum 0 0)) (λ x12 x13 : ι → ι . Inj0 (setsum 0 0)) 0) (λ x12 x13 : ι → ι . x3 (λ x14 : (ι → ι) → ι . λ x15 : (ι → ι → ι) → ι . λ x16 : ι → ι → ι . Inj0 (setsum 0 0)) (x0 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x16 . x15 (λ x17 : ι → ι . λ x18 . 0) (λ x17 . 0)) (λ x14 x15 . x1 (λ x16 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) (λ x14 . 0))) (x11 (setsum 0 (Inj0 0)) 0)) (x7 (Inj1 (setsum 0 0)) 0) = x2 (λ x9 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x11) (x7 (setsum (x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . 0) (x7 0 0)) 0) (x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . setsum (x7 0 0) (x7 0 0)) (setsum (Inj1 0) 0))) (λ x9 x10 : ι → ι . x2 (λ x11 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x12 : ι → ι → ι . λ x13 x14 . x1 (λ x15 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 x13) (setsum 0 0) (λ x11 x12 : ι → ι . x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) (x12 0) (x10 (x2 (λ x13 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . λ x15 x16 . 0) 0 (λ x13 x14 : ι → ι . 0) 0))) (x7 0 0)) (Inj1 0)) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . x10 (λ x12 . Inj0)) (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . x2 (λ x12 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . λ x14 x15 . setsum 0 0) x11 (λ x12 x13 : ι → ι . 0) (x3 (λ x12 : (ι → ι) → ι . λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι → ι . Inj1 0) 0)) (λ x9 x10 . Inj0 (x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . x11 (λ x12 . λ x13 : ι → ι . λ x14 . 0)) (setsum 0 0) 0)) (λ x9 . setsum 0 (x2 (λ x10 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . λ x12 x13 . x0 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x16 . 0) (λ x14 x15 . 0) (λ x14 . 0)) (x7 0) (λ x10 x11 : ι → ι . x9) (x2 (λ x10 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . λ x12 x13 . 0) 0 (λ x10 x11 : ι → ι . 0) 0)))) = Inj1 0) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → ι → ι → ι . ∀ x6 . ∀ x7 : ι → (ι → ι → ι) → ι . x2 (λ x9 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) x11 (x2 (λ x13 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . λ x15 x16 . setsum (Inj1 0) (setsum 0 0)) (setsum (Inj1 0) (x0 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x15 . 0) (λ x13 x14 . 0) (λ x13 . 0))) (λ x13 x14 : ι → ι . setsum 0 (x1 (λ x15 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0)) 0)) (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . 0) (λ x9 x10 . Inj1 (setsum 0 0)) (λ x9 . Inj0 (setsum (x5 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) 0 0 0) (setsum 0 0)))) (λ x9 x10 : ι → ι . x0 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . Inj0 0) (x10 (x0 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x16 . 0) (λ x14 x15 . 0) (λ x14 . 0))) (Inj0 0)) (λ x11 x12 . x0 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x15 . Inj0 (setsum 0 0)) (λ x13 x14 . x14) (λ x13 . x11)) (λ x11 . 0)) 0 = setsum (x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) (setsum 0 (x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) 0)) (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . 0) (λ x9 x10 . x10) (λ x9 . x2 (λ x10 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . λ x12 x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) 0 (λ x10 x11 : ι → ι . x0 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x14 . 0) (λ x12 x13 . 0) (λ x12 . 0)) 0)) 0) 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . Inj1 0) (x10 0 0) (setsum (setsum 0 x12) x11)) 0 (λ x9 x10 : ι → ι . x10 0) (Inj0 x4) = x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x7) x7 (x6 (x2 (λ x9 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x2 (λ x13 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . λ x15 x16 . 0) (x9 (λ x13 : ι → ι . λ x14 . 0) (λ x13 : ι → ι . 0)) (λ x13 x14 : ι → ι . x0 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x17 . 0) (λ x15 x16 . 0) (λ x15 . 0)) (x2 (λ x13 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . λ x15 x16 . 0) 0 (λ x13 x14 : ι → ι . 0) 0)) x4 (λ x9 x10 : ι → ι . x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x12 : (ι → ι) → ι . λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι → ι . 0) 0) 0 (x9 0)) x7))) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x9 (λ x10 . λ x11 : ι → ι . λ x12 . x10)) 0 (setsum x7 (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . x9 (x0 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x14 . 0) (λ x12 x13 . 0) (λ x12 . 0))) (λ x9 x10 . Inj0 (Inj1 0)) (λ x9 . Inj0 0))) = setsum (setsum 0 x6) x7) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x6 (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x11 : (ι → ι) → ι . λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι → ι . setsum 0 0) 0) (setsum 0 (x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x10 x11 . 0) (λ x10 . 0))) (x6 (x9 (λ x10 . λ x11 : ι → ι . λ x12 . 0)) 0)) (Inj1 (x6 (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) (Inj1 0)))) (x7 (λ x9 : ι → ι → ι . Inj0 (x9 0 (x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x10 x11 . 0) (λ x10 . 0))))) (x5 (x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . x10 (λ x12 x13 . x2 (λ x14 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x15 : ι → ι → ι . λ x16 x17 . 0) 0 (λ x14 x15 : ι → ι . 0) 0)) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0)))) = x5 (x6 (x7 (λ x9 : ι → ι → ι . x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x10 x11 . 0) (λ x10 . setsum 0 0))) (x5 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) (setsum 0 0) (x6 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . x11) (λ x9 x10 . x10) (λ x9 . x9) = x7 (λ x9 : ι → ι → ι . x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x10 x11 . x2 (λ x12 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . λ x14 x15 . x0 (λ x16 : ι → ι . λ x17 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x18 . setsum 0 0) (λ x16 x17 . Inj1 0) (λ x16 . x15)) (Inj0 0) (λ x12 x13 : ι → ι . x3 (λ x14 : (ι → ι) → ι . λ x15 : (ι → ι → ι) → ι . λ x16 : ι → ι → ι . x1 (λ x17 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) (setsum 0 0)) 0) (λ x10 . 0)) (λ x9 : ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . x3 (λ x12 : (ι → ι) → ι . λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι → ι . x1 (λ x15 : (ι → (ι → ι) → ι → ι) → ι . 0) (x0 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x17 . Inj1 0) (λ x15 x16 . x3 (λ x17 : (ι → ι) → ι . λ x18 : (ι → ι → ι) → ι . λ x19 : ι → ι → ι . 0) 0) (λ x15 . x13 (λ x16 x17 . 0))) (x0 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x17 . 0) (λ x15 x16 . setsum 0 0) (λ x15 . 0))) 0) (λ x9 x10 . 0) (λ x9 . x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x10 x11 . x9) (λ x10 . x6)) = setsum (x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . x10 (λ x12 x13 . x0 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x16 . x1 (λ x17 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) (λ x14 x15 . Inj1 0) (λ x14 . setsum 0 0))) x7) 0) ⟶ False (proof)
