Proofgold Address

Param int^int : ι
Param add_SNo^add_SNo : ι → ι → ι
Param mul_SNo^mul_SNo : ι → ι → ι
Param ordsucc^ordsucc : 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 748b5..^A6523 : ∀ 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 → 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 → 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 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ 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 . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x0 x25 x26 = add_SNo (mul_SNo x25 x26) x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x1 x25 = mul_SNo 2 (add_SNo x25 x25)) ⟶ x2 = 2 ⟶ (∀ 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 ⟶ x4 x25 = x3 (x1 x25) x2) ⟶ (∀ x25 . x25 ∈ int ⟶ x5 x25 = x4 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x6 x25 x26 = mul_SNo 2 (mul_SNo x25 x26)) ⟶ (∀ x25 . x25 ∈ int ⟶ x7 x25 = x25) ⟶ x8 = 2 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x9 x25 x26 = If_i (SNoLe x25 0) x26 (x6 (x9 (add_SNo x25 (minus_SNo 1)) x26) x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x10 x25 = x9 (x7 x25) x8) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x11 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x12 x25 x26 = add_SNo 2 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x13 x25 = x25) ⟶ x14 = 1 ⟶ x15 = add_SNo 1 2 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x16 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x11 (x16 (add_SNo x25 (minus_SNo 1)) x26 x27) (x17 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x17 x25 x26 x27 = If_i (SNoLe x25 0) x27 (x12 (x16 (add_SNo x25 (minus_SNo 1)) x26 x27) (x17 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x18 x25 = x16 (x13 x25) x14 x15) ⟶ (∀ x25 . x25 ∈ int ⟶ x19 x25 = mul_SNo (x10 x25) (x18 x25)) ⟶ x20 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ x21 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x22 x25 x26 = If_i (SNoLe x25 0) x26 (x19 (x22 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x23 x25 = x22 x20 (x21 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = x23 x25) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x5 x25 = x24 x25
Conjecture c5c90..^A65142 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ 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 : 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 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ 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 → 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 : 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 . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ x0 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x1 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x2 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x3 x25 = add_SNo (add_SNo x25 x25) x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x4 x25 = add_SNo 1 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x5 x25 x26 = If_i (SNoLe x25 0) x26 (x2 (x5 (add_SNo x25 (minus_SNo 1)) x26) x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x6 x25 = x5 (x3 x25) (x4 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x7 x25 = x6 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x8 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x8 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x9 x25 = x8 (x1 x25) (x7 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x10 x25 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x11 x25 x26 = mul_SNo 2 (mul_SNo x25 x26)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x12 x25 x26 = add_SNo 1 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x13 x25 = x25) ⟶ x14 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ x15 x25 = add_SNo 1 (add_SNo x25 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x16 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x11 (x16 (add_SNo x25 (minus_SNo 1)) x26 x27) (x17 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x17 x25 x26 x27 = If_i (SNoLe x25 0) x27 (x12 (x16 (add_SNo x25 (minus_SNo 1)) x26 x27) (x17 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x18 x25 = x16 (x13 x25) x14 (x15 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x19 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x20 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x21 x25 = add_SNo 1 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x22 x25 x26 = If_i (SNoLe x25 0) x26 (x19 (x22 (add_SNo x25 (minus_SNo 1)) x26) x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x23 x25 = x22 (x20 x25) (x21 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = mul_SNo (x18 x25) (x23 x25)) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture 4b044..