Proofgold Signed Transaction

Param int^int : ι
Param mul_SNo^mul_SNo : ι → ι → ι
Param ordsucc^ordsucc : ι → ι
Param add_SNo^add_SNo : ι → ι → ι
Param If_i^If_i : ο → ι → ι → ι
Param SNoLe^SNoLe : ι → ι → ο
Param minus_SNo^minus_SNo : ι → ι
Conjecture c936f..^A14905 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ x0 x17 = mul_SNo 2 (add_SNo 2 x17)) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x5 x17 x18 = add_SNo 1 (add_SNo (add_SNo (mul_SNo x4 x17) x17) x18)) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = x17) ⟶ x7 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x8 x17 x18 = If_i (SNoLe x17 0) x18 (x5 (x8 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x9 x17 = x8 (x6 x17) x7) ⟶ (∀ x17 . x17 ∈ int ⟶ x10 x17 = x9 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = mul_SNo (add_SNo 1 (mul_SNo 2 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))))) (add_SNo x17 x18)) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x17) ⟶ x13 = 0 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x11 (x14 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 (x12 x17) x13) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = add_SNo (x15 x17) (add_SNo 1 x17)) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x10 x17 = x16 x17
Conjecture 7fd24..^A14904 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ x0 x17 = mul_SNo 2 (add_SNo 2 x17)) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x5 x17 x18 = add_SNo 1 (add_SNo (mul_SNo x4 x17) x18)) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = x17) ⟶ x7 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x8 x17 x18 = If_i (SNoLe x17 0) x18 (x5 (x8 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x9 x17 = x8 (x6 x17) x7) ⟶ (∀ x17 . x17 ∈ int ⟶ x10 x17 = x9 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = add_SNo (mul_SNo (mul_SNo 2 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) x17) x18) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = add_SNo 1 x17) ⟶ x13 = 0 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x11 (x14 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 (x12 x17) x13) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = x15 x17) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x10 x17 = x16 x17
Conjecture 6b815..^A145721 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 : ι → ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x10 x11 x12 x13 ∈ int) ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ x0 x28 = mul_SNo (add_SNo 1 (add_SNo 2 2)) (add_SNo 1 x28)) ⟶ x1 = add_SNo 2 2 ⟶ x2 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x3 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x3 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x5 x28 x29 = add_SNo (mul_SNo x4 x28) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x7 x28 = x28) ⟶ x8 = 1 ⟶ x9 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x10 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x5 (x10 (add_SNo x28 (minus_SNo 1)) x29 x30) (x11 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x11 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x6 (x10 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x10 (x7 x28) x8 x9) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x14 x28 = add_SNo (mul_SNo (mul_SNo (add_SNo 2 x28) x28) x28) x28) ⟶ x15 = 1 ⟶ x16 = mul_SNo 2 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x17 x28 x29 = If_i (SNoLe x28 0) x29 (x14 (x17 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ x18 = x17 x15 x16 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x19 x28 x29 = add_SNo (mul_SNo (add_SNo 2 x18) x28) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x20 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x28) ⟶ x22 = 1 ⟶ x23 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x24 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x19 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30) (x25 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x25 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x20 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x24 (x21 x28) x22 x23) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = x26 x28) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture 405d5..