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Proofgold Term Root Disambiguation

(∀ 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(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0x8 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 x17))))))) = x17)(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0x7 x14 (x10 x15 (x12 x16 x17)) = x10 x15 (x12 x16 (x7 x14 x17)))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x9 x14 x15 (x12 x16 (x12 x17 x18)) = x12 x16 (x12 x17 (x9 x14 x15 x18)))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x7 x14 (x12 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x7 x14 (x12 x15 x18))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x12 x14 (x10 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x10 x15 x18))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x10 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x10 x14 (x12 x15 x18))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x7 x14 (x13 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x13 x15 x18))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x7 x14 (x10 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 x17 (x7 x14 (x10 x15 x18))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0x8 x14 x15 (x10 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x10 x16 x19))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0x9 x14 x15 (x13 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x9 x14 x15 (x13 x16 x19))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0x9 x14 x15 (x10 x16 (x8 x17 x18 (x13 x19 x20))) = x8 x17 x18 (x13 x19 (x9 x14 x15 (x10 x16 x20))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0x9 x14 x15 (x7 x16 (x8 x17 x18 (x13 x19 x20))) = x8 x17 x18 (x13 x19 (x9 x14 x15 (x7 x16 x20))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x9 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x9 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x13 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x13 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21)))))False)∀ x0 : ο . x0
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