Proofgold Asset

Known 68ce2.. : ∀ x0 x1 . (x0 = x1 ⟶ False) ⟶ x1 = x0 ⟶ False
Theorem 5f70e.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ In (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ In (x2 x3 x4) x0) ⟶ ∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . In x6 x0 ⟶ ∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ In (x5 x6 x7 x8) x0) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ ∀ x9 . In x9 x0 ⟶ In (x6 x7 x8 x9) x0) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . In x8 x0 ⟶ ∀ x9 . In x9 x0 ⟶ In (x7 x8 x9) x0) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ In (x8 x9 x10) x0) ⟶ ∀ x9 . In x9 x0 ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ In (x10 x11 x12) x0) ⟶ (∀ x11 . In x11 x0 ⟶ (x10 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x10 x11 x9 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x8 x11 (x10 x11 x12) = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x10 x11 (x8 x11 x12) = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ x10 x12 x11 = x10 x13 x11 ⟶ (x12 = x13 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x1 x11 x12 = x10 (x8 x11 x12) (x8 (x8 x11 x9) x9) ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x8 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x8 x11 x11 = x9 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x7 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x2 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x6 x9 x11 x12 = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x6 x11 x9 x12 = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x5 x9 x11 x12 = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ ∀ x14 . In x14 x0 ⟶ (x6 x11 x13 (x1 x12 (x2 x11 (x6 x13 x12 (x6 x11 x13 (x1 x12 (x2 x11 (x6 x13 x12 (x6 x11 x13 (x1 x12 (x2 x11 (x6 x13 x12 x14))))))))))) = x14 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ ∀ x14 . In x14 x0 ⟶ (x5 x11 x13 (x1 x12 (x7 x11 (x5 x13 x12 (x5 x11 x13 (x1 x12 (x7 x11 (x5 x13 x12 x14))))))) = x14 ⟶ False) ⟶ False) ⟶ (x10 x3 x4 = x10 x4 x3 ⟶ False) ⟶ False (proof)
Known b5371.. : ∀ 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 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x1 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x2 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x3 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x7 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ In (x8 x14 x15 x16) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ In (x9 x14 x15 x16) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x10 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x11 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x12 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x13 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ x1 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x1 x14 x4 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x2 x14 (x1 x14 x15) = x15) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x1 x14 (x2 x14 x15) = x15) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x3 (x1 x14 x15) x15 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x1 (x3 x14 x15) x15 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x1 x14 x15 = x1 x14 x16 ⟶ x15 = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x1 x14 x15 = x1 x16 x15 ⟶ x14 = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x5 x14 x15 = x2 (x1 x15 x14) (x1 x14 x15)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x6 x14 x15 x16 = x2 (x1 x14 (x1 x15 x16)) (x1 (x1 x14 x15) x16)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x7 x14 x15 = x2 x14 (x1 x15 x14)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x10 x14 x15 = x1 x14 (x1 x15 (x2 x14 x4))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x11 x14 x15 = x1 (x1 (x3 x4 x14) x15) x14) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x12 x14 x15 = x1 (x2 x14 x15) (x2 (x2 x14 x4) x4)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x13 x14 x15 = x1 (x3 x4 (x3 x4 x14)) (x3 x15 x14)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 x16 = x2 (x1 x15 x14) (x1 x15 (x1 x14 x16))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 x16 = x3 (x1 (x1 x16 x14) x15) (x1 x14 x15)) ⟶ (∀ x14 . In x14 x0 ⟶ x2 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x2 x14 x14 = x4) ⟶ (∀ x14 . In x14 x0 ⟶ x3 x14 x4 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x3 x14 x14 = x4) ⟶ (∀ x14 . In x14 x0 ⟶ x7 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x10 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x11 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x12 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x13 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x8 x4 x14 x15 = x15) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x8 x14 x4 x15 = x15) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x9 x4 x14 x15 = x15) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x9 x14 x4 x15 = x15) ⟶ ∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x1 x14 x15 = x1 x15 x14) ⟶ False
Known b4782..^contra : ∀ x0 : ο . (not x0 ⟶ False) ⟶ x0
Known notE^notE : ∀ x0 : ο . not x0 ⟶ x0 ⟶ False