^A145699 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 : ι → ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x10 x11 x12 x13 ∈ int) ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ x0 x28 = add_SNo 2 (mul_SNo (add_SNo 1 2) (mul_SNo x28 x28))) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x3 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x3 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x5 x28 x29 = add_SNo (mul_SNo x4 x28) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x7 x28 = x28) ⟶ x8 = 1 ⟶ x9 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x10 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x5 (x10 (add_SNo x28 (minus_SNo 1)) x29 x30) (x11 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x11 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x6 (x10 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x10 (x7 x28) x8 x9) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x14 x28 = mul_SNo x28 x28) ⟶ x15 = 1 ⟶ x16 = add_SNo 2 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x17 x28 x29 = If_i (SNoLe x28 0) x29 (x14 (x17 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ x18 = x17 x15 x16 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x19 x28 x29 = add_SNo (mul_SNo (add_SNo 2 (mul_SNo (add_SNo 1 2) x18)) x28) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x20 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x28) ⟶ x22 = 1 ⟶ x23 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x24 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x19 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30) (x25 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x25 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x20 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x24 (x21 x28) x22 x23) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = x26 x28) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture b9225..^A145529 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 : ι → ι → ι → ι . (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x29 x30 x31 x32 ∈ int) ⟶ ∀ x30 : ι → ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x30 x31 x32 x33 ∈ int) ⟶ ∀ x31 : ι → ι . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ ∀ x32 : ι → ι . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ int) ⟶ (∀ x33 . x33 ∈ int ⟶ x0 x33 = mul_SNo x33 x33) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x3 x33 x34 = If_i (SNoLe x33 0) x34 (x0 (x3 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = add_SNo (mul_SNo (add_SNo (add_SNo x33 (minus_SNo 1)) x33) x4) (minus_SNo 2)) ⟶ x6 = 2 ⟶ x7 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x8 x33 x34 = If_i (SNoLe x33 0) x34 (x5 (x8 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ x9 = x8 x6 x7 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x10 x33 x34 = add_SNo (mul_SNo x9 x33) (minus_SNo x34)) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x12 x33 = x33) ⟶ x13 = 1 ⟶ x14 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x15 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x10 (x15 (add_SNo x33 (minus_SNo 1)) x34 x35) (x16 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x16 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x11 (x15 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x17 x33 = x15 (x12 x33) x13 x14) ⟶ (∀ x33 . x33 ∈ int ⟶ x18 x33 = x17 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x19 x33 = mul_SNo (mul_SNo x33 x33) x33) ⟶ x20 = 1 ⟶ x21 = add_SNo 1 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x19 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ x23 = x22 x20 x21 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x24 x33 x34 = add_SNo (mul_SNo (mul_SNo 2 (add_SNo x23 (minus_SNo 2))) x33) (minus_SNo x34)) ⟶ (∀ x33 . x33 ∈ int ⟶ x25 x33 = x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x26 x33 = x33) ⟶ x27 = 1 ⟶ x28 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x29 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x24 (x29 (add_SNo x33 (minus_SNo 1)) x34 x35) (x30 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x30 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x25 (x29 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x31 x33 = x29 (x26 x33) x27 x28) ⟶ (∀ x33 . x33 ∈ int ⟶ x32 x33 = x31 x33) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x18 x33 = x32 x33
