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Proofgold Term Root Disambiguation

∀ x0 : (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 . ∀ x3 : ((ι → ι → ι)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 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x3 (λ x13 : ι → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x13 (x0 (λ x17 x18 . λ x19 : ι → ι . x2 (λ x20 x21 . 0) 0) 0 (λ x17 : (ι → ι) → ι . x14) (λ x17 x18 . Inj0 0)) 0) (λ x13 . x12) x10 (λ x13 : ι → ι . x12) (λ x13 . setsum x13 x13) (x0 (λ x13 x14 . λ x15 : ι → ι . x15 (x1 (λ x16 . 0) (λ x16 . 0) 0 (λ x16 . 0) (λ x16 . 0) 0)) 0 (λ x13 : (ι → ι) → ι . x13 (λ x14 . 0)) (λ x13 x14 . x11 (x1 (λ x15 . 0) (λ x15 . 0) 0 (λ x15 . 0) (λ x15 . 0) 0)))) (λ x9 . 0) 0 (λ x9 : ι → ι . setsum (x6 (x1 (λ x10 . x2 (λ x11 x12 . 0) 0) (λ x10 . x9 0) 0 (λ x10 . 0) (λ x10 . 0) (x5 (λ x10 . 0) (λ x10 . 0) (λ x10 . 0) 0))) (x1 (λ x10 . 0) (λ x10 . x6 0) (x5 (λ x10 . 0) (λ x10 . 0) (λ x10 . x3 (λ x11 : ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 . 0) 0 (λ x11 : ι → ι . 0) (λ x11 . 0) 0) (x5 (λ x10 . 0) (λ x10 . 0) (λ x10 . 0) 0)) (λ x10 . Inj1 (x6 0)) (λ x10 . setsum (x3 (λ x11 : ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 . 0) 0 (λ x11 : ι → ι . 0) (λ x11 . 0) 0) x7) 0)) (λ x9 . x3 (λ x10 : ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x10 . Inj0 (x3 (λ x11 : ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . setsum 0 0) (λ x11 . x10) 0 (λ x11 : ι → ι . x1 (λ x12 . 0) (λ x12 . 0) 0 (λ x12 . 0) (λ x12 . 0) 0) (λ x11 . 0) (Inj0 0))) 0 (λ x10 : ι → ι . setsum (x3 (λ x11 : ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . setsum 0 0) (λ x11 . x11) (x2 (λ x11 x12 . 0) 0) (λ x11 : ι → ι . x9) (λ x11 . Inj0 0) 0) (x1 (λ x11 . x0 (λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . 0)) (λ x11 . x0 (λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . 0)) (x0 (λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x11 : (ι → ι) → ι . 0) (λ x11 x12 . 0)) (λ x11 . x0 (λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . 0)) (λ x11 . x0 (λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . 0)) (setsum 0 0))) (λ x10 . 0) (x2 (λ x10 x11 . x0 (λ x12 x13 . λ x14 : ι → ι . x13) (x0 (λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . 0)) (λ x12 : (ι → ι) → ι . x2 (λ x13 x14 . 0) 0) (λ x12 x13 . x0 (λ x14 x15 . λ x16 : ι → ι . 0) 0 (λ x14 : (ι → ι) → ι . 0) (λ x14 x15 . 0))) (setsum (Inj0 0) (setsum 0 0)))) (x3 (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 . Inj0 0) (x1 (λ x9 . x6 (Inj0 0)) (λ x9 . 0) (setsum x7 (x0 (λ x9 x10 . λ x11 : ι → ι . 0) 0 (λ x9 : (ι → ι) → ι . 0) (λ x9 x10 . 0))) (λ x9 . setsum 0 (setsum 0 0)) (λ x9 . Inj0 (x1 (λ x10 . 0) (λ x10 . 0) 0 (λ x10 . 0) (λ x10 . 0) 0)) 0) (λ x9 : ι → ι . x2 (λ x10 x11 . x3 (λ x12 : ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) (λ x12 . x11) (x9 0) (λ x12 : ι → ι . setsum 0 0) (λ x12 . x2 (λ x13 x14 . 0) 0) 0) (x9 (x5 (λ x10 . 0) (λ x10 . 0) (λ x10 . 0) 0))) (λ x9 . x6 0) 0) = Inj0 (x5 (λ x9 . setsum 0 0) (λ x9 . setsum 0 (Inj0 0)) (setsum x7) (setsum (x4 (x2 (λ x9 x10 . 0) 0) (x3 (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 . 