^A65140 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ 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 : 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 → 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 ⟶ x0 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x1 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x2 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x3 x25 = add_SNo x25 x25) ⟶ x4 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x5 x25 x26 = If_i (SNoLe x25 0) x26 (x2 (x5 (add_SNo x25 (minus_SNo 1)) x26) x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x6 x25 = x5 (x3 x25) x4) ⟶ (∀ x25 . x25 ∈ int ⟶ x7 x25 = x6 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x8 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x8 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x9 x25 = x8 (x1 x25) (x7 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x10 x25 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x11 x25 x26 = mul_SNo 2 (mul_SNo x25 x26)) ⟶ (∀ x25 . x25 ∈ int ⟶ x12 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x13 x25 = add_SNo 1 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x14 x25 x26 = If_i (SNoLe x25 0) x26 (x11 (x14 (add_SNo x25 (minus_SNo 1)) x26) x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x15 x25 = x14 (x12 x25) (x13 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x16 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x17 x25 x26 = add_SNo 1 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x18 x25 = add_SNo x25 (minus_SNo 1)) ⟶ x19 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ x20 x25 = add_SNo 2 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 = mul_SNo (x15 x25) (x23 x25)) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture fc1a3..^A6483 : ∀ 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 : 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 . 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 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x0 x23 x24 = add_SNo x24 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x1 x23 x24 = mul_SNo 2 (add_SNo x23 x24)) ⟶ (∀ x23 . x23 ∈ int ⟶ x2 x23 = x23) ⟶ x3 = 0 ⟶ x4 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x5 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x0 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x6 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x1 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x5 (x2 x23) x3 x4) ⟶ (∀ x23 . x23 ∈ int ⟶ x8 x23 = add_SNo 1 (x7 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x9 x23 = add_SNo x23 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x10 x23 = add_SNo x23 (minus_SNo 1)) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x11 x23 x24 = add_SNo x23 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x12 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x13 x23 = add_SNo x23 (minus_SNo 2)) ⟶ x14 = 2 ⟶ x15 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x16 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x11 (x16 (add_SNo x23 (minus_SNo 1)) x24 x25) (x17 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x17 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x12 (x16 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x18 x23 = x16 (x13 x23) x14 x15) ⟶ (∀ x23 . x23 ∈ int ⟶ x19 x23 = If_i (SNoLe x23 0) 0 (x18 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x20 x23 x24 = If_i (SNoLe x23 0) x24 (x9 (x20 (add_SNo x23 (minus_SNo 1)) x24))) ⟶ (∀ x23 . x23 ∈ int ⟶ x21 x23 = x20 (x10 x23) (x19 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = add_SNo 1 (x21 x23)) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x8 x23 = x22 x23