Conjecture beedd..^A145123 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 : ι → ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x10 x11 x12 x13 ∈ int) ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ x0 x28 = add_SNo 2 (add_SNo (mul_SNo 2 (mul_SNo x28 x28)) x28)) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x3 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x3 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x5 x28 x29 = add_SNo (mul_SNo x4 x28) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x7 x28 = x28) ⟶ x8 = 1 ⟶ x9 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x10 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x5 (x10 (add_SNo x28 (minus_SNo 1)) x29 x30) (x11 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x11 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x6 (x10 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x10 (x7 x28) x8 x9) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x14 x28 = mul_SNo x28 x28) ⟶ x15 = 1 ⟶ x16 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x17 x28 x29 = If_i (SNoLe x28 0) x29 (x14 (x17 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ x18 = x17 x15 x16 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x19 x28 x29 = add_SNo (mul_SNo (add_SNo 2 (mul_SNo (add_SNo 1 2) x18)) x28) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x20 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x28) ⟶ x22 = 1 ⟶ x23 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x24 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x19 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30) (x25 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x25 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x20 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x24 (x21 x28) x22 x23) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = x26 x28) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture 4f6ec..^A144829 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x0 x20 x21 = add_SNo (add_SNo (add_SNo x20 (minus_SNo x21)) x20) x20) ⟶ x1 = 2 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x2 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x4 x20 x21 = x3 x1 (x2 x20 x21)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x5 x20 x21 = mul_SNo (x4 x20 x21) x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = If_i (SNoLe x20 0) x21 (x5 (x8 (add_SNo x20 (minus_SNo 1)) x21) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x9 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = mul_SNo x20 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = add_SNo 1 (add_SNo (mul_SNo 2 (add_SNo 2 2)) x21)) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 1 ⟶ x15 = add_SNo 2 2 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x16 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x11 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x17 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x12 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x16 (x13 x20) x14 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture b10de..^A14479 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x0 x12 x13 = mul_SNo 2 (add_SNo (mul_SNo x12 x13) x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x1 x12 = x12) ⟶ (∀ x12 . x12 ∈ int ⟶ x2 x12 = add_SNo 1 x12) ⟶ (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x3 x12 x13 = If_i (SNoLe x12 0) x13 (x0 (x3 (add_SNo x12 (minus_SNo 1)) x13) x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x4 x12 = x3 (x1 x12) (x2 x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x5 x12 = x4 x12) ⟶ (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x6 x12 x13 = mul_SNo 2 (mul_SNo x12 x13)) ⟶ (∀ x12 . x12 ∈ int ⟶ x7 x12 = x12) ⟶ x8 = 1 ⟶ (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x9 x12 x13 = If_i (SNoLe x12 0) x13 (x6 (x9 (add_SNo x12 (minus_SNo 1)) x13) x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x10 x12 = x9 (x7 x12) x8) ⟶ (∀ x12 . x12 ∈ int ⟶ x11 x12 = mul_SNo (add_SNo 1 (mul_SNo (add_SNo 2 x12) x12)) (x10 x12)) ⟶ ∀ x12 . x12 ∈ int ⟶ SNoLe 0 x12 ⟶ x5 x12 = x11 x12