Theorem 0eb92.. : ∀ x0 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x1 : (ι → ι → ι) → ι → (((ι → ι) → ι) → ι) → (ι → ι) → ι . ∀ x2 : (ι → ι) → (ι → ((ι → ι) → ι → ι) → ι) → ι . ∀ x3 : ((((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι → ι → ι . (∀ x4 x5 . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x3 (λ x9 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x5) x4 (x2 (λ x9 . Inj0 0) (λ x9 . λ x10 : (ι → ι) → ι → ι . 0)) 0 = Inj1 (x1 (λ x9 x10 . x9) (Inj0 0) (λ x9 : (ι → ι) → ι . x3 (λ x10 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum (x9 (λ x11 . 0)) (x0 (λ x11 . 0) 0 (λ x11 . 0) 0)) (Inj0 (Inj0 0)) (x2 (λ x10 . x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . Inj1 0)) x7) (λ x9 . x2 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . x7)))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x1 (λ x10 x11 . x10) (Inj1 (x2 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . setsum 0 0))) (λ x10 : (ι → ι) → ι . x9 (λ x11 : ι → ι . 0) (λ x11 : ι → ι . λ x12 . setsum x12 x12)) (λ x10 . Inj1 0)) x7 0 0 = Inj1 0) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x2 (λ x9 . x9) (λ x9 . λ x10 : (ι → ι) → ι → ι . setsum 0 (x1 (λ x11 x12 . x1 (λ x13 x14 . Inj0 0) (x3 (λ x13 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (λ x13 : (ι → ι) → ι . x3 (λ x14 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (λ x13 . x1 (λ x14 x15 . 0) 0 (λ x14 : (ι → ι) → ι . 0) (λ x14 . 0))) 0 (λ x11 : (ι → ι) → ι . 0) (λ x11 . x11))) = x6 (setsum (x1 (λ x9 . x3 (λ x10 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (Inj0 0) (x0 (λ x10 . 0) 0 (λ x10 . 0) 0)) (x3 (λ x9 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . Inj1 0) (x2 (λ x9 . 0) (λ x9 . λ x10 : (ι → ι) → ι → ι . 0)) (Inj0 0) x4) (λ x9 : (ι → ι) → ι . setsum (Inj0 0) (x2 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . 0))) (λ x9 . Inj0 x5)) 0)) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι . x2 (λ x9 . x6 (λ x10 : ι → ι → ι . Inj1 (x0 (λ x11 . x2 (λ x12 . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . 0)) (setsum 0 0) (λ x11 . 0) (Inj1 0)))) (λ x9 . λ x10 : (ι → ι) → ι → ι . x1 (λ x11 x12 . x9) (x1 (λ x11 x12 . x2 (λ x13 . x2 (λ x14 . 0) (λ x14 . λ x15 : (ι → ι) → ι → ι . 0)) (λ x13 . λ x14 : (ι → ι) → ι → ι . x11)) 0 (λ x11 : (ι → ι) → ι . 0) (λ x11 . setsum (x0 (λ x12 . 0) 0 (λ x12 . 0) 0) (x0 (λ x12 . 0) 0 (λ x12 . 0) 0))) (λ x11 : (ι → ι) → ι . Inj1 (Inj0 0)) (λ x11 . 0)) = x6 (λ x9 : ι → ι → ι . setsum 0 (x0 (λ x10 . x10) 0 (λ x10 . x9 x10 (x7 (λ x11 . λ x12 : ι → ι . 0) (λ x11 : ι → ι . 0))) (Inj1 (Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x1 (λ x9 x10 . x10) x4 (λ x9 : (ι → ι) → ι . 0) (λ x9 . x7 (Inj0 (x2 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . x0 (λ x12 . 0) 0 (λ x12 . 0) 0))) (λ x10 x11 . x11)) = x4) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 x10 . x1 (λ x11 x12 . Inj1 (x1 (λ x13 x14 . x11) (x1 (λ x13 x14 . 0) 0 (λ x13 : (ι → ι) → ι . 0) (λ x13 . 0)) (λ x13 : (ι → ι) → ι . 0) (λ x13 . 0))) 0 (λ x11 : (ι → ι) → ι . setsum (setsum (x0 (λ x12 . 0) 0 (λ x12 . 0) 0) 0) (x2 (λ x12 . setsum 0 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . 0))) (λ x11 . x9)) x4 (λ x9 : (ι → ι) → ι . x5) (λ x9 . x9) = x4) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 . x0 (λ x9 . x9) (x1 (λ x9 x10 . 0) (Inj0 (x3 (λ x9 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (setsum 0 0) 0 (setsum 0 0))) (λ x9 : (ι → ι) → ι . 0) (λ x9 . Inj1 (x5 (λ x10 . λ x11 : ι → ι . x11 0) (λ x10 x11 . Inj0 0) (λ x10 . Inj1 0)))) (λ x9 . x0 (λ x10 . x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 (x0 (λ x11 . x7) (x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι → ι . 0)) (λ x11 . x10) x10) x9) x7 (λ x10 . x1 (λ x11 x12 . x9) (x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x3 (λ x12 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (x0 (λ x11 . 0) 0 (λ x11 . 0) 0) (x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (Inj0 0)) (λ x11 : (ι → ι) → ι . Inj0 (x2 (λ x12 . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . 0))) (λ x11 . x3 (λ x12 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum 0 0) 0 x10 0)) 0) (x0 (λ x9 . x0 (λ x10 . 0) (x5 (λ x10 . λ x11 : ι → ι . setsum 0 0) (λ x10 x11 . x10) (λ x10 . x6 0 (λ x11 . 0))) (λ x10 . x0 (λ x11 . Inj0 0) x7 (λ x11 . x0 (λ x12 . 0) 0 (λ x12 . 0) 0) 0) (x2 (λ x10 . x10) (λ x10 . λ x11 : (ι → ι) → ι → ι . 0))) 0 (x3 (λ x9 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (x2 (λ x9 . x3 (λ x10 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (λ x9 . λ x10 : (ι → ι) → ι → ι . setsum 0 0)) 0) (Inj0 0)) = setsum (Inj1 (x1 (λ x9 x10 . x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x12 . 0) 0 (λ x12 . 0) 0) x9 (setsum 0 0) (x0 (λ x11 . 0) 0 (λ x11 . 0) 0)) (x6 x4 (λ x9 . x5 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 . 0) (λ x10 . 0))) (λ x9 : (ι → ι) → ι . Inj1 (x9 (λ x10 . 0))) Inj1)) (x5 (λ x9 . λ x10 : ι → ι . x2 (λ x11 . x10 (x10 0)) (λ x11 . λ x12 : (ι → ι) → ι → ι . 0)) (λ x9 x10 . Inj1 (x0 (λ x11 . x2 (λ x12 . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . 0)) (x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (λ x11 . x10) x9)) (λ x9 . x7))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 . x1 (λ x10 x11 . x0 (λ x12 . 0) (setsum 0 (x1 (λ x12 x13 . 0) 0 (λ x12 : (ι → ι) → ι . 0) (λ x12 . 0))) (λ x12 . x3 (λ x13 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum 0 0) 0 (x2 (λ x13 . 0) (λ x13 . λ x14 : (ι → ι) → ι → ι . 0)) x9) (x1 (λ x12 x13 . 0) x9 (λ x12 : (ι → ι) → ι . x11) (λ x12 . x9))) x7 (λ x10 : (ι → ι) → ι . x7) (λ x10 . 0)) x5 (λ x9 . setsum (x3 (λ x10 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι → ι . x10 (λ x13 : ι → ι . 0) (λ x13 : ι → ι . λ x14 . 0))) 0 (setsum 0 0) 0) x6) x7 = x5) ⟶ False (proof)
Theorem b1ccf.. : ∀ x0 : (((((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ((ι → ι) → ι) → ι) → ((ι → ι → ι) → ι) → (ι → (ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι → ι) → (((ι → ι) → ι → ι → ι) → ι → ι) → ι . ∀ x2 : (((ι → ι) → ι) → ι → ι → ι → ι → ι) → ι → ι . ∀ x3 : (((ι → ι → ι → ι) → ι → ι → ι → ι) → ι → ι) → ι → ι . (∀ x4 : ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x10 . setsum x10 (x0 (λ x11 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι . Inj1 (x1 (λ x14 x15 . 0) (λ x14 : (ι → ι) → ι → ι → ι . λ x15 . 0))) (λ x11 : ι → ι → ι . 0) (λ x11 . λ x12 : ι → ι . x2 (λ x13 : (ι → ι) → ι . λ x14 x15 x16 x17 . setsum 0 0)))) (x5 (λ x9 x10 x11 . x10)) = x5 (λ x9 x10 x11 . Inj1 x7)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι) → (ι → ι → ι) → (ι → ι) → ι . x3 (λ x9 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x10 . Inj1 0) 0 = x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . x11)) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : (ι → ι) → ι . λ x10 x11 x12 x13 . setsum (Inj1 (Inj0 (Inj1 0))) (Inj1 x12)) (setsum (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . Inj1 0)) (Inj1 0)) = Inj1 (x1 (λ x9 x10 . x6 x9) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . setsum (Inj0 (setsum 0 0)) 0))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x7 : ι → ι . x2 (λ x9 : (ι → ι) → ι . λ x10 x11 x12 x13 . x0 (λ x14 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι . setsum (x2 (λ x17 : (ι → ι) → ι . λ x18 x19 x20 x21 . 0) (setsum 0 0)) (x16 (λ x17 . x17))) (λ x14 : ι → ι → ι . setsum x11 (x1 (λ x15 x16 . 0) (λ x15 : (ι → ι) → ι → ι → ι . λ x16 . setsum 0 0))) (λ x14 . λ x15 : ι → ι . λ x16 . Inj0 x14)) (x4 (x0 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι . 0) (λ x9 : ι → ι → ι . x6 (λ x10 : (ι → ι) → ι . x6 (λ x11 : (ι → ι) → ι . 0) 0) (x1 (λ x10 x11 . 0) (λ x10 : (ι → ι) → ι → ι → ι . λ x11 . 0))) (λ x9 . λ x10 : ι → ι . λ x11 . x2 (λ x12 : (ι → ι) → ι . λ x13 x14 x15 x16 . x3 (λ x17 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x18 . 0) 0) 0)) (Inj0 0)) = Inj0 (x7 (x5 (λ x9 : ι → ι → ι . x3 (λ x10 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x11 . x10 (λ x12 x13 x14 . 0) 0 0 0) (Inj0 0))))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 x10 . x6) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . Inj1 0) = setsum (x0 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι . Inj0 (x11 (λ x12 . setsum 0 0))) (λ x9 : ι → ι → ι . Inj1 (x9 (x0 (λ x10 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι . 0) (λ x10 : ι → ι → ι . 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0)) (x3 (λ x10 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x11 . 0) 0))) (λ x9 . λ x10 : ι → ι . λ x11 . setsum x11 (Inj0 (x1 (λ x12 x13 . 0) (λ x12 : (ι → ι) → ι → ι → ι . λ x13 . 