Conjecture af699..^A64752 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 . x1 ∈ 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 . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ 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 . (∀ 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 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ 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 (mul_SNo x20 x21) x20) x21) ⟶ x1 = 2 ⟶ (∀ x20 . x20 ∈ int ⟶ x2 x20 = x20) ⟶ (∀ 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 ⟶ x4 x20 = x3 x1 (x2 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = x4 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = add_SNo 1 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x7 x20 = x20) ⟶ (∀ 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 ∈ int ⟶ x9 x20 = x8 (x6 x20) (x7 x20)) ⟶ (∀ 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 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = add_SNo 1 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x14 x20 = add_SNo 1 x20) ⟶ x15 = add_SNo 2 (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 x20) x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = add_SNo (x18 x20) (minus_SNo 1)) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture 11d0d..^A64749 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 . x1 ∈ 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 . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ 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 . (∀ 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 = mul_SNo (add_SNo 2 x21) x20) ⟶ x1 = 2 ⟶ (∀ x20 . x20 ∈ int ⟶ x2 x20 = x20) ⟶ (∀ 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 ⟶ x4 x20 = x3 x1 (x2 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = add_SNo (x4 x20) (minus_SNo x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x7 x20 = x20) ⟶ (∀ 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 ∈ int ⟶ x9 x20 = x8 (x6 x20) (x7 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = add_SNo 1 (x9 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = mul_SNo x20 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 1 ⟶ x15 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (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 = add_SNo 1 (mul_SNo x20 (x18 x20))) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture 32829..^A64671 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ 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 : 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 : 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 : 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 . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ (∀ x22 . x22 ∈ int ⟶ x0 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x1 x22 = x22) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x2 x22 x23 = add_SNo (add_SNo x22 x23) x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x3 x22 = x22) ⟶ x4 = 0 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x5 x22 x23 = If_i (SNoLe x22 0) x23 (x2 (x5 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x6 x22 = x5 (x3 x22) x4) ⟶ (∀ x22 . x22 ∈ int ⟶ x7 x22 = x6 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x8 x22 x23 = If_i (SNoLe x22 0) x23 (x0 (x8 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x9 x22 = x8 (x1 x22) (x7 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x10 x22 = add_SNo (x9 x22) x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x11 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x12 x22 = x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x13 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x14 x22 = x22) ⟶ x15 = 2 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x16 x22 x23 = If_i (SNoLe x22 0) x23 (x13 (x16 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x17 x22 = x16 (x14 x22) x15) ⟶ (∀ x22 . x22 ∈ int ⟶ x18 x22 = add_SNo (x17 x22) (minus_SNo (add_SNo 2 x22))) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x19 x22 x23 = If_i (SNoLe x22 0) x23 (x11 (x19 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x20 x22 = x19 (x12 x22) (x18 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x21 x22 = add_SNo (x20 x22) x22) ⟶ ∀ x22 . x22 ∈ int ⟶ SNoLe 0 x22 ⟶ x10 x22 = x21 x22
Conjecture 3329c..^A62395 : ∀ 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 x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x1 x17 = add_SNo (add_SNo x17 x17) x17) ⟶ x2 = 1 ⟶ (∀ 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 = add_SNo 1 (x4 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = mul_SNo (mul_SNo x17 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 1 (x15 x17)) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture 46e8b..^A6234 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 . x3 ∈ 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 → 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 : 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 (add_SNo x18 x18) x18) x19) ⟶ x1 = 0 ⟶ (∀ x18 . x18 ∈ int ⟶ x2 x18 = x18) ⟶ x3 = 1 ⟶ (∀ 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) ⟶ (∀ x18 . x18 ∈ int ⟶ x7 x18 = x5 (x2 x18) x3 (x4 x18)) ⟶ (∀ x18 . x18 ∈ int ⟶ x8 x18 = x7 x18) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x9 x18 x19 = mul_SNo x18 x19) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x10 x18 x19 = x19) ⟶ (∀ x18 . x18 ∈ int ⟶ x11 x18 = add_SNo x18 (minus_SNo 1)) ⟶ (∀ x18 . x18 ∈ int ⟶ x12 x18 = add_SNo 1 (add_SNo 2 x18)) ⟶ x13 = add_SNo 1 2 ⟶ (∀ 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 ∈ int ⟶ x17 x18 = If_i (SNoLe x18 0) 1 (x16 x18)) ⟶ ∀ x18 . x18 ∈ int ⟶ SNoLe 0 x18 ⟶ x8 x18 = x17 x18