0) 0 (λ x9 : ι → ι . 0) (λ x9 . 0) 0)) (x6 0))))(∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → (ι → ι → ι)(ι → ι) → ι . x3 (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 . 0) (setsum (x2 (λ x9 x10 . x3 (λ x11 : ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 . 0) (Inj1 0) (λ x11 : ι → ι . 0) (λ x11 . x2 (λ x12 x13 . 0) 0) x9) x5) (x1 (λ x9 . 0) (λ x9 . setsum (x2 (λ x10 x11 . 0) 0) (x1 (λ x10 . 0) (λ x10 . 0) 0 (λ x10 . 0) (λ x10 . 0) 0)) (setsum (Inj1 0) (x3 (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 . 0) 0 (λ x9 : ι → ι . 0) (λ x9 . 0) 0)) (λ x9 . x2 (λ x10 x11 . x0 (λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . 0)) (x3 (λ x10 : ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x10 . 0) 0 (λ x10 : ι → ι . 0) (λ x10 . 0) 0)) (λ x9 . x0 (λ x10 x11 . λ x12 : ι → ι . 0) x5 (λ x10 : (ι → ι) → ι . 0) (λ x10 x11 . x0 (λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . 0))) (x1 (λ x9 . x2 (λ x10 x11 . 0) 0) (λ x9 . 0) 0 (λ x9 . setsum 0 0) (λ x9 . x3 (λ x10 : ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x10 . 0) 0 (λ x10 : ι → ι . 0) (λ x10 . 0) 0) (setsum 0 0)))) (λ x9 : ι → ι . x6 (Inj0 (Inj1 0))) (λ x9 . x5) (x2 (λ x9 x10 . x7 (setsum x9 (x7 0 (λ x11 x12 . 0) (λ x11 . 0))) (λ x11 x12 . setsum 0 (setsum 0 0)) (λ x11 . setsum (Inj1 0) 0)) 0) = setsum (Inj1 0) 0)(∀ x4 : ι → ((ι → ι)ι → ι)ι → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι) → ι . ∀ x7 : ι → ι → ι . x2 (λ x9 x10 . setsum (x7 (Inj0 (x6 (λ x11 : ι → ι . 0))) (x2 (λ x11 x12 . Inj1 0) x10)) (x7 (x3 (λ x11 : ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 . Inj1 0) x10 (λ x11 : ι → ι . x10) (λ x11 . x0 (λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . 0)) (x0 (λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x11 : (ι → ι) → ι . 0) (λ x11 x12 . 0))) x9)) 0 = x4 (x4 (x0 (λ x9 x10 . λ x11 : ι → ι . 0) (Inj0 (x2 (λ x9 x10 . 0) 0)) (λ x9 : (ι → ι) → ι . 0) (λ x9 . setsum (x1 (λ x10 . 0) (λ x10 . 0) 0 (λ x10 . 0) (λ x10 . 0) 0))) (λ x9 : ι → ι . λ x10 . Inj1 (x2 (λ x11 x12 . x10) (Inj0 0))) (x6 (λ x9 : ι → ι . x0 (λ x10 x11 . λ x12 : ι → ι . x11) (x6 (λ x10 : ι → ι . 0)) (λ x10 : (ι → ι) → ι . x10 (λ x11 . 0)) (λ x10 x11 . x2 (λ x12 x13 . 0) 0)))) (λ x9 : ι → ι . λ x10 . 0) (x2 (λ x9 x10 . x6 (λ x11 : ι → ι . x7 (x2 (λ x12 x13 . 0) 0) x10)) (x2 (λ x9 x10 . x9) (x3 (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 0) (λ x9 . 0) x5 (λ x9 : ι → ι . Inj0 0) (λ x9 . 0) (x6 (λ x9 : ι → ι . 0))))))(∀ x4 : (ι → ι)ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x2 (λ x9 x10 . x7 (x2 (λ x11 x12 . x10) (Inj0 x9))) (x2 (λ x9 x10 . x7 (setsum 0 (x0 (λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x11 : (ι → ι) → ι . 0) (λ x11 x12 . 0)))) 0) = x7 x6)(∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 . x1 (λ x9 . x0 (λ x10 x11 . λ x12 : ι → ι . setsum (Inj1 0) 0) (setsum (Inj0 x5) (x1 (λ x10 . x0 (λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x11 : (ι → ι) → ι . 0) (λ x11 x12 . 0)) (λ x10 . x6 0 0) 0 (λ x10 . x7) (λ x10 . setsum 0 0) (setsum 0 0))) (λ x10 : (ι → ι) → ι . Inj0 (x0 (λ x11 x12 . λ x13 : ι → ι . Inj0 0) x9 (λ x11 : (ι → ι) → ι . x7) (λ x11 x12 . x12))) (λ x10 x11 . setsum (setsum 0 x10) (setsum 0 (x1 (λ x12 . 