0))))) x6) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x7 . x1 (λ x9 x10 . x7) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . Inj1 (x6 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι . x15) (λ x14 : ι → ι → ι . Inj1 0) (λ x14 . λ x15 : ι → ι . λ x16 . x13)))) = x7) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x0 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι . x1 (λ x12 x13 . 0) (λ x12 : (ι → ι) → ι → ι → ι . λ x13 . x0 (λ x14 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι . x3 (λ x17 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x18 . Inj1 0) (Inj0 0)) (λ x14 : ι → ι → ι . 0) (λ x14 . λ x15 : ι → ι . λ x16 . 0))) (λ x9 : ι → ι → ι . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0) = x1 (λ x9 x10 . x7 (λ x11 : ι → ι → ι . x9)) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . setsum 0 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι . x3 (λ x12 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x13 . 0) (x9 (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . Inj1 0) (λ x12 x13 . Inj0 (Inj0 0)) (x2 (λ x12 : (ι → ι) → ι . λ x13 x14 x15 x16 . x0 (λ x17 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x18 . λ x19 : (ι → ι) → ι . 0) (λ x17 : ι → ι → ι . 0) (λ x17 . λ x18 : ι → ι . λ x19 . 0)) x10) 0)) (λ x9 : ι → ι → ι . x9 (x6 (λ x10 : (ι → ι) → ι → ι . λ x11 . Inj0 (x2 (λ x12 : (ι → ι) → ι . λ x13 x14 x15 x16 . 0) 0))) 0) (λ x9 . λ x10 : ι → ι . λ x11 . x9) = setsum (x3 (λ x9 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x10 . x2 (λ x11 : (ι → ι) → ι . λ x12 x13 x14 x15 . x13) (x1 (λ x11 x12 . x3 (λ x13 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x14 . 0) 0) (λ x11 : (ι → ι) → ι → ι → ι . λ x12 . x9 (λ x13 x14 x15 . 0) 0 0 0))) (x4 (λ x9 . λ x10 : ι → ι . λ x11 . x3 (λ x12 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x13 . setsum 0 0) 0) (x4 (λ x9 . λ x10 : ι → ι . λ x11 . x2 (λ x12 : (ι → ι) → ι . λ x13 x14 x15 x16 . 0) 0) (x0 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι . 0) (λ x9 : ι → ι → ι . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0))))) (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . 0))) ⟶ False (proof)
Theorem 822fd.. : ∀ x0 : (((((ι → ι) → ι → ι) → ι → ι) → ι) → ι) → (ι → ι) → ι → ι . ∀ x1 : (((((ι → ι) → ι → ι) → ι) → ι → ι) → ι → ι → (ι → ι) → ι) → ι → (ι → (ι → ι) → ι) → ι . ∀ x2 : (ι → ι → ι) → (((ι → ι → ι) → (ι → ι) → ι → ι) → ι) → (ι → ι) → ι → (ι → ι) → ι . ∀ x3 : (ι → ι) → ((ι → ι) → ι → ι → ι → ι) → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . x7) (λ x9 : ι → ι . λ x10 x11 x12 . x3 (λ x13 . x3 (λ x14 . setsum x13 (setsum 0 0)) (λ x14 : ι → ι . λ x15 x16 x17 . x14 x15)) (λ x13 : ι → ι . λ x14 x15 x16 . x16)) = x3 (λ x9 . x6) (λ x9 : ι → ι . λ x10 x11 x12 . x12)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x3 (λ x9 . x2 (λ x10 x11 . x2 (λ x12 x13 . setsum 0 0) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . Inj0 0) (setsum (setsum 0 0)) (setsum (Inj1 0) x11) (λ x12 . Inj1 x10)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 . 0) (x6 (Inj1 0) 0 (x5 0 (λ x10 . setsum 0 0) (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0))) (setsum 0 0)) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . x12) (x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) (x6 0 0 0 0) (λ x11 . λ x12 : ι → ι . Inj1 0)) (λ x11 . λ x12 : ι → ι . x10))) (λ x9 : ι → ι . λ x10 x11 x12 . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) x11 (λ x13 . λ x14 : ι → ι . x14 0)) = Inj1 (setsum (x6 (Inj0 (Inj1 0)) 0 0 x7) x7)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x2 (λ x9 x10 . x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . x2 (λ x12 x13 . x1 (λ x14 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x15 x16 . λ x17 : ι → ι . Inj1 0) 0 (λ x14 . λ x15 : ι → ι . 0)) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . x11 (λ x13 : (ι → ι) → ι → ι . λ x14 . setsum 0 0)) (λ x12 . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) (setsum 0 0) (λ x13 . λ x14 : ι → ι . x12)) 0 (λ x12 . Inj0 0)) (λ x11 . x7 (x7 0 (λ x12 : ι → ι . λ x13 . x0 (λ x14 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x14 . 0) 0) (λ x12 . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) 0 (λ x13 . λ x14 : ι → ι . 0))) (λ x12 : ι → ι . setsum x10) (λ x12 . 0)) 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x6) (λ x10 . 0) (setsum (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 x14 x15 . 0))) (x3 (λ x10 . x6) (λ x10 : ι → ι . λ x11 x12 x13 . Inj0 0)))) (λ x9 . setsum (setsum (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0)) (setsum 0 0)) (Inj1 0)) (setsum x6 0)) 0 (λ x9 . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . 0)) = setsum (setsum 0 (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . x0 (λ x13 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x13 . x11) 0) (x2 (λ x9 x10 . setsum 0 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . setsum 0 0) (λ x9 . Inj1 0) 0 (λ x9 . Inj1 0)) (λ x9 . λ x10 : ι → ι . x7 (x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)) (λ x11 : ι → ι . λ x12 . x10 0) (λ x11 . 0)))) (x3 (λ x9 . x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x10 . x9) (Inj0 0)) (λ x9 : ι → ι . λ x10 x11 x12 . 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι) → ι → ι → ι → ι . x2 (λ x9 x10 . Inj0 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0)) (λ x9 . setsum (Inj0 (Inj0 (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . 0)))) x6) (x2 (λ x9 x10 . setsum (x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x11 . x2 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 . 0) 0 (λ x12 . 0)) (x3 (λ x11 . 0) (λ x11 : ι → ι . λ x12 x13 x14 . 0))) (setsum (setsum 0 0) (setsum 0 0))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 . 0) 0 (λ x9 . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x2 (λ x14 x15 . x12) (λ x14 : (ι → ι → ι) → (ι → ι) → ι → ι . setsum 0 0) (λ x14 . setsum 0 0) x11 (λ x14 . x3 (λ x15 . 0) (λ x15 : ι → ι . λ x16 x17 x18 . 0))) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) (λ x10 . 0) (x7 (λ x10 . λ x11 : ι → ι . 0) 0 0 0)) (λ x10 . λ x11 : ι → ι . setsum (x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . 0)) x9))) (λ x9 . x5 (Inj0 (x2 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x7 (λ x11 . λ x12 : ι → ι . 0) 0 0 0) (λ x10 . setsum 0 0) (setsum 0 0) (λ x10 . x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)))) (setsum (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x10 (λ x14 : (ι → ι) → ι → ι . 0) 0) (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0)) (λ x10 . λ x11 : ι → ι . x7 (λ x12 . λ x13 : ι → ι . 0) 0 0 0)) (setsum x6 (x7 (λ x10 . λ x11 : ι → ι . 0) 0 0 0))) 0 (x5 (setsum x9 0) (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x11) (Inj0 0) (λ x10 . λ x11 : ι → ι . x11 0)) 0 0)) = x2 (λ x9 x10 . Inj0 (x7 (λ x11 . λ x12 : ι → ι . x12 x11) (x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x11 . 0) 0) 0 (setsum x10 x9))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . x7 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . x10) (λ x12 : ι → ι . λ x13 x14 x15 . 0)) 0 (x7 (λ x10 . λ x11 : ι → ι . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) x10 (λ x12 . λ x13 : ι → ι . x3 (λ x14 . 0) (λ x14 : ι → ι . λ x15 x16 x17 . 0))) (Inj0 (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0))) (Inj0 0) 0) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . setsum 0 (x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0))) (λ x10 . 0) (Inj1 (Inj0 0)))) (λ x9 . x2 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 . 0) (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) (x5 0 0 (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0)) (setsum 0 0)) (λ x10 . λ x11 : ι → ι . setsum 0 (Inj0 0))) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . x12) 0 (λ x11 . λ x12 : ι → ι . x3 (λ x13 . x12 0) (λ x13 : ι → ι . λ x14 x15 x16 . 