Theorem f5674.. : ∀ 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 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x7 x14 (x9 x15 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 x18)) = x10 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x12 x16 (x7 x17 x18))) = x12 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 x0 ⟶ x10 x14 (x12 x15 (x13 x16 (x12 x17 x18))) = x13 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 x0 ⟶ x13 x14 (x12 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x13 x16 (x10 x17 x18))) = x13 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 x0 ⟶ x12 x14 (x13 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x13 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 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x7 x18 x19))) = x7 x17 (x7 x18 (x9 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 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x8 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 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 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 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x8 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 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 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 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 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 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 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 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 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 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 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 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 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 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 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 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ False (proof)
Theorem 71b5d.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ In (x1 x2 x3) x0) ⟶ ∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ ∀ x4 : ι → ι → ι → ι . (∀ x5 . In x5 x0 ⟶ ∀ x6 . In x6 x0 ⟶ ∀ x7 . In x7 x0 ⟶ In (x4 x5 x6 x7) x0) ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . In x6 x0 ⟶ ∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ In (x5 x6 x7 x8) x0) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ In (x6 x7 x8) x0) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . In x8 x0 ⟶ ∀ x9 . In x9 x0 ⟶ In (x7 x8 x9) x0) ⟶ ∀ x8 . In x8 x0 ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ In (x9 x10 x11) x0) ⟶ (∀ x10 . In x10 x0 ⟶ (x9 x8 x10 = x10 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ (x9 x10 x8 = x10 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x7 x10 (x9 x10 x11) = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x9 x10 (x7 x10 x11) = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ x9 x10 x11 = x9 x10 x12 ⟶ (x11 = x12 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ x9 x11 x10 = x9 x12 x10 ⟶ (x11 = x12 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x6 x10 x11 = x9 (x7 x10 x11) (x7 (x7 x10 x8) x8) ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ (x7 x8 x10 = x10 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ (x7 x10 x10 = x8 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ (x1 x8 x10 = x10 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x5 x8 x10 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x5 x10 x8 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x4 x8 x10 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x4 x10 x8 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ (x4 x10 x12 (x1 x11 (x6 x10 (x4 x12 x11 (x4 x10 x12 (x1 x11 (x6 x10 (x4 x12 x11 (x4 x10 x12 (x1 x11 (x6 x10 (x4 x12 x11 x13))))))))))) = x13 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ (x4 x10 x12 (x6 x11 (x1 x10 (x5 x12 x11 (x4 x10 x12 (x6 x11 (x1 x10 (x5 x12 x11 (x4 x10 x12 (x6 x11 (x1 x10 (x5 x12 x11 (x4 x10 x12 (x6 x11 (x1 x10 (x5 x12 x11 x13))))))))))))))) = x13 ⟶ False) ⟶ False) ⟶ (x9 x3 x2 = x9 x2 x3 ⟶ False) ⟶ False (proof)
Theorem 24e23.. : ∀ 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 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x9 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x9 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x9 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 x18)) = x12 x16 (x13 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 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 x0 ⟶ x7 x14 (x10 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 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 ⟶ x12 x14 (x7 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x7 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 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x9 x14 x15 (x12 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 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x8 x14 x15 (x12 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 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x12 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 ⟶ x9 x14 x15 (x10 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 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 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 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 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 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 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 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 x0 ⟶ x8 x14 x15 (x13 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x13 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 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x13 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 x0 ⟶ x9 x14 x15 (x13 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 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 x0 ⟶ x9 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 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ False (proof)