Conjecture d70e8..^A144345 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x0 x22 x23 = add_SNo (mul_SNo (add_SNo 1 2) (mul_SNo x22 x23)) (minus_SNo x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x1 x22 x23 = x23) ⟶ x2 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x3 x22 x23 = If_i (SNoLe x22 0) x23 (x0 (x3 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x4 x22 x23 = x3 (x1 x22 x23) x2) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x5 x22 x23 = add_SNo (add_SNo (x4 x22 x23) (mul_SNo (add_SNo 1 2) (mul_SNo x22 x23))) x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x6 x22 = x22) ⟶ x7 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x8 x22 x23 = If_i (SNoLe x22 0) x23 (x5 (x8 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x9 x22 = x8 (x6 x22) x7) ⟶ (∀ x22 . x22 ∈ int ⟶ x10 x22 = x9 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x11 x22 x23 = add_SNo (mul_SNo (add_SNo 1 2) (mul_SNo x22 x23)) (minus_SNo x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x12 x22 x23 = x23) ⟶ x13 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x14 x22 x23 = If_i (SNoLe x22 0) x23 (x11 (x14 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x15 x22 x23 = x14 (x12 x22 x23) x13) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x16 x22 x23 = add_SNo (x15 x22 x23) (mul_SNo (add_SNo (add_SNo (add_SNo x23 x23) x23) 1) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x17 x22 = x22) ⟶ x18 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x19 x22 x23 = If_i (SNoLe x22 0) x23 (x16 (x19 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x20 x22 = x19 (x17 x22) x18) ⟶ (∀ x22 . x22 ∈ int ⟶ x21 x22 = x20 x22) ⟶ ∀ x22 . x22 ∈ int ⟶ SNoLe 0 x22 ⟶ x10 x22 = x21 x22
Conjecture 0298d..^A14401 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x10 x11 x12 x13 ∈ int) ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x0 x30 x31 = mul_SNo 2 (mul_SNo x30 x31)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x1 x30 x31 = x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x2 x30 = x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x3 x30 x31 = If_i (SNoLe x30 0) x31 (x0 (x3 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x4 x30 x31 = x3 (x1 x30 x31) (x2 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x5 x30 x31 = x4 x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x6 x30 x31 = add_SNo (add_SNo 1 2) x31) ⟶ x7 = 2 ⟶ x8 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ x9 x30 = x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x10 x30 x31 x32 = If_i (SNoLe x30 0) x31 (x5 (x10 (add_SNo x30 (minus_SNo 1)) x31 x32) (x11 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x11 x30 x31 x32 = If_i (SNoLe x30 0) x32 (x6 (x10 (add_SNo x30 (minus_SNo 1)) x31 x32) (x11 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ x12 x30 = x10 x7 x8 (x9 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x13 x30 = x12 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x14 x30 x31 = mul_SNo 2 (mul_SNo x30 x31)) ⟶ (∀ x30 . x30 ∈ int ⟶ x15 x30 = add_SNo 1 (add_SNo 2 x30)) ⟶ x16 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x17 x30 x31 = If_i (SNoLe x30 0) x31 (x14 (x17 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x18 x30 = x17 (x15 x30) x16) ⟶ (∀ x30 . x30 ∈ int ⟶ x19 x30 = add_SNo x30 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x20 x30 = x30) ⟶ x21 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x22 x30 x31 = If_i (SNoLe x30 0) x31 (x19 (x22 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x23 x30 = x22 (x20 x30) x21) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x24 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x25 x30 = x30) ⟶ x26 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x27 x30 x31 = If_i (SNoLe x30 0) x31 (x24 (x27 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x28 x30 = x27 (x25 x30) x26) ⟶ (∀ x30 . x30 ∈ int ⟶ x29 x30 = mul_SNo (mul_SNo (x18 x30) (x23 x30)) (x28 x30)) ⟶ ∀ x30 . x30 ∈ int ⟶ SNoLe 0 x30 ⟶ x13 x30 = x29 x30
Conjecture f3eab..^A143248 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x0 x17 x18 = mul_SNo (add_SNo 1 x18) (mul_SNo (add_SNo 2 x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x1 x17 = x17) ⟶ x2 = 2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x4 x17 = x3 (x1 x17) x2) ⟶ (∀ x17 . x17 ∈ int ⟶ x5 x17 = If_i (SNoLe x17 0) 0 (x4 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = mul_SNo x17 x17) ⟶ x7 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x8 x17 x18 = mul_SNo x17 x18) ⟶ (∀ x17 . x17 ∈ int ⟶ x9 x17 = add_SNo x17 (minus_SNo 1)) ⟶ (∀ x17 . x17 ∈ int ⟶ x10 x17 = x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = If_i (SNoLe x17 0) x18 (x8 (x11 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x11 (x9 x17) (x10 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x13 x17 = mul_SNo (add_SNo 1 x17) (x12 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x6 (x14 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 x7 (x13 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = mul_SNo (x15 x17) (add_SNo 2 x17)) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture 8c305..