0)))) x6 (λ x9 . Inj1 (setsum x6 (Inj1 (Inj0 0))))) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . Inj0 (x3 (λ x13 . setsum x13 (x3 (λ x14 . 0) (λ x14 : ι → ι . λ x15 x16 x17 . 0))) (λ x13 : ι → ι . λ x14 x15 x16 . x1 (λ x17 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x18 x19 . λ x20 : ι → ι . setsum 0 0) (setsum 0 0) (λ x17 . λ x18 : ι → ι . x3 (λ x19 . 0) (λ x19 : ι → ι . λ x20 x21 x22 . 0))))) (x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x9 . setsum (x5 (λ x10 : (ι → ι) → ι . λ x11 . Inj0 0)) (x2 (λ x10 x11 . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . 0)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0)) (λ x10 . x9) 0 (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0)))) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . Inj0 (x12 0)) 0 (λ x9 . λ x10 : ι → ι . x3 (λ x11 . x11) (λ x11 : ι → ι . λ x12 x13 x14 . Inj1 0)))) (λ x9 . λ x10 : ι → ι . 0) = x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x0 (λ x14 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x14 . x3 (λ x15 . x1 (λ x16 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x17 x18 . λ x19 : ι → ι . 0) 0 (λ x16 . λ x17 : ι → ι . 0)) (λ x15 : ι → ι . λ x16 x17 x18 . setsum 0 0)) 0) (x2 (λ x10 x11 . setsum (x2 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 . 0) 0 (λ x12 . 0)) (Inj1 0)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x10 (λ x11 x12 . 0) (λ x11 . x11) 0) (λ x10 . x3 (λ x11 . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . 0)) (λ x11 : ι → ι . λ x12 x13 x14 . 0)) (x7 (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0))) (λ x10 . 0)) (λ x10 . λ x11 : ι → ι . x7 (λ x12 . x10))) (λ x9 . x6 (x7 (λ x10 . x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . setsum 0 0) (λ x11 . Inj1 0) (x6 0)))) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . 0) 0 (λ x9 . λ x10 : ι → ι . 0))) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . setsum (x9 (λ x13 : (ι → ι) → ι → ι . x3 (λ x14 . 0) (λ x14 : ι → ι . λ x15 x16 x17 . x2 (λ x18 x19 . 0) (λ x18 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x18 . 0) 0 (λ x18 . 0))) x10) 0) 0 (λ x9 . λ x10 : ι → ι . 0) = x4 (λ x9 : ι → ι → ι . x6 (λ x10 . λ x11 : ι → ι . λ x12 . Inj1 (x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . setsum 0 0) 0 (λ x13 . λ x14 : ι → ι . setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . x5 (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . setsum (setsum 0 0) (x2 (λ x13 x14 . 0) (λ x13 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x13 . 0) 0 (λ x13 . 0))))) (λ x9 . Inj1 0) (x5 (λ x9 . x2 (λ x10 x11 . x9) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x10 (λ x11 x12 . Inj1 0) (λ x11 . x10 (λ x12 x13 . 0) (λ x12 . 0) 0) (Inj0 0)) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . x1 (λ x15 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x16 x17 . λ x18 : ι → ι . 0) 0 (λ x15 . λ x16 : ι → ι . 0)) (x3 (λ x11 . 0) (λ x11 : ι → ι . λ x12 x13 x14 . 0)) (λ x11 . λ x12 : ι → ι . Inj1 0)) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) (λ x10 . x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)) 0) (λ x10 . setsum (x3 (λ x11 . 0) (λ x11 : ι → ι . λ x12 x13 x14 . 0)) (x7 0 0)))) = setsum (setsum (x2 (λ x9 x10 . x7 (x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)) (x7 0 0)) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . setsum 0 (Inj1 0)) (λ x9 . 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) 0 (λ x13 . λ x14 : ι → ι . 0)) (x7 0 0) (λ x9 . λ x10 : ι → ι . setsum 0 0)) (λ x9 . 0)) 0) (Inj1 (x5 (λ x9 . 0)))) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι . x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . setsum 0 x6) (λ x9 . 0) (setsum 0 (x7 (x3 (λ x9 . setsum 0 0) (λ x9 : ι → ι . λ x10 x11 x12 . Inj1 0)) (λ x9 : ι → ι . 0) 0)) = Inj0 0) ⟶ False (proof)
Theorem 99962.. : ∀ x0 : ((ι → (ι → ι → ι) → ι) → (ι → ι → ι → ι) → ι) → (ι → ι → ι → ι → ι) → (ι → ι → ι) → ι . ∀ x1 : (ι → ι → ι) → (((ι → ι → ι) → ι) → ι) → ι → (ι → ι) → ι → ι → ι . ∀ x2 : ((ι → ((ι → ι) → ι) → ι → ι) → ((ι → ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x3 : ((((ι → ι) → ι) → ι → (ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι → ι . (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 x6 (x1 (λ x9 x10 . setsum 0 (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . setsum 0 0) (λ x11 : ι → ι . x9) (x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)) (x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)) (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0))) (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . Inj1 (Inj0 0)) (λ x10 : ι → ι . x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . x1 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . 0) 0 (λ x12 . 0) 0 0) (x10 0) (λ x11 . 0) (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . 0) 0 0 0) (x10 0)) (x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . x1 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . 0) 0 (λ x12 . 0) 0 0) (λ x10 x11 x12 x13 . x10) (λ x10 x11 . Inj1 0)) (x7 0) (x2 (λ x10 : ι → ((ι → ι) → ι) → ι → ι . λ x11 : (ι → ι → ι) → ι . 0) (λ x10 : ι → ι . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)))) (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι → ι) → ι . x5 (λ x10 : ι → ι → ι . 0) (x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . 0) (λ x10 x11 x12 x13 . 0) (λ x10 x11 . 0))) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . x6) (λ x9 x10 x11 x12 . setsum 0 0) (λ x9 x10 . Inj0 0)) (λ x9 . 0) (Inj0 (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 0 0)) (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι → ι) → ι . x7 0) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . 0)) (λ x9 . x2 (λ x10 : ι → ((ι → ι) → ι) → ι → ι . λ x11 : (ι → ι → ι) → ι . 0) (λ x10 : ι → ι . 0)) (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 0 0) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . 0) (λ x9 x10 x11 x12 . 0) (λ x9 x10 . 0)))) (λ x9 . Inj1 0) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . x9 0) (λ x10 x11 x12 x13 . x2 (λ x14 : ι → ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι → ι) → ι . 0) (λ x14 : ι → ι . 0)) (λ x10 x11 . Inj0 0))) (x5 (λ x9 : ι → ι → ι . setsum (x9 0 0) (x5 (λ x10 : ι → ι → ι . 0) 0)) 0)) = x6) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . setsum 0 (x1 (λ x10 x11 . x0 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 : ι → ι → ι → ι . x2 (λ x14 : ι → ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι → ι) → ι . 0) (λ x14 : ι → ι . 0)) (λ x12 x13 x14 x15 . x0 (λ x16 : ι → (ι → ι → ι) → ι . λ x17 : ι → ι → ι → ι . 0) (λ x16 x17 x18 x19 . 0) (λ x16 x17 . 0)) (λ x12 x13 . x3 (λ x14 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . 0) 0 0 0)) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . setsum 0 0)) (setsum (x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . 0) 0 0 0) 0) (λ x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . x11 0 (λ x13 x14 . 0)) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)) (setsum (x9 (λ x10 : ι → ι . 0) 0 (λ x10 . 0) 0) (setsum 0 0)) (Inj0 x7))) (λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . 0) (λ x10 x11 x12 x13 . x1 (λ x14 x15 . x13) (λ x14 : (ι → ι → ι) → ι . x11) 0 (λ x14 . x2 (λ x15 : ι → ((ι → ι) → ι) → ι → ι . λ x16 : (ι → ι → ι) → ι . x0 (λ x17 : ι → (ι → ι → ι) → ι . λ x18 : ι → ι → ι → ι . 0) (λ x17 x18 x19 x20 . 0) (λ x17 x18 . 0)) (λ x15 : ι → ι . 0)) (x3 (λ x14 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . x3 (λ x15 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x15 : ι → ι . 0) 0 0 0) (λ x14 : ι → ι . Inj1 0) 0 0 (Inj0 0)) (setsum x12 (x3 (λ x14 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . 