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 2f869.. := 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) ⟶ x0 x3 x4 ⟶ x5) ⟶ x5
Definition 87c36.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 . ∀ x6 : ο . (2f869.. 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) ⟶ x0 x2 x5 ⟶ not (x0 x3 x5) ⟶ x0 x4 x5 ⟶ x6) ⟶ x6
Definition f6f09.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (87c36.. 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 ⟶ x0 x3 x6 ⟶ not (x0 x4 x6) ⟶ not (x0 x5 x6) ⟶ x7) ⟶ x7
Definition 88b7c.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (f6f09.. 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 b33d3.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (88b7c.. 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) ⟶ not (x0 x4 x8) ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ x0 x7 x8 ⟶ x9) ⟶ x9
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 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 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 05a8c.. := 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) ⟶ x0 x1 x9 ⟶ x0 x2 x9 ⟶ not (x0 x3 x9) ⟶ not (x0 x4 x9) ⟶ x0 x5 x9 ⟶ not (x0 x6 x9) ⟶ not (x0 x7 x9) ⟶ not (x0 x8 x9) ⟶ x10) ⟶ x10
Definition 2b028.. := 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) ⟶ x0 x2 x5 ⟶ x0 x3 x5 ⟶ x0 x4 x5 ⟶ x6) ⟶ x6
Definition 9ab39.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (2b028.. 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 7f522.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (9ab39.. 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) ⟶ not (x0 x3 x7) ⟶ not (x0 x4 x7) ⟶ not (x0 x5 x7) ⟶ x0 x6 x7 ⟶ x8) ⟶ x8
Definition 24054.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (7f522.. 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 4086f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (24054.. 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 ⟶ x0 x4 x9 ⟶ not (x0 x5 x9) ⟶ not (x0 x6 x9) ⟶ not (x0 x7 x9) ⟶ not (x0 x8 x9) ⟶ x10) ⟶ x10
Definition 182cc.. := 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) ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition c148f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (182cc.. 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) ⟶ 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 b43ab.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (c148f.. 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 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 d2827.. := 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) ⟶ x0 x3 x8 ⟶ not (x0 x4 x8) ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 62ac7.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (d2827.. 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 ⟶ not (x0 x8 x9) ⟶ x10) ⟶ x10
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 3a674.. := 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) ⟶ x0 x1 x8 ⟶ not (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 0db75.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (3a674.. 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) ⟶ x0 x4 x9 ⟶ not (x0 x5 x9) ⟶ not (x0 x6 x9) ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 30a11.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (3a674.. 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 ⟶ x0 x3 x9 ⟶ x0 x4 x9 ⟶ not (x0 x5 x9) ⟶ not (x0 x6 x9) ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition d03a7.. := 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) ⟶ x0 x1 x8 ⟶ not (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 fa0f3.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (d03a7.. 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 02f3e.. := 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 ⟶ x0 x4 x7 ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition 7676b.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (02f3e.. 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) ⟶ x0 x1 x8 ⟶ not (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 4d3d7.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (7676b.. 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 ⟶ x0 x3 x9 ⟶ x0 x4 x9 ⟶ not (x0 x5 x9) ⟶ not (x0 x6 x9) ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 185eb.. := 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 ⟶ x0 x3 x7 ⟶ x0 x4 x7 ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition fd83c.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (185eb.. 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 f3db6.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (fd83c.. 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) ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 6648a.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (87c36.. 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 ⟶ not (x0 x4 x6) ⟶ not (x0 x5 x6) ⟶ x7) ⟶ x7
Definition 836ee.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (6648a.. 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) ⟶ not (x0 x3 x7) ⟶ not (x0 x4 x7) ⟶ x0 x5 x7 ⟶ x0 x6 x7 ⟶ x8) ⟶ x8
Definition 50d07.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (836ee.. 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 8be9f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (50d07.. 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) ⟶ x0 x3 x9 ⟶ not (x0 x4 x9) ⟶ x0 x5 x9 ⟶ not (x0 x6 x9) ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition df271.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (6648a.. 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) ⟶ not (x0 x3 x7) ⟶ not (x0 x4 x7) ⟶ not (x0 x5 x7) ⟶ x0 x6 x7 ⟶ x8) ⟶ x8
