Proofgold Signed Transaction

Param 4402e.. : ι → (ι → ι → ο) → ο
Param cf2df.. : ι → (ι → ι → ο) → ο
Definition Subq^Subq := λ x0 x1 . ∀ x2 . x2 ∈ x0 ⟶ x2 ∈ x1
Param setminus^setminus : ι → ι → ι
Param Sing^Sing : ι → ι
Definition False^False := ∀ x0 : ο . x0
Definition not^not := λ x0 : ο . x0 ⟶ False
Definition 8b6ad.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 . ∀ x5 : ο . ((x1 = x2 ⟶ ∀ x6 : ο . x6) ⟶ (x1 = x3 ⟶ ∀ x6 : ο . x6) ⟶ (x2 = x3 ⟶ ∀ x6 : ο . x6) ⟶ (x1 = x4 ⟶ ∀ x6 : ο . x6) ⟶ (x2 = x4 ⟶ ∀ x6 : ο . x6) ⟶ (x3 = x4 ⟶ ∀ x6 : ο . x6) ⟶ not (x0 x1 x2) ⟶ not (x0 x1 x3) ⟶ not (x0 x2 x3) ⟶ not (x0 x1 x4) ⟶ not (x0 x2 x4) ⟶ not (x0 x3 x4) ⟶ x5) ⟶ x5
Definition c5756.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 . ∀ x6 : ο . (8b6ad.. x0 x1 x2 x3 x4 ⟶ (x1 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x2 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x3 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x4 = x5 ⟶ ∀ x7 : ο . x7) ⟶ not (x0 x1 x5) ⟶ not (x0 x2 x5) ⟶ x0 x3 x5 ⟶ x0 x4 x5 ⟶ x6) ⟶ x6
Definition 2de86.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (c5756.. x0 x1 x2 x3 x4 x5 ⟶ (x1 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ not (x0 x1 x6) ⟶ x0 x2 x6 ⟶ not (x0 x3 x6) ⟶ x0 x4 x6 ⟶ not (x0 x5 x6) ⟶ x7) ⟶ x7
Definition 36d58.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (2de86.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ not (x0 x2 x7) ⟶ x0 x3 x7 ⟶ x0 x4 x7 ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition af16d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (36d58.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ not (x0 x2 x8) ⟶ not (x0 x3 x8) ⟶ x0 x4 x8 ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 654b9.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (af16d.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ not (x0 x1 x9) ⟶ x0 x2 x9 ⟶ not (x0 x3 x9) ⟶ not (x0 x4 x9) ⟶ x0 x5 x9 ⟶ not (x0 x6 x9) ⟶ x0 x7 x9 ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 3906f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (654b9.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ not (x0 x1 x10) ⟶ not (x0 x2 x10) ⟶ x0 x3 x10 ⟶ not (x0 x4 x10) ⟶ not (x0 x5 x10) ⟶ x0 x6 x10 ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition f8709.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (c5756.. x0 x1 x2 x3 x4 x5 ⟶ (x1 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ not (x0 x1 x6) ⟶ x0 x2 x6 ⟶ x0 x3 x6 ⟶ x0 x4 x6 ⟶ not (x0 x5 x6) ⟶ x7) ⟶ x7
Definition 16c0f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (f8709.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ x0 x2 x7 ⟶ not (x0 x3 x7) ⟶ x0 x4 x7 ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition 00e1f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (16c0f.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ not (x0 x2 x8) ⟶ not (x0 x3 x8) ⟶ x0 x4 x8 ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition ed012.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (00e1f.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ x0 x1 x9 ⟶ not (x0 x2 x9) ⟶ not (x0 x3 x9) ⟶ not (x0 x4 x9) ⟶ x0 x5 x9 ⟶ x0 x6 x9 ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 4f588.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (ed012.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ x0 x2 x10 ⟶ x0 x3 x10 ⟶ not (x0 x4 x10) ⟶ not (x0 x5 x10) ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition d17b7.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (4f588.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ not (x0 x1 x11) ⟶ x0 x2 x11 ⟶ not (x0 x3 x11) ⟶ not (x0 x4 x11) ⟶ x0 x5 x11 ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ not (x0 x8 x11) ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition 27260.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (f8709.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ x0 x2 x7 ⟶ not (x0 x3 x7) ⟶ not (x0 x4 x7) ⟶ x0 x5 x7 ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition dfcf9.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (27260.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ x0 x2 x8 ⟶ not (x0 x3 x8) ⟶ not (x0 x4 x8) ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 729bd.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (dfcf9.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ not (x0 x1 x9) ⟶ not (x0 x2 x9) ⟶ x0 x3 x9 ⟶ x0 x4 x9 ⟶ not (x0 x5 x9) ⟶ not (x0 x6 x9) ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 9e253.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (729bd.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ not (x0 x2 x10) ⟶ not (x0 x3 x10) ⟶ not (x0 x4 x10) ⟶ x0 x5 x10 ⟶ x0 x6 x10 ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 580d8.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (9e253.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x0 x1 x11 ⟶ not (x0 x2 x11) ⟶ not (x0 x3 x11) ⟶ x0 x4 x11 ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ not (x0 x8 x11) ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition fa706.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (3906f.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x0 x1 x11 ⟶ not (x0 x2 x11) ⟶ not (x0 x3 x11) ⟶ not (x0 x4 x11) ⟶ x0 x5 x11 ⟶ x0 x6 x11 ⟶ not (x0 x7 x11) ⟶ not (x0 x8 x11) ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition 62523.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 . ∀ x6 : ο . (8b6ad.. x0 x1 x2 x3 x4 ⟶ (x1 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x2 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x3 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x4 = x5 ⟶ ∀ x7 : ο . x7) ⟶ not (x0 x1 x5) ⟶ not (x0 x2 x5) ⟶ not (x0 x3 x5) ⟶ x0 x4 x5 ⟶ x6) ⟶ x6