0) 0 0 0))) (λ x10 x11 . Inj0 x10)) 0 (Inj1 (x1 (λ x9 x10 . Inj1 (Inj1 0)) (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . x3 (λ x12 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . 0) 0 0 0) (λ x10 x11 x12 x13 . Inj1 0) (λ x10 x11 . 0)) (setsum (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 0 0) 0) (λ x9 . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . x7) (λ x10 x11 x12 x13 . 0) (λ x10 x11 . 0)) (setsum (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 0 0) 0) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . 0) (λ x11 : ι → ι . 0)) (λ x9 x10 x11 x12 . Inj0 0) (λ x9 x10 . x6)))) (Inj0 x7) = x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . Inj0 (Inj0 0)) (λ x9 x10 x11 x12 . x1 (λ x13 x14 . x13) (λ x13 : (ι → ι → ι) → ι . 0) 0 (λ x13 . x2 (λ x14 : ι → ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι → ι) → ι . x0 (λ x16 : ι → (ι → ι → ι) → ι . λ x17 : ι → ι → ι → ι . setsum 0 0) (λ x16 x17 x18 x19 . x19) (λ x16 x17 . x1 (λ x18 x19 . 0) (λ x18 : (ι → ι → ι) → ι . 0) 0 (λ x18 . 0) 0 0)) (λ x14 : ι → ι . x3 (λ x15 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . x1 (λ x16 x17 . 0) (λ x16 : (ι → ι → ι) → ι . 0) 0 (λ x16 . 0) 0 0) (λ x15 : ι → ι . x0 (λ x16 : ι → (ι → ι → ι) → ι . λ x17 : ι → ι → ι → ι . 0) (λ x16 x17 x18 x19 . 0) (λ x16 x17 . 0)) (Inj1 0) 0 (setsum 0 0))) (Inj1 0) 0) (λ x9 x10 . setsum 0 (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . setsum 0 0) (λ x11 : ι → ι . x10) (Inj1 (Inj1 0)) x6 (x1 (λ x11 x12 . x11) (λ x11 : (ι → ι → ι) → ι . x10) x10 (λ x11 . setsum 0 0) (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0) x7)))) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . 0)) (λ x9 : ι → ι . 0) = x5) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x7 . x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . 0) = Inj0 (x5 (x6 (λ x9 . λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x9 : ι → ι . x6 (λ x10 . λ x11 : ι → ι . λ x12 . Inj0 0) (λ x10 : ι → ι . Inj0 0))) 0 0 (x4 0 (λ x9 : ι → ι . λ x10 . setsum (x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)) (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . 0) 0 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι → ι . ∀ x7 . x1 (λ x9 x10 . x9) (λ x9 : (ι → ι → ι) → ι . Inj0 (x6 (λ x10 . λ x11 : ι → ι . x10) 0 (x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . x9 (λ x11 x12 . 0)) x5 (Inj1 0) (setsum 0 0)))) (setsum (setsum (setsum (Inj0 0) (Inj0 0)) (setsum (setsum 0 0) (setsum 0 0))) x4) (λ x9 . setsum (x1 (λ x10 x11 . x10) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . 0)) (x1 (λ x10 x11 . x7) (λ x10 : (ι → ι → ι) → ι . 0) (x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . 0) 0 0 0) (λ x10 . Inj0 0) 0 (Inj0 0)) (λ x10 . x7) (x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . Inj1 0) (λ x10 x11 x12 x13 . 0) (λ x10 x11 . x1 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . 0) 0 (λ x12 . 0) 0 0)) x7) (Inj1 x5)) (x6 (λ x9 . λ x10 : ι → ι . x9) (setsum (Inj0 (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 0 0)) 0) (x1 (λ x9 x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . setsum 0 0) (λ x11 x12 x13 x14 . x12) (λ x11 x12 . setsum 0 0)) (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . setsum 0 0) (λ x10 x11 x12 x13 . setsum 0 0) (λ x10 x11 . setsum 0 0)) (setsum 0 (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι → ι) → ι . 0) 0 (λ x9 . 0) 0 0)) (λ x9 . Inj0 (x1 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 . 0) 0 0)) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . Inj1 0) (λ x9 : ι → ι . x9 0)) (Inj0 (Inj0 0)))) x4 = x4) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 x10 . x9) (λ x9 : (ι → ι → ι) → ι . x7) 0 (λ x9 . x5 (x5 x9 (λ x10 . x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . Inj1 0) (setsum 0 0) (x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)) (setsum 0 0)) Inj1 0) (λ x10 . 0) (λ x10 . x6) 0) x7 (x1 (λ x9 x10 . x7) (λ x9 : (ι → ι → ι) → ι . Inj1 x6) x7 (λ x9 . x5 0 (λ x10 . setsum 0 x6) (λ x10 . x9) (Inj1 (x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . 0) 0 0 0))) (Inj1 (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . setsum 0 0) (λ x9 : ι → ι . x1 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 . 0) 0 0) (setsum 0 0) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . 0) (λ x9 x10 x11 x12 . 0) (λ x9 x10 . 0)) (setsum 0 0))) (setsum (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . 0) (λ x11 : ι → ι . 0)) (λ x9 x10 x11 x12 . 0) (λ x9 x10 . 0)) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . 0) (λ x9 x10 x11 x12 . x1 (λ x13 x14 . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 (λ x13 . 0) 0 0) (λ x9 x10 . x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . 0) 0 0 0)))) = Inj0 x6) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . Inj0 (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . x11 (λ x12 : ι → ι . setsum 0 0) (x2 (λ x12 : ι → ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι → ι) → ι . 0) (λ x12 : ι → ι . 0)) (λ x12 . x10 0 0 0) (setsum 0 0)) (λ x11 : ι → ι . x0 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 : ι → ι → ι → ι . setsum 0 0) (λ x12 x13 x14 x15 . x13) (λ x12 x13 . setsum 0 0)) (x10 (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0) 0 0) (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . 0) (setsum 0 0) (x6 (λ x11 : ι → ι . λ x12 . 0)) (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0)) 0)) (λ x9 x10 x11 x12 . 0) (λ x9 x10 . Inj1 (Inj1 x9)) = setsum (setsum (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . Inj1 (x10 0 0 0)) (λ x9 x10 x11 x12 . x10) (λ x9 x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . x3 (λ x15 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x15 : ι → ι . 0) 0 0 0) (λ x11 x12 . setsum 0 0))) (x6 (λ x9 : ι → ι . λ x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . x2 (λ x13 : ι → ((ι → ι) → ι) → ι → ι . λ x14 : (ι → ι → ι) → ι . 0) (λ x13 : ι → ι . 0)) (λ x11 x12 x13 x14 . x0 (λ x15 : ι → (ι → ι → ι) → ι . λ x16 : ι → ι → ι → ι . 0) (λ x15 x16 x17 x18 . 0) (λ x15 x16 . 0)) (λ x11 x12 . setsum 0 0)))) (x7 0 (λ x9 : ι → ι . 0))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι → ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . x10 (x12 (λ x13 x14 . x3 (λ x15 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x15 : ι → ι . 0) 0 0 0)) (x2 (λ x13 : ι → ((ι → ι) → ι) → ι → ι . λ x14 : (ι → ι → ι) → ι . x11 0 (λ x15 : ι → ι . 0) 0) (λ x13 : ι → ι . x12 (λ x14 x15 . 0))) 0) (λ x11 : ι → ι . 0)) (λ x9 x10 x11 x12 . x12) (λ x9 x10 . x1 (λ x11 . x1 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . setsum (x12 (λ x13 x14 . 0)) x11) (x1 (λ x12 x13 . setsum 0 0) (λ x12 : (ι → ι → ι) → ι . x3 (λ x13 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x13 : ι → ι . 0) 0 0 0) x9 (λ x12 . x3 (λ x13 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x13 : ι → ι . 0) 0 0 0) (x3 (λ x12 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . 0) 0 0 0) x10) (λ x12 . 0) x11) (λ x11 : (ι → ι → ι) → ι . 0) (x1 (λ x11 x12 . x12) (λ x11 : (ι → ι → ι) → ι . x9) 0 (λ x11 . 0) x7 0) (λ x11 . 0) (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . x9) (λ x11 : ι → ι . x0 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 : ι → ι → ι → ι . x3 (λ x14 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . 0) 0 0 0) (λ x12 x13 x14 x15 . x12) (λ x12 x13 . x10)) (setsum x6 (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0)) (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . x11 (λ x12 x13 . 0)) 0 (λ x11 . x3 (λ x12 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . 0) 0 0 0) x9 x6) 0) 0) = setsum (x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . Inj0 0) (λ x9 : ι → ι . Inj0 0)) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . x9 (setsum 0 x7) (λ x11 : ι → ι . 0) (x2 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . x10 (λ x13 x14 . 0)) (λ x11 : ι → ι . 0))) (λ x9 : ι → ι . x2 (λ x10 : ι → ((ι → ι) → ι) → ι → ι . λ x11 : (ι → ι → ι) → ι . x0 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 : ι → ι → ι → ι . 0) (λ x12 x13 x14 x15 . x12) (λ x12 x13 . x1 (λ x14 x15 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 (λ x14 . 0) 0 0)) (λ x10 : ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . x0 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 : ι → ι → ι → ι . 0) (λ x13 x14 x15 x16 . 0) (λ x13 x14 . 0)) (λ x11 : ι → ι . x7))))) ⟶ False (proof)