Theorem 551a2.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ In (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ In (x2 x3 x4) x0) ⟶ ∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . In x6 x0 ⟶ ∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ In (x5 x6 x7 x8) x0) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ In (x6 x7 x8) x0) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . In x8 x0 ⟶ ∀ x9 . In x9 x0 ⟶ In (x7 x8 x9) x0) ⟶ ∀ x8 . In x8 x0 ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ In (x9 x10 x11) x0) ⟶ (∀ x10 . In x10 x0 ⟶ (x9 x8 x10 = x10 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x1 x10 (x9 x10 x11) = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x7 x10 x11 = x9 (x1 x10 x11) (x1 (x1 x10 x8) x8) ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ (x1 x10 x10 = x8 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ (x6 x8 x10 = x10 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ (x2 x8 x10 = x10 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x5 x8 x10 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x5 x10 x8 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x5 x10 x11 (x6 x10 (x7 x11 (x5 x10 x11 (x6 x10 (x7 x11 (x5 x10 x11 (x6 x10 (x7 x11 (x5 x10 x11 (x6 x10 (x7 x11 x12))))))))))) = x12 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x5 x10 x11 (x7 x10 (x2 x11 (x5 x10 x11 (x7 x10 (x2 x11 (x5 x10 x11 (x7 x10 (x2 x11 (x5 x10 x11 (x7 x10 (x2 x11 (x5 x10 x11 (x7 x10 (x2 x11 x12)))))))))))))) = x12 ⟶ False) ⟶ False) ⟶ (x9 x4 x3 = x9 x3 x4 ⟶ False) ⟶ False (proof)
Theorem 4bcbc.. : ∀ 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 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x7 x14 (x12 x15 (x8 x14 x15 (x7 x14 (x12 x15 (x8 x14 x15 (x7 x14 (x12 x15 (x8 x14 x15 (x7 x14 (x12 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x12 x14 (x13 x15 (x8 x14 x15 (x12 x14 (x13 x15 (x8 x14 x15 (x12 x14 (x13 x15 (x8 x14 x15 (x12 x14 (x13 x15 (x8 x14 x15 (x12 x14 (x13 x15 x16)))))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x13 x15 (x10 x16 x17)) = x13 x15 (x10 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 x18)) = x12 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 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 x0 ⟶ x10 x14 (x7 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 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 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 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 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x10 x18 x19))) = x10 x17 (x10 x18 (x8 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x10 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x8 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 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x12 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 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 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 x0 ⟶ x8 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 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 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 x0 ⟶ x8 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 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 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 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False (proof)
Theorem 4a0f9.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ In (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ In (x2 x3 x4) x0) ⟶ ∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . In x6 x0 ⟶ ∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ In (x5 x6 x7 x8) x0) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ ∀ x9 . In x9 x0 ⟶ In (x6 x7 x8 x9) x0) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . In x8 x0 ⟶ ∀ x9 . In x9 x0 ⟶ In (x7 x8 x9) x0) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ In (x8 x9 x10) x0) ⟶ ∀ x9 . In x9 x0 ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ In (x10 x11 x12) x0) ⟶ (∀ x11 . In x11 x0 ⟶ (x10 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x10 x11 x9 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x8 x11 (x10 x11 x12) = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x10 x11 (x8 x11 x12) = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ x10 x12 x11 = x10 x13 x11 ⟶ (x12 = x13 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x1 x11 x12 = x10 (x8 x11 x12) (x8 (x8 x11 x9) x9) ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x8 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x8 x11 x11 = x9 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x7 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x2 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x6 x9 x11 x12 = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x6 x11 x9 x12 = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x5 x9 x11 x12 = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x5 x11 x9 x12 = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ ∀ x14 . In x14 x0 ⟶ (x5 x11 x13 (x1 x12 (x2 x11 (x6 x13 x12 (x5 x11 x13 (x1 x12 (x2 x11 (x6 x13 x12 (x5 x11 x13 (x1 x12 (x2 x11 (x6 x13 x12 x14))))))))))) = x14 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ ∀ x14 . In x14 x0 ⟶ (x6 x11 x13 (x1 x12 (x7 x11 (x6 x13 x12 (x6 x11 x13 (x1 x12 (x7 x11 (x6 x13 x12 (x6 x11 x13 (x1 x12 (x7 x11 (x6 x13 x12 (x6 x11 x13 (x1 x12 (x7 x11 (x6 x13 x12 x14))))))))))))))) = x14 ⟶ False) ⟶ False) ⟶ (x10 x4 x3 = x10 x3 x4 ⟶ False) ⟶ False (proof)