0) (λ x12 . 0) 0 (λ x12 . 0) (λ x12 . 0) 0)))) (λ x9 . Inj1 (Inj1 (x6 0 (Inj1 0)))) (x4 (λ x9 . 0)) (λ x9 . Inj1 0) (λ x9 . x9) x5 = setsum (setsum (setsum (Inj0 (setsum 0 0)) 0) (setsum (setsum x5 (x3 (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 . 0) 0 (λ x9 : ι → ι . 0) (λ x9 . 0) 0)) (setsum (x1 (λ x9 . 0) (λ x9 . 0) 0 (λ x9 . 0) (λ x9 . 0) 0) 0))) (x6 0 (x0 (λ x9 x10 . λ x11 : ι → ι . x0 (λ x12 x13 . λ x14 : ι → ι . x2 (λ x15 x16 . 0) 0) x7 (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . x12)) (Inj0 (setsum 0 0)) (λ x9 : (ι → ι) → ι . Inj0 x7) (λ x9 x10 . x0 (λ x11 x12 . λ x13 : ι → ι . 0) (x6 0 0) (λ x11 : (ι → ι) → ι . setsum 0 0) (λ x11 x12 . setsum 0 0)))))(∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x7 : (((ι → ι) → ι)ι → ι → ι) → ι . x1 (λ x9 . Inj1 x5) (λ x9 . Inj1 (x0 (λ x10 x11 . λ x12 : ι → ι . setsum (setsum 0 0) (x2 (λ x13 x14 . 0) 0)) 0 (λ x10 : (ι → ι) → ι . 0) (λ x10 x11 . setsum 0 (Inj0 0)))) (x2 (λ x9 x10 . 0) x5) (λ x9 . 0) (λ x9 . 0) (x3 (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 . 0) (Inj1 (x6 (x6 0 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) 0) (λ x9 : ι → ι . λ x10 . x2 (λ x11 x12 . 0) 0) (λ x9 . x9) 0)) (λ x9 : ι → ι . x6 (x7 (λ x10 : (ι → ι) → ι . λ x11 x12 . x1 (λ x13 . 0) (λ x13 . 0) 0 (λ x13 . 0) (λ x13 . 0) 0)) (λ x10 : ι → ι . λ x11 . x2 (λ x12 x13 . x12) (x9 0)) (λ x10 . 0) (Inj0 (x6 0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0) 0))) (λ x9 . setsum 0 (setsum 0 (Inj1 0))) (x2 (λ x9 x10 . x2 (λ x11 x12 . 0) (setsum 0 0)) (setsum (x3 (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 . 0) 0 (λ x9 : ι → ι . 0) (λ x9 . 0) 0) (x6 0 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) 0)))) = Inj0 0)(∀ x4 x5 . ∀ x6 : ((ι → ι) → ι)ι → ι → ι → ι . ∀ x7 . x0 (λ x9 x10 . λ x11 : ι → ι . x2 (λ x12 x13 . x0 (λ x14 x15 . λ x16 : ι → ι . 0) (setsum 0 (Inj0 0)) (λ x14 : (ι → ι) → ι . x3 (λ x15 : ι → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . x16) (λ x15 . 0) 0 (λ x15 : ι → ι . 0) (λ x15 . Inj1 0) (Inj0 0)) (λ x14 x15 . x12)) 0) x7 (λ x9 : (ι → ι) → ι . x5) (λ x9 x10 . x9) = x2 (λ x9 x10 . setsum x7 (x1 (λ x11 . x11) (λ x11 . Inj1 (setsum 0 0)) (setsum (x1 (λ x11 . 0) (λ x11 . 0) 0 (λ x11 . 0) (λ x11 . 0) 0) (x1 (λ x11 . 0) (λ x11 . 0) 0 (λ x11 . 0) (λ x11 . 0) 0)) (λ x11 . x9) (λ x11 . x11) (x6 (λ x11 : ι → ι . Inj1 0) 0 (Inj1 0) 0))) (Inj1 (Inj1 (x2 (λ x9 x10 . setsum 0 0) (x3 (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 . 0) 0 (λ x9 : ι → ι . 0) (λ x9 . 0) 0)))))(∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → (ι → ι)ι → ι) → ι . ∀ x7 : (((ι → ι) → ι)ι → ι → ι)ι → (ι → ι) → ι . x0 (λ x9 x10 . λ x11 : ι → ι . x2 (λ x12 x13 . x1 (λ x14 . x11 x13) (λ x14 . 0) 0 (λ x14 . x0 (λ x15 x16 . λ x17 : ι → ι . x2 (λ x18 x19 . 0) 0) (Inj1 0) (λ x15 : (ι → ι) → ι . Inj0 0) (λ x15 x16 . x14)) (λ x14 . 0) (Inj1 0)) (setsum 0 0)) 0 (λ x9 : (ι → ι) → ι . 0) (λ x9 x10 . x6 (λ x11 . λ x12 : ι → ι . λ x13 . 0)) = x6 (λ x9 . λ x10 : ι → ι . λ x11 . x10 0))False
as obj
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as prop
e5aca..
theory
HF
stx
12ce4..
address
TMWbf..