Definition a542b.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (62523.. x0 x1 x2 x3 x4 x5 ⟶ (x1 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ not (x0 x1 x6) ⟶ not (x0 x2 x6) ⟶ x0 x3 x6 ⟶ not (x0 x4 x6) ⟶ x0 x5 x6 ⟶ x7) ⟶ x7
Definition 2fb86.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (a542b.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ x0 x2 x7 ⟶ not (x0 x3 x7) ⟶ not (x0 x4 x7) ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition 14b71.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2fb86.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ x0 x2 x8 ⟶ not (x0 x3 x8) ⟶ not (x0 x4 x8) ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 286f8.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (14b71.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ not (x0 x1 x9) ⟶ not (x0 x2 x9) ⟶ x0 x3 x9 ⟶ x0 x4 x9 ⟶ not (x0 x5 x9) ⟶ not (x0 x6 x9) ⟶ x0 x7 x9 ⟶ not (x0 x8 x9) ⟶ x10) ⟶ x10
Definition 68d0b.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (286f8.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ x0 x2 x10 ⟶ x0 x3 x10 ⟶ x0 x4 x10 ⟶ not (x0 x5 x10) ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ not (x0 x8 x10) ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 44299.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (68d0b.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x0 x1 x11 ⟶ not (x0 x2 x11) ⟶ x0 x3 x11 ⟶ x0 x4 x11 ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition ba720.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (c5756.. x0 x1 x2 x3 x4 x5 ⟶ (x1 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ x0 x1 x6 ⟶ x0 x2 x6 ⟶ not (x0 x3 x6) ⟶ x0 x4 x6 ⟶ not (x0 x5 x6) ⟶ x7) ⟶ x7
Definition 28532.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (ba720.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ x0 x2 x7 ⟶ x0 x3 x7 ⟶ x0 x4 x7 ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition 5072f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (28532.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ x0 x2 x8 ⟶ not (x0 x3 x8) ⟶ x0 x4 x8 ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition b19dd.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (5072f.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ not (x0 x1 x9) ⟶ not (x0 x2 x9) ⟶ x0 x3 x9 ⟶ not (x0 x4 x9) ⟶ not (x0 x5 x9) ⟶ x0 x6 x9 ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 33d88.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (b19dd.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ x0 x2 x10 ⟶ not (x0 x3 x10) ⟶ not (x0 x4 x10) ⟶ x0 x5 x10 ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ not (x0 x8 x10) ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition dafd9.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (33d88.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x0 x1 x11 ⟶ not (x0 x2 x11) ⟶ not (x0 x3 x11) ⟶ not (x0 x4 x11) ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition e8ae3.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (f8709.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ not (x0 x2 x7) ⟶ x0 x3 x7 ⟶ x0 x4 x7 ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition fa72d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (e8ae3.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ not (x0 x2 x8) ⟶ not (x0 x3 x8) ⟶ x0 x4 x8 ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition d92ce.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (fa72d.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ not (x0 x1 x9) ⟶ x0 x2 x9 ⟶ not (x0 x3 x9) ⟶ not (x0 x4 x9) ⟶ x0 x5 x9 ⟶ not (x0 x6 x9) ⟶ x0 x7 x9 ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition d2465.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (d92ce.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ x0 x2 x10 ⟶ not (x0 x3 x10) ⟶ not (x0 x4 x10) ⟶ x0 x5 x10 ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ not (x0 x8 x10) ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 380c0.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (d2465.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ not (x0 x1 x11) ⟶ not (x0 x2 x11) ⟶ x0 x3 x11 ⟶ not (x0 x4 x11) ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition 34ae8.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (af16d.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ x0 x1 x9 ⟶ x0 x2 x9 ⟶ x0 x3 x9 ⟶ not (x0 x4 x9) ⟶ not (x0 x5 x9) ⟶ not (x0 x6 x9) ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition d7308.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (34ae8.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ not (x0 x2 x10) ⟶ not (x0 x3 x10) ⟶ not (x0 x4 x10) ⟶ x0 x5 x10 ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ not (x0 x8 x10) ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 4cf61.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (d7308.