| ∀ 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_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ In x4 x0 ⟶ ∀ x14 : ο . (∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ not (x5 (x1 (x2 (x8 x15 x16 x17) x4) x17) x18 = x4) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ In (x1 x19 x20) x0) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ In (x3 x19 x20) x0) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ In (x2 x19 x20) x0) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x5 x19 x20 = x2 (x1 x20 x19) (x1 x19 x20)) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ In (x5 x19 x20) x0) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x6 x19 x20 x21 = x2 (x1 x19 (x1 x20 x21)) (x1 (x1 x19 x20) x21)) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ In (x6 x19 x20 x21) x0) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x7 x19 x20 = x2 x19 (x1 x20 x19)) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ In (x7 x19 x20) x0) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x19 x20 x21 = x2 (x1 x20 x19) (x1 x20 (x1 x19 x21))) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ In (x8 x19 x20 x21) x0) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x19 x20 x21 = x3 (x1 (x1 x21 x19) x20) (x1 x19 x20)) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ In (x9 x19 x20 x21) x0) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x10 x19 x20 = x1 x19 (x1 x20 (x2 x19 x4))) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ In (x10 x19 x20) x0) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x12 x19 x20 = x1 (x2 x19 x20) (x2 (x2 x19 x4) x4)) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ In (x12 x19 x20) x0) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x11 x19 x20 = x1 (x1 (x3 x4 x19) x20) x19) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ In (x11 x19 x20) x0) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x13 x19 x20 = x1 (x3 x4 (x3 x4 x19)) (x3 x20 x19)) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ In (x13 x19 x20) x0) ⟶ (∀ x19 . In x19 x0 ⟶ x1 x4 x19 = x19) ⟶ (∀ x19 . In x19 x0 ⟶ x1 x19 x4 = x19) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x2 x19 (x1 x19 x20) = x20) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x1 x19 (x2 x19 x20) = x20) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x3 (x1 x19 x20) x20 = x19) ⟶ (∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x1 (x3 x19 x20) x20 = x19) ⟶ x14) ⟶ x14 |
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