Definition 7b2a6.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (df271.. 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) ⟶ not (x0 x4 x8) ⟶ not (x0 x5 x8) ⟶ x0 x6 x8 ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 858ba.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (7b2a6.. 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 80211.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (836ee.. 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) ⟶ not (x0 x4 x8) ⟶ not (x0 x5 x8) ⟶ x0 x6 x8 ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 17819.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (80211.. 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 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 6ca1f.. := 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 ⟶ not (x0 x4 x7) ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition aa9ff.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (6ca1f.. 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 1e021.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (aa9ff.. 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 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 2319a.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (9ab39.. 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) ⟶ not (x0 x3 x7) ⟶ x0 x4 x7 ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition dbaa8.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2319a.. 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 ⟶ x0 x4 x8 ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 1cf57.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (dbaa8.. 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 3d3e7.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (d03a7.. 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 14be0.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (d2827.. 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 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 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 be87d.. : ∀ 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 ⟶ b33d3.. x2 x4 x5 x6 x7 x8 x9 x10 x11 ⟶ ∀ x12 : ο . (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ x12) ⟶ (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) ⟶ not (x2 x11 x3) ⟶ x12) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ x2 x6 x3 ⟶ not (x2 x7 x3) ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ x12) ⟶ (not (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) ⟶ not (x2 x11 x3) ⟶ x12) ⟶ (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) ⟶ not (x2 x11 x3) ⟶ x12) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ x2 x7 x3 ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ x12) ⟶ (x2 x4 x3 ⟶ x2 x5 x3 ⟶ not (x2 x6 x3) ⟶ x2 x7 x3 ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ x12) ⟶ (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) ⟶ x12) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ x2 x6 x3 ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ x12) ⟶ (not (x2 x4 x3) ⟶ not (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 ⟶ x12) ⟶ (x2 x4 x3 ⟶ not (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 ⟶ x12) ⟶ (not (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 ⟶ x12) ⟶ (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 ⟶ x12) ⟶ (not (x2 x4 x3) ⟶ not (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 ⟶ x12) ⟶ (x2 x4 x3 ⟶ not (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 ⟶ x12) ⟶ (not (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 ⟶ x12) ⟶ (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 ⟶ x12) ⟶ (not (x2 x4 x3) ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ x2 x7 x3 ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ x12) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ x2 x7 x3 ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ x12) ⟶ (not (x2 x4 x3) ⟶ x2 x5 x3 ⟶ not (x2 x6 x3) ⟶ x2 x7 x3 ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ x12) ⟶ (x2 x4 x3 ⟶ x2 x5 x3 ⟶ not (x2 x6 x3) ⟶ x2 x7 x3 ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ x12) ⟶ (not (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 ⟶ x12) ⟶ (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 ⟶ x12) ⟶ (not (x2 x4 x3) ⟶ not (x2 x5 x3) ⟶ x2 x6 x3 ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ x12) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ x2 x6 x3 ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ x12) ⟶ (not (x2 x4 x3) ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ not (x2 x8 x3) ⟶ x2 x9 x3 ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ x12) ⟶ (not (x2 x4 x3) ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ x2 x7 x3 ⟶ not (x2 x8 x3) ⟶ x2 x9 x3 ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ x12) ⟶ (not (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 ⟶ x12) ⟶ x12
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 6c174.. : ∀ 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 ⟶ b33d3.. x2 x4 x5 x6 x7 x8 x9 x10 x11 ⟶ ∀ x12 : ο . (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 05a8c.. x2 x13 x3 x14 x15 x16 x17 x18 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 4086f.. x2 x13 x14 x3 x15 x16 x17 x18 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ b43ab.. x2 x3 x13 x14 x15 x16 x17 x18 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 62ac7.. x2 x13 x14 x15 x16 x17 x18 x19 x3 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 0db75.. x2 x13 x14 x3 x15 x16 x17 x18 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 30a11.. x2 x13 x14 x3 x15 x16 x17 x18 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ fa0f3.. x2 x13 x3 x14 x15 x16 x17 x18 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 4d3d7.. x2 x13 x3 x14 x15 x16 x17 x18 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ f3db6.. x2 x13 x14 x15 x16 x3 x17 x18 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 8be9f.. x2 x13 x14 x15 x16 x17 x18 x3 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 858ba.. x2 x13 x14 x15 x16 x17 x18 x3 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 17819.. x2 x13 x14 x15 x16 x17 x18 x3 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 1e021.. x2 x13 x14 x15 x16 x17 x18 x3 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ b19dd.. x2 x13 x14 x15 x16 x17 x18 x3 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 1cf57.. x2 x13 x14 x15 x16 x17 x3 x18 x19 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 3d3e7.. x2 x13 x14 x15 x16 x17 x18 x19 x3 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 14be0.. x2 x13 x14 x15 x16 x17 x18 x19 x3 x20 ⟶ x12) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ 654b9.. x2 x13 x14 x15 x16 x17 x18 x19 x3 x20 ⟶ x12) ⟶ x12 (proof)