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ not (x0 x1 x11) ⟶ x0 x2 x11 ⟶ not (x0 x3 x11) ⟶ not (x0 x4 x11) ⟶ x0 x5 x11 ⟶ not (x0 x6 x11) ⟶ x0 x7 x11 ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition 1668d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (dfcf9.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ x0 x1 x9 ⟶ not (x0 x2 x9) ⟶ not (x0 x3 x9) ⟶ not (x0 x4 x9) ⟶ x0 x5 x9 ⟶ x0 x6 x9 ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 87bb9.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (1668d.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ not (x0 x2 x10) ⟶ x0 x3 x10 ⟶ x0 x4 x10 ⟶ not (x0 x5 x10) ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition fd9fb.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (87bb9.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ not (x0 x1 x11) ⟶ not (x0 x2 x11) ⟶ not (x0 x3 x11) ⟶ x0 x4 x11 ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition 3819d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (2de86.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ x0 x2 x7 ⟶ x0 x3 x7 ⟶ not (x0 x4 x7) ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition 1b79b.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (3819d.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ not (x0 x2 x8) ⟶ x0 x3 x8 ⟶ not (x0 x4 x8) ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 37e04.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (1b79b.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ x0 x1 x9 ⟶ not (x0 x2 x9) ⟶ not (x0 x3 x9) ⟶ not (x0 x4 x9) ⟶ x0 x5 x9 ⟶ x0 x6 x9 ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 97406.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (37e04.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ x0 x2 x10 ⟶ not (x0 x3 x10) ⟶ not (x0 x4 x10) ⟶ x0 x5 x10 ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 0a04b.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (97406.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ not (x0 x1 x11) ⟶ not (x0 x2 x11) ⟶ not (x0 x3 x11) ⟶ x0 x4 x11 ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition 07f55.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (d92ce.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ x0 x2 x10 ⟶ not (x0 x3 x10) ⟶ not (x0 x4 x10) ⟶ x0 x5 x10 ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 8dc75.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (07f55.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ not (x0 x1 x11) ⟶ not (x0 x2 x11) ⟶ x0 x3 x11 ⟶ not (x0 x4 x11) ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition and^and := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Definition nIn^nIn := λ x0 x1 . not (x0 ∈ x1)
Known setminusE^setminusE : ∀ x0 x1 x2 . x2 ∈ setminus x0 x1 ⟶ and (x2 ∈ x0) (nIn x2 x1)
Known 2ac84.. : ∀ x0 x1 . ∀ x2 : ι → ι → ο . (∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ⟶ x2 x4 x3) ⟶ 4402e.. x1 x2 ⟶ cf2df.. x1 x2 ⟶ ∀ x3 . x3 ∈ x1 ⟶ x0 ⊆ setminus x1 (Sing x3) ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ 3906f.. x2 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ ∀ x14 : ο . (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ x2 x5 x3 ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ x2 x9 x3 ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ x2 x5 x3 ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ x2 x5 x3 ⟶ x2 x6 x3 ⟶ not (x2 x7 x3) ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ x2 x5 x3 ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ x2 x9 x3 ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ not (x2 x12 x3) ⟶ x2 x13 x3 ⟶ x14) ⟶ (x2 x4 x3 ⟶ x2 x5 x3 ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ not (x2 x12 x3) ⟶ x2 x13 x3 ⟶ x14) ⟶ x14
Known neq_i_sym^neq_i_sym : ∀ x0 x1 . (x0 = x1 ⟶ ∀ x2 : ο . x2) ⟶ x1 = x0 ⟶ ∀ x2 : ο . x2
Known Subq_tra^Subq_tra : ∀ x0 x1 x2 . x0 ⊆ x1 ⟶ x1 ⊆ x2 ⟶ x0 ⊆ x2
Known setminus_Subq^{setminus_Subq} : ∀ x0 x1 . setminus x0 x1 ⊆ x0
Known SingI^SingI : ∀ x0 . x0 ∈ Sing x0
Theorem 9bcc2.. : ∀ x0 x1 . ∀ x2 : ι → ι → ο . (∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ⟶ x2 x4 x3) ⟶ 4402e.. x1 x2 ⟶ cf2df.. x1 x2 ⟶ ∀ x3 . x3 ∈ x1 ⟶ x0 ⊆ setminus x1 (Sing x3) ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ 3906f.. x2 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ ∀ x14 : ο . (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ d17b7.. x2 x15 x3 x16 x17 x18 x19 x20 x21 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 580d8.. x2 x3 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ fa706.. x2 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x3 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 44299.. x2 x15 x16 x17 x18 x19 x3 x20 x21 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ dafd9.. x2 x15 x16 x17 x18 x19 x20 x21 x3 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 380c0.. x2 x15 x16 x17 x18 x19 x20 x21 x3 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 4cf61.. x2 x15 x3 x16 x17 x18 x19 x20 x21 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ fd9fb.. x2 x15 x16 x17 x18 x19 x20 x21 x3 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 0a04b.. x2 x15 x16 x17 x3 x18 x19 x20 x21 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 8dc75.. x2 x15 x16 x17 x18 x19 x20 x3 x21 x22 x23 x24 ⟶ x14) ⟶ x14 (proof)