^A14298 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 . x5 ∈ int ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x7 x8 x9 x10 ∈ int) ⟶ ∀ x8 : ι → ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x8 x9 x10 x11 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ x0 x28 = add_SNo x28 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x1 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x2 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x3 x28 x29 = add_SNo 1 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x4 x28 = add_SNo x28 (minus_SNo 1)) ⟶ x5 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = add_SNo 2 (add_SNo x28 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x7 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x2 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30) (x8 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x8 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x3 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30) (x8 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x7 (x4 x28) x5 (x6 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = x9 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x11 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x11 (x1 x28) (x10 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x14 x28 = add_SNo x28 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x28) ⟶ x16 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x17 x28 x29 = If_i (SNoLe x28 0) x29 (x14 (x17 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x18 x28 = x17 (x15 x28) x16) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x19 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x20 x28 x29 = add_SNo 1 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = add_SNo x28 (minus_SNo 1)) ⟶ x22 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ x23 x28 = add_SNo 2 (add_SNo x28 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x24 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x19 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30) (x25 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x25 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x20 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30) (x25 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x24 (x21 x28) x22 (x23 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = mul_SNo (x18 x28) (x26 x28)) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture 78fb1..^A14297 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x0 x17 x18 = mul_SNo 2 (mul_SNo (add_SNo 2 x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x1 x17 = x17) ⟶ x2 = 2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x4 x17 = x3 (x1 x17) x2) ⟶ (∀ x17 . x17 ∈ int ⟶ x5 x17 = x4 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x7 x17 = x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x8 x17 = add_SNo 1 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x9 x17 x18 = If_i (SNoLe x17 0) x18 (x6 (x9 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x10 x17 = x9 (x7 x17) (x8 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = mul_SNo x17 x18) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x13 x17 = add_SNo 2 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x11 (x14 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 (x12 x17) (x13 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = mul_SNo (x10 x17) (x15 x17)) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture dd117..