Theorem 79c01.. : ∀ 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 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x9 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x9 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x7 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x7 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x7 x14 (x8 x15 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 x18)) = x12 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x13 x16 (x7 x17 x18))) = x13 x16 (x7 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 x0 ⟶ x7 x14 (x10 x15 (x12 x16 (x13 x17 x18))) = x12 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 ⟶ x12 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x7 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x10 x14 (x7 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 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x8 x14 x15 (x12 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 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x8 x14 x15 (x7 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 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 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 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x12 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 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 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 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 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 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 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 x0 ⟶ x8 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 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 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 x0 ⟶ x8 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 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ False (proof)
Theorem 76cd3.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ In (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ι → ι . (∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ ∀ x5 . In x5 x0 ⟶ In (x2 x3 x4 x5) x0) ⟶ ∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . In x6 x0 ⟶ ∀ x7 . In x7 x0 ⟶ In (x5 x6 x7) x0) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ In (x6 x7 x8) x0) ⟶ ∀ x7 . In x7 x0 ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ In (x8 x9 x10) x0) ⟶ (∀ x9 . In x9 x0 ⟶ (x8 x7 x9 = x9 ⟶ False) ⟶ False) ⟶ (∀ x9 . In x9 x0 ⟶ (x8 x9 x7 = x9 ⟶ False) ⟶ False) ⟶ (∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ (x6 x9 (x8 x9 x10) = x10 ⟶ False) ⟶ False) ⟶ (∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ (x1 x9 x10 = x8 (x6 x9 x10) (x6 (x6 x9 x7) x7) ⟶ False) ⟶ False) ⟶ (∀ x9 . In x9 x0 ⟶ (x6 x7 x9 = x9 ⟶ False) ⟶ False) ⟶ (∀ x9 . In x9 x0 ⟶ (x6 x9 x9 = x7 ⟶ False) ⟶ False) ⟶ (∀ x9 . In x9 x0 ⟶ (x5 x7 x9 = x9 ⟶ False) ⟶ False) ⟶ (∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ (x2 x7 x9 x10 = x10 ⟶ False) ⟶ False) ⟶ (∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ (x2 x9 x7 x10 = x10 ⟶ False) ⟶ False) ⟶ (∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x2 x9 x11 (x5 x10 (x1 x9 (x2 x11 x10 (x2 x9 x11 (x5 x10 (x1 x9 (x2 x11 x10 (x2 x9 x11 (x5 x10 (x1 x9 (x2 x11 x10 (x2 x9 x11 (x5 x10 (x1 x9 (x2 x11 x10 x12))))))))))))))) = x12 ⟶ False) ⟶ False) ⟶ (∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x2 x9 x10 (x1 x9 (x1 x10 (x2 x9 x10 (x1 x9 (x1 x10 (x2 x9 x10 (x1 x9 (x1 x10 (x2 x9 x10 (x1 x9 (x1 x10 (x2 x9 x10 (x1 x9 (x1 x10 x11)))))))))))))) = x11 ⟶ False) ⟶ False) ⟶ (x8 x4 x3 = x8 x3 x4 ⟶ False) ⟶ False (proof)
Theorem cfccf.. : ∀ 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 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x12 x14 (x12 x15 (x9 x14 x15 (x12 x14 (x12 x15 (x9 x14 x15 (x12 x14 (x12 x15 (x9 x14 x15 (x12 x14 (x12 x15 (x9 x14 x15 (x12 x14 (x12 x15 x16)))))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x13 x15 (x7 x16 x17)) = x13 x15 (x7 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 x18)) = x10 x16 (x12 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x13 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 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 x0 ⟶ x7 x14 (x13 x15 (x10 x16 (x12 x17 x18))) = x10 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 x0 ⟶ x7 x14 (x10 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 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 ⟶ x12 x14 (x12 x15 (x13 x16 (x13 x17 x18))) = x13 x16 (x13 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x13 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 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 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x8 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 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x8 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x12 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x12 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 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x9 x14 x15 (x12 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 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 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 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x7 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 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 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 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x7 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 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x7 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 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 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 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ False (proof)