Theorem e2151.. : ∀ x0 : (ι → ι) → (ι → ι → (ι → ι) → ι → ι) → ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x1 : (((((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι) → ι → ι → ι → ι . ∀ x2 : (ι → ι) → (ι → ι) → ι . ∀ x3 : (((((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι) → ι) → ι → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι . x3 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0 = x6 (setsum 0 0) (λ x9 : ι → ι . Inj0 (x6 (setsum (Inj0 0) (x5 0)) (λ x10 : ι → ι . setsum (x9 0) (x3 (λ x11 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . Inj1 (x2 (λ x11 . setsum 0 0) (λ x11 . 0))) (x2 (λ x9 . 0) (λ x9 . x7)) (Inj1 0) (Inj1 (x0 (λ x9 . Inj1 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x2 (λ x13 . 0) (λ x13 . 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0 0 0)))) = Inj0 (x0 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x0 (λ x13 . x2 (λ x14 . 0) (λ x14 . 0)) (λ x13 x14 . λ x15 : ι → ι . x1 (λ x16 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x17 : ((ι → ι) → ι → ι) → (ι → ι) → ι . setsum 0 0) 0 (x15 0)) (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x9 0 (Inj1 x11)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 . x2 (λ x9 . 0) (λ x9 . x2 (λ x10 . x0 (λ x11 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . x3 (λ x15 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . Inj0 0) (x13 0)) (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0)) (λ x10 . x0 (λ x11 . x7) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι . λ x12 : ι → ι . Inj1))) = Inj1 0) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι) → ι . ∀ x7 : (ι → ι) → ι → ι . x2 (λ x9 . Inj0 (x3 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . x2 (λ x11 . x2 (λ x12 . 0) (λ x12 . 0)) (λ x11 . 0)) x5)) (λ x9 . x6 (λ x10 : ι → ι . x2 (λ x11 . x3 (λ x12 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . setsum 0 0) 0) (λ x11 . 0))) = setsum (setsum 0 0) 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) x7 0 0 = x7) ⟶ (∀ x4 x5 x6 : ι → ι . ∀ x7 . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . Inj1 0) (x6 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . x7) (Inj0 (x4 (x6 0))) (setsum (Inj1 (x3 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0)) (x6 0)) 0) (x6 (x0 (λ x9 . Inj1 (x5 0)) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x2 (λ x13 . Inj0 0) (λ x13 . Inj1 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0))) = setsum (x0 (λ x9 . Inj0 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x12) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0)) 0) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x0 (λ x9 . setsum (Inj0 0) (x0 (λ x10 . Inj0 (x3 (λ x11 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0)) (λ x10 x11 . λ x12 : ι → ι . λ x13 . x3 (λ x14 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . x2 (λ x15 . 0) (λ x15 . 0)) x10) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x3 (λ x13 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . x12) 0))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x2 (λ x13 . x10) (λ x13 . x10)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (x9 (Inj1 0) x7) x7 (x0 (λ x12 . x11) (λ x12 x13 . λ x14 : ι → ι . λ x15 . Inj0 0) (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . setsum 0 (Inj1 0)))) = setsum (setsum (x0 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . x11) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . setsum x11 (Inj1 0))) (Inj0 (setsum 0 (setsum 0 0)))) (setsum 0 0)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x7 : (ι → ι) → ι → ι . x0 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . setsum (x2 (λ x12 . Inj0 0) (λ x12 . x11)) (x2 (λ x12 . x2 (λ x13 . Inj1 0) (λ x13 . Inj1 0)) (λ x12 . 0))) = x7 (λ x9 . Inj1 (x3 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . x2 (λ x11 . 0) (λ x11 . x0 (λ x12 . 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . 0) (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . 0))) (Inj0 0))) (Inj0 0)) ⟶ False (proof)
Theorem 89179.. : ∀ x0 : (ι → ι) → (ι → ι) → ι → ι → ι . ∀ x1 : (ι → (ι → ι → ι → ι) → (ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι → ι) → ι → ι . ∀ x2 : ((ι → ι) → (((ι → ι) → ι → ι) → ι) → ι) → (ι → ι) → (ι → ι) → ι . ∀ x3 : ((((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι) → (ι → ι) → ((ι → ι) → ι) → ι) → ((((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι) → ι . (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x3 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . setsum (Inj1 0) 0) (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι) → ι → ι . setsum 0 (x3 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . x3 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . x1 (λ x17 . λ x18 : ι → ι → ι → ι . λ x19 x20 : ι → ι . λ x21 . 0) 0 (λ x17 x18 . 0) 0) (λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι) → ι → ι . x3 (λ x16 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x17 : ι → ι . λ x18 : (ι → ι) → ι . 0) (λ x16 : ((ι → ι) → ι) → ι → ι . λ x17 : (ι → ι) → ι → ι . 0))) (λ x11 : ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι) → ι → ι . x11 (λ x13 : ι → ι . Inj0 0) (Inj0 0)))) = x5 (λ x9 x10 x11 . setsum (setsum (x3 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . Inj1 0) (λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι) → ι → ι . Inj1 0)) (Inj0 x9)) (x1 (λ x12 . λ x13 : ι → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . x15 (x14 0)) (x7 (λ x12 . x9)) (λ x12 x13 . 0) (x1 (λ x12 . λ x13 : ι → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . Inj0 0) (x7 (λ x12 . 0)) (λ x12 x13 . x2 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → ι . 0) (λ x14 . 0) (λ x14 . 0)) 0))) (λ x9 x10 . 0)) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 x6 x7 . x3 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . x1 (λ x12 . λ x13 : ι → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . x1 (λ x17 . λ x18 : ι → ι → ι → ι . λ x19 x20 : ι → ι . λ x21 . x21) 0 (λ x17 x18 . x3 (λ x19 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x20 : ι → ι . λ x21 : (ι → ι) → ι . Inj0 0) (λ x19 : ((ι → ι) → ι) → ι → ι . λ x20 : (ι → ι) → ι → ι . x3 (λ x21 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x22 : ι → ι . λ x23 : (ι → ι) → ι . 0) (λ x21 : ((ι → ι) → ι) → ι → ι . λ x22 : (ι → ι) → ι → ι . 0))) (x0 (λ x17 . x14 0) (λ x17 . 0) (setsum 0 0) (x0 (λ x17 . 0) (λ x17 . 0) 0 0))) (Inj0 (Inj0 (x3 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι) → ι → ι . 0)))) (λ x12 x13 . setsum x12 (x1 (λ x14 . λ x15 : ι → ι → ι → ι . λ x16 x17 : ι → ι . λ x18 . Inj1 0) (Inj0 0) (λ x14 x15 . 0) (x3 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι) → ι → ι . 0)))) 0) (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι) → ι → ι . 0) = setsum x5 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι → ι . ∀ x6 x7 . x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι . Inj1 (x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . x2 (λ x16 : ι → ι . λ x17 : ((ι → ι) → ι → ι) → ι . x1 (λ x18 . λ x19 : ι → ι → ι → ι . λ x20 x21 : ι → ι . λ x22 . 0) 0 (λ x18 x19 . 0) 0) (λ x16 . x16) (λ x16 . x3 (λ x17 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x18 : ι → ι . λ x19 : (ι → ι) → ι . 