^A14286 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x0 x18 x19 = add_SNo (add_SNo x18 (minus_SNo 1)) x19) ⟶ (∀ x18 . x18 ∈ int ⟶ x1 x18 = add_SNo x18 (minus_SNo 1)) ⟶ (∀ x18 . x18 ∈ int ⟶ x2 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x3 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x4 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x5 x18 x19 x20 = If_i (SNoLe x18 0) x19 (x0 (x5 (add_SNo x18 (minus_SNo 1)) x19 x20) (x6 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x6 x18 x19 x20 = If_i (SNoLe x18 0) x20 (x1 (x5 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ x7 x18 = x5 (x2 x18) (x3 x18) (x4 x18)) ⟶ (∀ x18 . x18 ∈ int ⟶ x8 x18 = x7 x18) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x9 x18 x19 = add_SNo x18 x19) ⟶ (∀ x18 . x18 ∈ int ⟶ x10 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x11 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x12 x18 = add_SNo x18 (minus_SNo 2)) ⟶ (∀ x18 . x18 ∈ int ⟶ x13 x18 = add_SNo x18 (minus_SNo 1)) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x14 x18 x19 x20 = If_i (SNoLe x18 0) x19 (x9 (x14 (add_SNo x18 (minus_SNo 1)) x19 x20) (x15 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x15 x18 x19 x20 = If_i (SNoLe x18 0) x20 (x10 (x14 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ x16 x18 = x14 (x11 x18) (x12 x18) (x13 x18)) ⟶ (∀ x18 . x18 ∈ int ⟶ x17 x18 = add_SNo 2 (x16 x18)) ⟶ ∀ x18 . x18 ∈ int ⟶ SNoLe 0 x18 ⟶ x8 x18 = x17 x18
Conjecture af7d0..^A14145 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x0 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x1 x25 x26 = x26) ⟶ x2 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x3 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x3 (add_SNo x25 (minus_SNo 1)) x26) x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x4 x25 x26 = x3 (x1 x25 x26) x2) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x5 x25 x26 = add_SNo (x4 x25 x26) x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x6 x25 x26 = x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x7 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x8 x25 x26 = If_i (SNoLe x25 0) x26 (x5 (x8 (add_SNo x25 (minus_SNo 1)) x26) x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x9 x25 x26 = x8 (x6 x25 x26) (x7 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x10 x25 x26 = x9 x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x11 x25 = x25) ⟶ x12 = 0 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x13 x25 x26 = If_i (SNoLe x25 0) x26 (x10 (x13 (add_SNo x25 (minus_SNo 1)) x26) x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x14 x25 = x13 (x11 x25) x12) ⟶ (∀ x25 . x25 ∈ int ⟶ x15 x25 = x14 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x16 x25 x26 = add_SNo 1 (mul_SNo x25 x26)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x17 x25 x26 = add_SNo x26 (minus_SNo 1)) ⟶ (∀ x25 . x25 ∈ int ⟶ x18 x25 = x25) ⟶ x19 = 0 ⟶ (∀ x25 . x25 ∈ int ⟶ x20 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x21 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x16 (x21 (add_SNo x25 (minus_SNo 1)) x26 x27) (x22 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x22 x25 x26 x27 = If_i (SNoLe x25 0) x27 (x17 (x21 (add_SNo x25 (minus_SNo 1)) x26 x27) (x22 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x23 x25 = x21 (x18 x25) x19 (x20 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = add_SNo (mul_SNo (x23 x25) (add_SNo 1 x25)) (minus_SNo x25)) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x15 x25 = x24 x25
Conjecture 14541..^A14144 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x0 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x1 x30 x31 = add_SNo x31 (minus_SNo 1)) ⟶ x2 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x3 x30 x31 = If_i (SNoLe x30 0) x31 (x0 (x3 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x4 x30 x31 = x3 (x1 x30 x31) x2) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x5 x30 x31 = add_SNo (x4 x30 x31) x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x6 x30 x31 = x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x7 x30 = x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x8 x30 x31 = If_i (SNoLe x30 0) x31 (x5 (x8 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x9 x30 x31 = x8 (x6 x30 x31) (x7 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x10 x30 x31 = x9 x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x11 x30 = x30) ⟶ x12 = 0 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x13 x30 x31 = If_i (SNoLe x30 0) x31 (x10 (x13 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x14 x30 = x13 (x11 x30) x12) ⟶ (∀ x30 . x30 ∈ int ⟶ x15 x30 = x14 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x16 x30 x31 = add_SNo 1 (mul_SNo x30 x31)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x17 x30 x31 = add_SNo x31 (minus_SNo 1)) ⟶ (∀ x30 . x30 ∈ int ⟶ x18 x30 = add_SNo x30 (minus_SNo 1)) ⟶ x19 = 0 ⟶ (∀ x30 . x30 ∈ int ⟶ x20 x30 = x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x21 x30 x31 x32 = If_i (SNoLe x30 0) x31 (x16 (x21 (add_SNo x30 (minus_SNo 1)) x31 x32) (x22 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x22 x30 x31 x32 = If_i (SNoLe x30 0) x32 (x17 (x21 (add_SNo x30 (minus_SNo 1)) x31 x32) (x22 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ x23 x30 = x21 (x18 x30) x19 (x20 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x24 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x25 x30 = x30) ⟶ x26 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x27 x30 x31 = If_i (SNoLe x30 0) x31 (x24 (x27 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x28 x30 = x27 (x25 x30) x26) ⟶ (∀ x30 . x30 ∈ int ⟶ x29 x30 = add_SNo (add_SNo (add_SNo (mul_SNo (x23 x30) x30) 1) (minus_SNo (x28 x30))) x30) ⟶ ∀ x30 . x30 ∈ int ⟶ SNoLe 0 x30 ⟶ x15 x30 = x29 x30
Conjecture 72ad9..^A140961 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 : ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x30 x31 x32 ∈ int) ⟶ ∀ x31 : ι → ι . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ ∀ x32 : ι → ι . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ int) ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι → ι . (∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x35 x36 x37 ∈ int) ⟶ ∀ x36 : ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x36 x37 x38 ∈ int) ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 : ι → ι → ι . (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x40 x41 x42 ∈ int) ⟶ ∀ x41 : ι → ι . (∀ x42 . x42 ∈ int ⟶ x41 x42 ∈ int) ⟶ ∀ x42 : ι → ι . (∀ x43 . x43 ∈ int ⟶ x42 x43 ∈ int) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x0 x43 x44 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x43 x43)) x44)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x1 x43 x44 = mul_SNo 2 (add_SNo (add_SNo x44 x44) x44)) ⟶ (∀ x43 . x43 ∈ int ⟶ x2 x43 = x43) ⟶ x3 = 1 ⟶ x4 = 2 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x5 x43 x44 x45 = If_i (SNoLe x43 0) x44 (x0 (x5 (add_SNo x43 (minus_SNo 1)) x44 x45) (x6 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x6 x43 x44 x45 = If_i (SNoLe x43 0) x45 (x1 (x5 (add_SNo x43 (minus_SNo 1)) x44 x45) (x6 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ x7 x43 = x5 (x2 x43) x3 x4) ⟶ (∀ x43 . x43 ∈ int ⟶ x8 x43 = x7 x43) ⟶ x9 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x10 x43 x44 = x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x11 x43 x44 = If_i (SNoLe x43 0) x44 (x8 (x11 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x12 x43 x44 = x11 x9 (x10 x43 x44)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x13 x43 x44 = add_SNo (add_SNo (x12 x43 x44) (mul_SNo 2 (add_SNo x43 x43))) x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x14 x43 = x43) ⟶ x15 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x16 x43 x44 = If_i (SNoLe x43 0) x44 (x13 (x16 (add_SNo x43 (minus_SNo 1)) x44) x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x17 x43 = x16 (x14 x43) x15) ⟶ (∀ x43 . x43 ∈ int ⟶ x18 x43 = x17 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x19 x43 x44 = add_SNo (mul_SNo 2 (add_SNo x43 x43)) x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x20 x43 x44 = add_SNo (add_SNo x44 x44) x44) ⟶ (∀ x43 . x43 ∈ int ⟶ x21 x43 = x43) ⟶ x22 = 1 ⟶ x23 = 2 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x24 x43 x44 x45 = If_i (SNoLe x43 0) x44 (x19 (x24 (add_SNo x43 (minus_SNo 1)) x44 x45) (x25 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x25 x43 x44 x45 = If_i (SNoLe x43 0) x45 (x20 (x24 (add_SNo x43 (minus_SNo 1)) x44 x45) (x25 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ x26 x43 = x24 (x21 x43) x22 x23) ⟶ (∀ x43 . x43 ∈ int ⟶ x27 x43 = add_SNo x43 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x28 x43 = x43) ⟶ x29 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x30 x43 x44 = If_i (SNoLe x43 0) x44 (x27 (x30 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ x31 x43 = x30 (x28 x43) x29) ⟶ (∀ x43 . x43 ∈ int ⟶ x32 x43 = mul_SNo (x26 x43) (x31 x43)) ⟶ x33 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x34 x43 x44 = x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x35 x43 x44 = If_i (SNoLe x43 0) x44 (x32 (x35 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x36 x43 x44 = x35 x33 (x34 x43 x44)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x37 x43 x44 = add_SNo (add_SNo (x36 x43 x44) x43) (mul_SNo (add_SNo x43 x43) 2)) ⟶ (∀ x43 . x43 ∈ int ⟶ x38 x43 = x43) ⟶ x39 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x40 x43 x44 = If_i (SNoLe x43 0) x44 (x37 (x40 (add_SNo x43 (minus_SNo 1)) x44) x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x41 x43 = x40 (x38 x43) x39) ⟶ (∀ x43 . x43 ∈ int ⟶ x42 x43 = x41 x43) ⟶ ∀ x43 . x43 ∈ int ⟶ SNoLe 0 x43 ⟶ x18 x43 = x42 x43
