| ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ ∀ x14 : ο . (Loop x0 x1 x2 x3 x4 ⟶ (∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x5 x15 x16 = x2 (x1 x16 x15) (x1 x15 x16)) ⟶ (∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x6 x15 x16 x17 = x2 (x1 x15 (x1 x16 x17)) (x1 (x1 x15 x16) x17)) ⟶ (∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ and (and (and (and (x7 x15 x16 = x2 x15 (x1 x16 x15)) (x10 x15 x16 = x1 x15 (x1 x16 (x2 x15 x4)))) (x11 x15 x16 = x1 (x1 (x3 x4 x15) x16) x15)) (x12 x15 x16 = x1 (x2 x15 x16) (x2 (x2 x15 x4) x4))) (x13 x15 x16 = x1 (x3 x4 (x3 x4 x15)) (x3 x16 x15))) ⟶ (∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ and (x8 x15 x16 x17 = x2 (x1 x16 x15) (x1 x16 (x1 x15 x17))) (x9 x15 x16 x17 = x3 (x1 (x1 x17 x15) x16) (x1 x15 x16))) ⟶ x14) ⟶ x14 |
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