0) (λ x17 : ((ι → ι) → ι) → ι → ι . λ x18 : (ι → ι) → ι → ι . 0))) x6 (λ x11 x12 . setsum (x2 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → ι . 0) (λ x13 . 0) (λ x13 . 0)) 0) (x2 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . 0) (λ x11 . x3 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι) → ι → ι . 0)) (λ x11 . 0)))) (λ x9 . x6) (λ x9 . 0) = x6) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι . Inj0 (x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . x1 (λ x16 . λ x17 : ι → ι → ι → ι . λ x18 x19 : ι → ι . λ x20 . x18 0) (x1 (λ x16 . λ x17 : ι → ι → ι → ι . λ x18 x19 : ι → ι . λ x20 . 0) 0 (λ x16 x17 . 0) 0) (λ x16 x17 . x14 0) (x1 (λ x16 . λ x17 : ι → ι → ι → ι . λ x18 x19 : ι → ι . λ x20 . 0) 0 (λ x16 x17 . 0) 0)) (setsum 0 (x0 (λ x11 . 0) (λ x11 . 0) 0 0)) (λ x11 x12 . setsum (Inj1 0) (setsum 0 0)) 0)) (λ x9 . 0) (λ x9 . x5) = x5) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . Inj0 (x10 (setsum (x10 0 0 0) (Inj0 0)) (x12 (x3 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι) → ι → ι . 0))) 0)) (Inj0 0) (λ x9 x10 . x2 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . x2 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → ι . x3 (λ x15 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x16 : ι → ι . λ x17 : (ι → ι) → ι . Inj1 0) (λ x15 : ((ι → ι) → ι) → ι → ι . λ x16 : (ι → ι) → ι → ι . setsum 0 0)) (λ x13 . setsum 0 (Inj1 0)) (λ x13 . x1 (λ x14 . λ x15 : ι → ι → ι → ι . λ x16 x17 : ι → ι . λ x18 . x3 (λ x19 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x20 : ι → ι . λ x21 : (ι → ι) → ι . 0) (λ x19 : ((ι → ι) → ι) → ι → ι . λ x20 : (ι → ι) → ι → ι . 0)) 0 (λ x14 x15 . x1 (λ x16 . λ x17 : ι → ι → ι → ι . λ x18 x19 : ι → ι . λ x20 . 0) 0 (λ x16 x17 . 0) 0) (Inj0 0))) (λ x11 . Inj1 x10) (λ x11 . 0)) (setsum x5 (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0) (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . x11 0) x4 (λ x9 x10 . x10) x7) (λ x9 x10 . x10) 0)) = Inj0 (x6 (Inj0 0))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι . x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . x3 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . x0 (λ x17 . x15 (x16 (λ x18 . 0))) (λ x17 . setsum (x3 (λ x18 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x19 : ι → ι . λ x20 : (ι → ι) → ι . 0) (λ x18 : ((ι → ι) → ι) → ι → ι . λ x19 : (ι → ι) → ι → ι . 0)) 0) 0 (x2 (λ x17 : ι → ι . λ x18 : ((ι → ι) → ι → ι) → ι . x17 0) (λ x17 . Inj0 0) (λ x17 . x16 (λ x18 . 0)))) (λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι) → ι → ι . setsum (x12 0) (Inj1 (x12 0)))) (setsum 0 0) (λ x9 x10 . x6) (setsum (Inj1 (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0) x5 (λ x9 x10 . setsum 0 0) (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0) 0 (λ x9 x10 . 0) 0))) (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . x11 (x12 0)) (x0 (λ x9 . 0) (λ x9 . 0) (setsum 0 0) (x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι . 0) (λ x9 . 0) (λ x9 . 0))) (λ x9 x10 . 0) (Inj0 0))) = x6) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . x0 (λ x9 . Inj1 0) (setsum 0) 0 (Inj0 (x5 (λ x9 : (ι → ι) → ι . λ x10 . 0) 0 (λ x9 . 0) (x3 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . 0) (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι) → ι → ι . 0)))) = setsum (setsum 0 (setsum (Inj0 (setsum 0 0)) (x0 (λ x9 . x5 (λ x10 : (ι → ι) → ι . λ x11 . 0) 0 (λ x10 . 0) 0) (λ x9 . setsum 0 0) (setsum 0 0) (Inj0 0)))) (x0 (λ x9 . Inj1 (x5 (λ x10 : (ι → ι) → ι . λ x11 . x2 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → ι . 0) (λ x12 . 0) (λ x12 . 0)) (x2 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → ι . 0) (λ x10 . 0) (λ x10 . 0)) (λ x10 . 0) (setsum 0 0))) (λ x9 . x0 (λ x10 . x6 (λ x11 : (ι → ι) → ι . x3 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι) → ι → ι . 0))) (λ x10 . setsum (x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . 0) 0 (λ x11 x12 . 0) 0) x9) 0 (Inj0 (setsum 0 0))) x4 0)) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι → ι) → ι → ι . x0 (λ x9 . x1 (λ x10 . λ x11 : ι → ι → ι → ι . λ x12 x13 : ι → ι . λ x14 . 0) (x5 (Inj0 x9) (λ x10 : ι → ι . λ x11 . x9) (λ x10 . x0 (λ x11 . x7 (λ x12 x13 . 0) 0) (λ x11 . 0) x10 (x7 (λ x11 x12 . 0) 0))) (λ x10 x11 . x11) (x7 (λ x10 x11 . x7 (λ x12 x13 . x13) x9) (x7 (λ x10 x11 . Inj1 0) (x0 (λ x10 . 0) (λ x10 . 0) 0 0)))) (λ x9 . x7 (λ x10 x11 . x3 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . x12 (λ x15 : ι → ι → ι . λ x16 : ι → ι . λ x17 . x0 (λ x18 . 0) (λ x18 . 0) 0 0) (λ x15 : ι → ι . λ x16 . Inj1 0)) (λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι) → ι → ι . x12 (λ x14 : ι → ι . x12 (λ x15 : ι → ι . 0) 0) (Inj0 0))) (x7 (λ x10 x11 . x9) (x3 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 : (ι → ι) → ι . x9) (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : (ι → ι) → ι → ι . Inj1 0)))) x4 x6 = setsum (x7 (λ x9 x10 . 0) x4) 0) ⟶ False (proof)
Theorem 71531.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : ((((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι) → ι) → ι → ((ι → ι → ι) → ι) → ι . ∀ x2 : (ι → (((ι → ι) → ι → ι) → ι → ι) → ι) → (ι → ((ι → ι) → ι) → ι) → ι . ∀ x3 : ((ι → ι → ι) → ι) → ((((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι) → (((ι → ι) → ι) → ι) → ι → ι . (∀ x4 : ι → ι → ι → ι . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x3 (λ x9 : ι → ι → ι . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . x6) (λ x9 : (ι → ι) → ι . setsum x6 0) (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . x3 (λ x11 : ι → ι → ι . 0) (λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 . 0) (λ x11 : (ι → ι) → ι . 0) 0) (λ x9 . λ x10 : (ι → ι) → ι . setsum (x7 0 x9) x6)) = x6) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι . x3 (λ x9 : ι → ι → ι . x3 (λ x10 : ι → ι → ι . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . x0 (λ x12 . x9 0 (Inj0 0)) 0) (λ x10 : (ι → ι) → ι . x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι → ι . Inj0 (x0 (λ x13 . 0) 0)) (λ x11 . λ x12 : (ι → ι) → ι . Inj0 0)) 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . 0) (λ x9 : (ι → ι) → ι . 0) (x3 (λ x9 : ι → ι → ι . Inj0 (x3 (λ x10 : ι → ι → ι . Inj0 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . Inj0 0) (λ x10 : (ι → ι) → ι . x1 (λ x11 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . 0) 0 (λ x11 : ι → ι → ι . 0)) (Inj0 0))) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . Inj1 (x3 (λ x11 : ι → ι → ι . 0) (λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 . setsum 0 0) (λ x11 : (ι → ι) → ι . x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . 0)) (Inj0 0))) (λ x9 : (ι → ι) → ι . 0) (Inj1 (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . x10 (λ x11 : ι → ι . λ x12 . 0) 0) (λ x9 . λ x10 : (ι → ι) → ι . setsum 0 0)))) = setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . x10 (λ x11 . 0))) (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . x6) (λ x9 . λ x10 : (ι → ι) → ι . Inj1 (Inj0 0)))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . x6) = x6) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 x6 x7 . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . Inj0 (x3 (λ x11 : ι → ι → ι . setsum (x3 (λ x12 : ι → ι → ι . 0) (λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι . 0) 0) x7) (λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 . x11 (λ x13 : ι → ι . λ x14 . x11 (λ x15 : ι → ι . λ x16 . 0) 0 0) 0 (Inj0 0)) (λ x11 : (ι → ι) → ι . x9) (Inj1 (Inj0 0)))) (λ x9 . λ x10 : (ι → ι) → ι . setsum 0 (setsum x9 0)) = x6) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι → ι . x7) (λ x10 . λ x11 : (ι → ι) → ι . x10)) 0 (λ x9 : ι → ι → ι . setsum 0 (x0 (x3 (λ x10 : ι → ι → ι . x1 (λ x11 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . 0) 0 (λ x11 : ι → ι → ι . 0)) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . x11) (λ x10 : (ι → ι) → ι . x9 0 0)) 0)) = setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . x3 (λ x11 : ι → ι → ι . x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . x2 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x14 . λ x15 : (ι → ι) → ι . 0))) (λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 . x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι → ι . Inj1 0) (λ x13 . λ x14 : (ι → ι) → ι . Inj1 0)) (λ x11 : (ι → ι) → ι . 0) (x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . Inj0 0)))) 0) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x1 (λ x9 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι → ι . x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . setsum x12 (setsum 0 0))) (λ x10 . λ x11 : (ι → ι) → ι . setsum (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι → ι . setsum 0 0) (λ x12 . λ x13 : (ι → ι) → ι . x0 (λ x14 . 0) 0)) 0)) x5 (λ x9 : ι → ι → ι . Inj0 (Inj1 (Inj0 0))) = setsum 0 (Inj1 x5)) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 . 0) x7 = setsum (setsum 0 0) (setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . setsum (Inj0 0) (setsum 0 0)) (λ x9 . λ x10 : (ι → ι) → ι . 0)) x5)) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 . x1 (λ x10 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . 0) x6 (λ x10 : ι → ι → ι . setsum 0 x9)) (setsum (x1 (λ x9 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . x6) (x3 (λ x9 : ι → ι → ι . Inj1 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . setsum 0 0) (λ x9 : (ι → ι) → ι . x3 (λ x10 : ι → ι → ι . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . 0) (λ x10 : (ι → ι) → ι . 0) 0) (setsum 0 0)) (λ x9 : ι → ι → ι . 0)) 0) = x1 (λ x9 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . setsum (x3 (λ x10 : ι → ι → ι . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . 0) (λ x10 : (ι → ι) → ι . setsum (x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0)) 0) (x5 (λ x10 x11 x12 . x11) (λ x10 : ι → ι . λ x11 . 0))) (Inj1 (Inj0 0))) (Inj1 0) (λ x9 : ι → ι → ι . Inj0 (setsum x7 (x0 (λ x10 . x6) (Inj0 0))))) ⟶ False (proof)
Theorem 43419.. : ∀ x0 : (ι → ι → ι) → ι → ι . ∀ x1 : (ι → ι → ι) → (ι → ι → (ι → ι) → ι → ι) → ι . ∀ x2 : (ι → ι) → (ι → ((ι → ι) → ι) → ι) → ι → ι . ∀ x3 : (ι → (((ι → ι) → ι) → ι) → ι) → (((ι → ι) → ι) → ι) → ι → ι . (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . Inj1 x7) (λ x9 : (ι → ι) → ι . setsum (setsum 0 (x2 (λ x10 . x9 (λ x11 . 0)) (λ x10 . λ x11 : (ι → ι) → ι . setsum 0 0) (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . 0) (λ x10 : (ι → ι) → ι . 0) 0))) 0) (x2 (λ x9 . x0 (λ x10 x11 . Inj0 0) (x0 (λ x10 x11 . 0) 0)) (λ x9 . λ x10 : (ι → ι) → ι . x1 (λ x11 x12 . x2 (λ x13 . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) x9) (λ x11 x12 . λ x13 : ι → ι . λ x14 . setsum 0 (Inj1 0))) x5) = x2 (λ x9 . x1 (λ x10 x11 . x9) (λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj0 (Inj1 0))) (λ x9 . λ x10 : (ι → ι) → ι . Inj0 (x0 (λ x11 x12 . 0) x9)) (x0 (λ x9 x10 . x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι . setsum 0 (x3 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . 0) (λ x13 : (ι → ι) → ι . 0) 0)) (Inj1 (x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) 0))) (x0 (λ x9 x10 . x1 (λ x11 x12 . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . 0) (λ x13 : (ι → ι) → ι . 0) 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . x3 (λ x15 . λ x16 : ((ι → ι) → ι) → ι . 0) (λ x15 : (ι → ι) → ι . 0) 0)) 0))) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι → ι → ι . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . x9) (λ x9 : (ι → ι) → ι . setsum 0 (x9 (λ x10 . x0 (λ x11 x12 . x11) (Inj1 0)))) (x1 (λ x9 x10 . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . x2 (λ x13 . x3 (λ x14 . λ x15 : ((ι → ι) → ι) → ι . 0) (λ x14 : (ι → ι) → ι . 0) 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) (x2 (λ x13 . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) 0)) (λ x11 : (ι → ι) → ι . x0 (λ x12 x13 . x10) 0) x10) (λ x9 x10 . λ x11 : ι → ι . Inj1)) = Inj0 (x2 (λ x9 . 0) (λ x9 . λ x10 : (ι → ι) → ι . 0) 0)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι → ι . x2 (λ x9 . setsum 0 (x6 (λ x10 x11 x12 . setsum (x0 (λ x13 x14 . 0) 0) (Inj0 0)))) (λ x9 . λ x10 : (ι → ι) → ι . x0 (λ x11 x12 . setsum (Inj1 (Inj0 0)) (Inj0 x11)) (x7 (λ x11 . λ x12 : ι → ι . x1 (λ x13 x14 . Inj1 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . setsum 0 0)) 0)) (x6 (λ x9 x10 x11 . 0)) = x0 (λ x9 x10 . Inj1 (x0 (λ x11 x12 . setsum 0 (x2 (λ x13 . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) 0)) (x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . x1 (λ x13 x14 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (λ x11 : (ι → ι) → ι . x11 (λ x12 . 0)) (Inj1 0)))) (setsum (Inj0 0) (Inj0 (setsum (setsum 0 0) (setsum 0 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x2 (λ x9 . x2 (λ x10 . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . x12 (λ x13 : ι → ι . 0)) (λ x11 : (ι → ι) → ι . x9) 0) (λ x10 . λ x11 : (ι → ι) → ι . x9) (setsum (setsum x5 x6) (x1 (λ x10 x11 . x2 (λ x12 . 0) (λ x12 . λ x13 : (ι → ι) → ι . 0) 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0)))) (λ x9 . λ x10 : (ι → ι) → ι . x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . 0) (λ x13 : (ι → ι) → ι . Inj1 x11) (x12 (λ x13 . setsum 0 0))) 0) 0 = x2 (λ x9 . x6) (λ x9 . λ x10 : (ι → ι) → ι . setsum (setsum 0 (Inj0 0)) (setsum (setsum (x0 (λ x11 x12 . 0) 0) x9) 0)) (x0 (λ x9 x10 . setsum x6 0) (x7 (setsum (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . 0) (λ x9 : (ι → ι) → ι . 0) 0) x5)))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . x1 (λ x9 x10 . Inj0 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) = x4) ⟶ (∀ x4 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι) → ι) → ι → (ι → ι) → ι . x1 (λ x9 x10 . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) = setsum (Inj1 0) x6) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι) → ι → ι → ι . ∀ x7 : (ι → ι → ι) → ι . x0 (λ x9 x10 . x6 (λ x11 : ι → ι → ι . x7 (λ x12 x13 . x3 (λ x14 . λ x15 : ((ι → ι) → ι) → ι . x13) (λ x14 : (ι → ι) → ι . x13) (x1 (λ x14 x15 . 0) (λ x14 x15 . λ x16 : ι → ι . λ x17 . 0)))) (setsum (setsum (Inj1 0) (x1 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0))) 0) (setsum (x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . setsum 0 0) (λ x11 : (ι → ι) → ι . 0) (setsum 0 0)) (Inj1 (x1 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0))))) (setsum (Inj0 (Inj1 0)) (x1 (λ x9 x10 . x2 (λ x11 . x10) (λ x11 . λ x12 : (ι → ι) → ι . x1 (λ x13 x14 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (x6 (λ x11 : ι → ι → ι . 0) 0 0)) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0))) = x6 (λ x9 : ι → ι → ι . setsum (setsum x5 x5) (x9 (x0 (λ x10 x11 . x1 (λ x12 x13 . 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . 0)) (x9 0 0)) (setsum (x6 (λ x10 : ι → ι → ι . 0) 0 0) (x0 (λ x10 x11 . 0) 0)))) x5 (Inj0 (x7 (λ x9 x10 . x9)))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x9 x10 . x2 (λ x11 . x7 0) (λ x11 . λ x12 : (ι → ι) → ι . x1 (λ x13 x14 . Inj1 (Inj1 0)) (λ x13 x14 . λ x15 : ι → ι . λ x16 . setsum 0 x13)) 0) (x0 (λ x9 x10 . x2 (λ x11 . x0 (λ x12 x13 . 0) (setsum 0 0)) (λ x11 . λ x12 : (ι → ι) → ι . x1 (λ x13 x14 . x0 (λ x15 x16 . 0) 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (x7 (x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) 0))) (setsum (x2 (λ x9 . x0 (λ x10 x11 . 0) 0) (λ x9 . λ x10 : (ι → ι) → ι . setsum 0 0) (x0 (λ x9 x10 . 0) 0)) (x7 (Inj1 0)))) = x2 (λ x9 . Inj1 0) (λ x9 . λ x10 : (ι → ι) → ι . Inj0 (setsum x9 0)) (x7 (x4 (Inj1 (x7 0)) (x0 (λ x9 x10 . x1 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0)) 0)))) ⟶ False (proof)