Conjecture b3cc8..^A140529 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ x0 x17 = add_SNo 1 (add_SNo x17 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x1 x17 = add_SNo 1 (add_SNo x17 x17)) ⟶ x2 = 2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x4 x17 = x3 (x1 x17) x2) ⟶ (∀ x17 . x17 ∈ int ⟶ x5 x17 = x4 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = mul_SNo x17 x17) ⟶ x7 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ x8 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x9 x17 = x17) ⟶ x10 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = If_i (SNoLe x17 0) x18 (x8 (x11 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x11 (x9 x17) x10) ⟶ (∀ x17 . x17 ∈ int ⟶ x13 x17 = x12 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x6 (x14 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 x7 (x13 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = add_SNo (mul_SNo 2 (mul_SNo (add_SNo 1 2) (x15 x17))) (minus_SNo 1)) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture 23b63..^A140230 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x0 x18 x19 = add_SNo x18 x19) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x1 x18 x19 = add_SNo x19 (minus_SNo x18)) ⟶ (∀ x18 . x18 ∈ int ⟶ x2 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x3 x18 = add_SNo 1 x18) ⟶ x4 = 1 ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x5 x18 x19 x20 = If_i (SNoLe x18 0) x19 (x0 (x5 (add_SNo x18 (minus_SNo 1)) x19 x20) (x6 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x6 x18 x19 x20 = If_i (SNoLe x18 0) x20 (x1 (x5 (add_SNo x18 (minus_SNo 1)) x19 x20) (x6 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ x7 x18 = x5 (x2 x18) (x3 x18) x4) ⟶ (∀ x18 . x18 ∈ int ⟶ x8 x18 = x7 x18) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x9 x18 x19 = add_SNo x18 (minus_SNo x19)) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x10 x18 x19 = add_SNo x18 x19) ⟶ (∀ x18 . x18 ∈ int ⟶ x11 x18 = add_SNo x18 (minus_SNo 1)) ⟶ (∀ x18 . x18 ∈ int ⟶ x12 x18 = add_SNo 2 x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x13 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x14 x18 x19 x20 = If_i (SNoLe x18 0) x19 (x9 (x14 (add_SNo x18 (minus_SNo 1)) x19 x20) (x15 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x15 x18 x19 x20 = If_i (SNoLe x18 0) x20 (x10 (x14 (add_SNo x18 (minus_SNo 1)) x19 x20) (x15 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ x16 x18 = x14 (x11 x18) (x12 x18) (x13 x18)) ⟶ (∀ x18 . x18 ∈ int ⟶ x17 x18 = If_i (SNoLe x18 0) 1 (x16 x18)) ⟶ ∀ x18 . x18 ∈ int ⟶ SNoLe 0 x18 ⟶ x8 x18 = x17 x18
Conjecture 5d7e3..^A140062 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ (∀ x22 . x22 ∈ int ⟶ x0 x22 = add_SNo 1 (mul_SNo (add_SNo 2 x22) x22)) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x3 x22 x23 = If_i (SNoLe x22 0) x23 (x0 (x3 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x22 . x22 ∈ int ⟶ x5 x22 = add_SNo (add_SNo x4 x22) x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x6 x22 = x22) ⟶ x7 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x8 x22 x23 = If_i (SNoLe x22 0) x23 (x5 (x8 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x9 x22 = x8 (x6 x22) x7) ⟶ (∀ x22 . x22 ∈ int ⟶ x10 x22 = x9 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x11 x22 = mul_SNo x22 x22) ⟶ x12 = 1 ⟶ x13 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x14 x22 x23 = If_i (SNoLe x22 0) x23 (x11 (x14 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ x15 = x14 x12 x13 ⟶ (∀ x22 . x22 ∈ int ⟶ x16 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x17 x22 = x22) ⟶ x18 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x19 x22 x23 = If_i (SNoLe x22 0) x23 (x16 (x19 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x20 x22 = x19 (x17 x22) x18) ⟶ (∀ x22 . x22 ∈ int ⟶ x21 x22 = add_SNo (mul_SNo (add_SNo 1 x15) (add_SNo (x20 x22) (minus_SNo 1))) 1) ⟶ ∀ x22 . x22 ∈ int ⟶ SNoLe 0 x22 ⟶ x10 x22 = x21 x22