Theorem 8ee0e.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ In (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ι → ι . (∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ ∀ x5 . In x5 x0 ⟶ In (x2 x3 x4 x5) x0) ⟶ ∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . In x6 x0 ⟶ ∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ In (x5 x6 x7 x8) x0) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ In (x6 x7 x8) x0) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . In x8 x0 ⟶ ∀ x9 . In x9 x0 ⟶ In (x7 x8 x9) x0) ⟶ ∀ x8 . In x8 x0 ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ In (x9 x10 x11) x0) ⟶ (∀ x10 . In x10 x0 ⟶ (x9 x10 x8 = x10 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x9 x10 (x1 x10 x11) = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x7 x10 x11 = x1 x10 (x9 x11 x10) ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ (x1 x8 x10 = x10 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ (x6 x8 x10 = x10 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x2 x10 x8 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x5 x10 x8 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x2 x10 x11 (x7 x10 (x6 x11 (x2 x10 x11 (x7 x10 (x6 x11 (x2 x10 x11 (x7 x10 (x6 x11 (x2 x10 x11 (x7 x10 (x6 x11 x12))))))))))) = x12 ⟶ False) ⟶ False) ⟶ (∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x5 x10 x11 (x7 x10 (x7 x11 (x5 x10 x11 (x7 x10 (x7 x11 (x5 x10 x11 (x7 x10 (x7 x11 x12)))))))) = x12 ⟶ False) ⟶ False) ⟶ (x9 x4 x3 = x9 x3 x4 ⟶ False) ⟶ False (proof)
Theorem 700a7.. : ∀ 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 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x7 x14 (x13 x15 (x8 x14 x15 (x7 x14 (x13 x15 (x8 x14 x15 (x7 x14 (x13 x15 (x8 x14 x15 (x7 x14 (x13 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x7 x14 (x7 x15 (x9 x14 x15 (x7 x14 (x7 x15 (x9 x14 x15 (x7 x14 (x7 x15 x16)))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 x18)) = x7 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 x0 ⟶ x12 x14 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x13 x15 (x10 x16 (x13 x17 x18))) = x10 x16 (x13 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 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 x0 ⟶ x10 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x13 x16 (x7 x17 x18))) = x13 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 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x9 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 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x7 x18 x19))) = x12 x17 (x7 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 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x12 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 ⟶ x8 x14 x15 (x12 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x8 x14 x15 (x12 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 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 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 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 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 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 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 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 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 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x7 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 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 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 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 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 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ False (proof)
Theorem 99683.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ In (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ In (x2 x3 x4) x0) ⟶ ∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ ∀ x5 . In x5 x0 ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ In (x6 x7 x8) x0) ⟶ ∀ x7 : ι → ι → ι → ι . (∀ x8 . In x8 x0 ⟶ ∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ In (x7 x8 x9 x10) x0) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ In (x8 x9 x10) x0) ⟶ ∀ x9 . In x9 x0 ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ In (x10 x11 x12) x0) ⟶ (∀ x11 . In x11 x0 ⟶ (x10 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x10 x11 x9 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x8 (x10 x12 x11) x11 = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x10 (x8 x12 x11) x11 = x12 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ (x7 x11 x12 x13 = x8 (x10 (x10 x13 x11) x12) (x10 x11 x12) ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x1 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x6 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ (x2 x9 x11 = x11 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ ∀ x14 . In x14 x0 ⟶ (x7 x11 x13 (x1 x12 (x2 x11 (x7 x13 x12 (x7 x11 x13 (x1 x12 (x2 x11 (x7 x13 x12 (x7 x11 x13 (x1 x12 (x2 x11 (x7 x13 x12 x14))))))))))) = x14 ⟶ False) ⟶ False) ⟶ (∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ ∀ x14 . In x14 x0 ⟶ (x7 x11 x13 (x1 x12 (x6 x11 (x7 x13 x12 (x7 x11 x13 (x1 x12 (x6 x11 (x7 x13 x12 (x7 x11 x13 (x1 x12 (x6 x11 (x7 x13 x12 (x7 x11 x13 (x1 x12 (x6 x11 (x7 x13 x12 (x7 x11 x13 (x1 x12 (x6 x11 (x7 x13 x12 x14))))))))))))))))))) = x14 ⟶ False) ⟶ False) ⟶ (x10 (x10 x3 x4) x5 = x10 x3 (x10 x4 x5) ⟶ False) ⟶ False (proof)
Known 7c609.. : ∀ 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_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ In x4 x0 ⟶ ((∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x1 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x2 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x3 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x7 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ In (x8 x14 x15 x16) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ In (x9 x14 x15 x16) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x10 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x11 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x12 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ In (x13 x14 x15) x0) ⟶ (∀ x14 . In x14 x0 ⟶ x1 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x1 x14 x4 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x2 x14 (x1 x14 x15) = x15) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x1 x14 (x2 x14 x15) = x15) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x3 (x1 x14 x15) x15 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x1 (x3 x14 x15) x15 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x1 x14 x15 = x1 x14 x16 ⟶ x15 = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x1 x14 x15 = x1 x16 x15 ⟶ x14 = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x5 x14 x15 = x2 (x1 x15 x14) (x1 x14 x15)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x6 x14 x15 x16 = x2 (x1 x14 (x1 x15 x16)) (x1 (x1 x14 x15) x16)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x7 x14 x15 = x2 x14 (x1 x15 x14)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x10 x14 x15 = x1 x14 (x1 x15 (x2 x14 x4))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x11 x14 x15 = x1 (x1 (x3 x4 x14) x15) x14) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x12 x14 x15 = x1 (x2 x14 x15) (x2 (x2 x14 x4) x4)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x13 x14 x15 = x1 (x3 x4 (x3 x4 x14)) (x3 x15 x14)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 x16 = x2 (x1 x15 x14) (x1 x15 (x1 x14 x16))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 x16 = x3 (x1 (x1 x16 x14) x15) (x1 x14 x15)) ⟶ (∀ x14 . In x14 x0 ⟶ x2 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x2 x14 x14 = x4) ⟶ (∀ x14 . In x14 x0 ⟶ x3 x14 x4 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x3 x14 x14 = x4) ⟶ (∀ x14 . In x14 x0 ⟶ x7 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x10 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x11 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x12 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ x13 x4 x14 = x14) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x8 x4 x14 x15 = x15) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x8 x14 x4 x15 = x15) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x9 x4 x14 x15 = x15) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x9 x14 x4 x15 = x15) ⟶ ∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x1 x14 (x1 x15 x16) = x1 (x1 x14 x15) x16) ⟶ False
Known 15e97..^eq_sym_i : ∀ x0 x1 . x0 = x1 ⟶ x1 = x0
Theorem c4c9a.. : ∀ 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_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ In x4 x0 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x10 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x10 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x10 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x10 x14 (x9 x15 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x17 x18)) = x7 x16 (x13 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 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 x0 ⟶ x10 x14 (x7 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 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 x0 ⟶ x13 x14 (x7 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x13 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x12 x14 (x7 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 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x10 x18 x19))) = x10 x17 (x10 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 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x13 x18 x19))) = x12 x17 (x13 x18 (x9 x14 x15 (x12 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 x0 ⟶ x8 x14 x15 (x13 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x13 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 ⟶ x9 x14 x15 (x13 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x13 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 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 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 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 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 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 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 x0 ⟶ x9 x14 x15 (x7 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 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 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 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 x0 ⟶ x9 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 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 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 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ False (proof)