Conjecture c2780..^A6231 : ∀ 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 x22 x23) x23) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x1 x22 x23 = x23) ⟶ x2 = 0 ⟶ (∀ 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 (x4 x22 x23) x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x6 x22 = x22) ⟶ x7 = 0 ⟶ (∀ 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 1 (mul_SNo x22 x23)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x12 x22 x23 = add_SNo x23 (minus_SNo 1)) ⟶ 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 (mul_SNo (x15 x22 x23) x23) x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x17 x22 = x22) ⟶ x18 = 0 ⟶ (∀ 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 83b45..^A62119 : ∀ 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 : 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 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x0 x12 x13 = add_SNo (mul_SNo x12 x13) x12) ⟶ (∀ x12 . x12 ∈ int ⟶ x1 x12 = x12) ⟶ (∀ x12 . x12 ∈ int ⟶ x2 x12 = 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 x12 x13) ⟶ (∀ x12 . x12 ∈ int ⟶ x7 x12 = x12) ⟶ (∀ x12 . x12 ∈ int ⟶ x8 x12 = x12) ⟶ (∀ 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 . x12 ∈ int ⟶ x11 x12 = mul_SNo (add_SNo 1 x12) (x10 x12)) ⟶ ∀ x12 . x12 ∈ int ⟶ SNoLe 0 x12 ⟶ x5 x12 = x11 x12
Conjecture 66ba6..^A61788 : ∀ 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 → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ 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 . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x13 x14 x15 x16 ∈ int) ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ 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 . (∀ 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 . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x25 x26 x27 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x28 x29 x30 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 : ι → ι . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ int) ⟶ ∀ x31 : ι → ι . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ ∀ x32 : ι → ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x32 x33 x34 x35 ∈ int) ⟶ ∀ x33 : ι → ι → ι → ι . (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x33 x34 x35 x36 ∈ int) ⟶ ∀ x34 : ι → ι . (∀ x35 . x35 ∈ int ⟶ x34 x35 ∈ 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 . (∀ x38 . x38 ∈ int ⟶ x37 x38 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ ∀ x40 : ι → ι → ι → ι . (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x40 x41 x42 x43 ∈ int) ⟶ ∀ x41 : ι → ι → ι → ι . (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x41 x42 x43 x44 ∈ int) ⟶ ∀ x42 : ι → ι . (∀ x43 . x43 ∈ int ⟶ x42 x43 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 : ι → ι → ι . (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x45 x46 x47 ∈ int) ⟶ ∀ x46 : ι → ι → ι . (∀ x47 . x47 ∈ int ⟶ ∀ x48 . x48 ∈ int ⟶ x46 x47 x48 ∈ int) ⟶ ∀ x47 : ι → ι → ι . (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x47 x48 x49 ∈ int) ⟶ ∀ x48 : ι → ι → ι . (∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x48 x49 x50 ∈ int) ⟶ ∀ x49 : ι → ι . (∀ x50 . x50 ∈ int ⟶ x49 x50 ∈ int) ⟶ ∀ x50 . x50 ∈ int ⟶ ∀ x51 : ι → ι → ι . (∀ x52 . x52 ∈ int ⟶ ∀ x53 . x53 ∈ int ⟶ x51 x52 x53 ∈ int) ⟶ ∀ x52 : ι → ι . (∀ x53 . x53 ∈ int ⟶ x52 x53 ∈ int) ⟶ ∀ x53 : ι → ι . (∀ x54 . x54 ∈ int ⟶ x53 x54 ∈ int) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x0 x54 x55 = mul_SNo x54 x55) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x1 x54 x55 = x55) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x2 x54 x55 = x55) ⟶ x3 = 1 ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x4 x54 x55 = x55) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ ∀ x56 . x56 ∈ int ⟶ x5 x54 x55 x56 = If_i (SNoLe x54 0) x55 (x0 (x5 (add_SNo x54 (minus_SNo 1)) x55 x56) (x6 (add_SNo x54 (minus_SNo 1)) x55 x56))) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ ∀ x56 . x56 ∈ int ⟶ x6 x54 x55 x56 = If_i (SNoLe x54 0) x56 (x1 (x5 (add_SNo x54 (minus_SNo 1)) x55 x56) (x6 (add_SNo x54 (minus_SNo 1)) x55 x56))) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x7 x54 x55 = x5 (x2 x54 x55) x3 (x4 x54 x55)) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x8 x54 x55 = add_SNo (x7 x54 x55) x54) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x9 x54 x55 = add_SNo 2 x55) ⟶ (∀ x54 . x54 ∈ int ⟶ x10 x54 = add_SNo x54 1) ⟶ x11 = 0 ⟶ x12 = 2 ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ ∀ x56 . x56 ∈ int ⟶ x13 x54 x55 x56 = If_i (SNoLe x54 0) x55 (x8 (x13 (add_SNo x54 (minus_SNo 1)) x55 x56) (x14 (add_SNo x54 (minus_SNo 1)) x55 x56))) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ ∀ x56 . x56 ∈ int ⟶ x14 x54 x55 x56 = If_i (SNoLe x54 0) x56 (x9 (x13 (add_SNo x54 (minus_SNo 1)) x55 x56) (x14 (add_SNo x54 (minus_SNo 1)) x55 x56))) ⟶ (∀ x54 . x54 ∈ int ⟶ x15 x54 = x13 (x10 x54) x11 x12) ⟶ (∀ x54 . x54 ∈ int ⟶ x16 x54 = x15 x54) ⟶ (∀ x54 . x54 ∈ int ⟶ x17 x54 = mul_SNo x54 x54) ⟶ x18 = 1 ⟶ (∀ x54 . x54 ∈ int ⟶ x19 x54 = add_SNo x54 x54) ⟶ (∀ x54 . x54 ∈ int ⟶ x20 x54 = x54) ⟶ x21 = 1 ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x22 x54 x55 = If_i (SNoLe x54 0) x55 (x19 (x22 (add_SNo x54 (minus_SNo 1)) x55))) ⟶ (∀ x54 . x54 ∈ int ⟶ x23 x54 = x22 (x20 x54) x21) ⟶ (∀ x54 . x54 ∈ int ⟶ x24 x54 = x23 x54) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x25 x54 x55 = If_i (SNoLe x54 0) x55 (x17 (x25 (add_SNo x54 (minus_SNo 1)) x55))) ⟶ (∀ x54 . x54 ∈ int ⟶ x26 x54 = x25 x18 (x24 x54)) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x27 x54 x55 = mul_SNo x54 x55) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x28 x54 x55 = x55) ⟶ (∀ x54 . x54 ∈ int ⟶ x29 x54 = x54) ⟶ (∀ x54 . x54 ∈ int ⟶ x30 x54 = add_SNo 1 x54) ⟶ (∀ x54 . x54 ∈ int ⟶ x31 x54 = add_SNo 1 x54) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ ∀ x56 . x56 ∈ int ⟶ x32 x54 x55 x56 = If_i (SNoLe x54 0) x55 (x27 (x32 (add_SNo x54 (minus_SNo 1)) x55 x56) (x33 (add_SNo x54 (minus_SNo 1)) x55 x56))) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ ∀ x56 . x56 ∈ int ⟶ x33 x54 x55 x56 = If_i (SNoLe x54 0) x56 (x28 (x32 (add_SNo x54 (minus_SNo 1)) x55 x56) (x33 (add_SNo x54 (minus_SNo 1)) x55 x56))) ⟶ (∀ x54 . x54 ∈ int ⟶ x34 x54 = x32 (x29 x54) (x30 x54) (x31 x54)) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x35 x54 x55 = mul_SNo x54 x55) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x36 x54 x55 = x55) ⟶ (∀ x54 . x54 ∈ int ⟶ x37 x54 = x54) ⟶ (∀ x54 . x54 ∈ int ⟶ x38 x54 = add_SNo 1 x54) ⟶ (∀ x54 . x54 ∈ int ⟶ x39 x54 = add_SNo 1 x54) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ ∀ x56 . x56 ∈ int ⟶ x40 x54 x55 x56 = If_i (SNoLe x54 0) x55 (x35 (x40 (add_SNo x54 (minus_SNo 1)) x55 x56) (x41 (add_SNo x54 (minus_SNo 1)) x55 x56))) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ ∀ x56 . x56 ∈ int ⟶ x41 x54 x55 x56 = If_i (SNoLe x54 0) x56 (x36 (x40 (add_SNo x54 (minus_SNo 1)) x55 x56) (x41 (add_SNo x54 (minus_SNo 1)) x55 x56))) ⟶ (∀ x54 . x54 ∈ int ⟶ x42 x54 = x40 (x37 x54) (x38 x54) (x39 x54)) ⟶ (∀ x54 . x54 ∈ int ⟶ x43 x54 = mul_SNo (mul_SNo (mul_SNo 2 (x26 x54)) (x34 x54)) (x42 x54)) ⟶ x44 = 1 ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x45 x54 x55 = x55) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x46 x54 x55 = If_i (SNoLe x54 0) x55 (x43 (x46 (add_SNo x54 (minus_SNo 1)) x55))) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x47 x54 x55 = x46 x44 (x45 x54 x55)) ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x48 x54 x55 = add_SNo (x47 x54 x55) x54) ⟶ (∀ x54 . x54 ∈ int ⟶ x49 x54 = x54) ⟶ x50 = 1 ⟶ (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x51 x54 x55 = If_i (SNoLe x54 0) x55 (x48 (x51 (add_SNo x54 (minus_SNo 1)) x55) x54)) ⟶ (∀ x54 . x54 ∈ int ⟶ x52 x54 = x51 (x49 x54) x50) ⟶ (∀ x54 . x54 ∈ int ⟶ x53 x54 = add_SNo (mul_SNo (x52 x54) 2) 2) ⟶ ∀ x54 . x54 ∈ int ⟶ SNoLe 0 x54 ⟶ x16 x54 = x53 x54
Conjecture 6584a..^A61787 : ∀ 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 → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ 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 . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x13 x14 x15 x16 ∈ int) ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x23 x24 x25 x26 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x25 x26 x27 ∈ int) ⟶ ∀ x26 : ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 : ι → ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x30 x31 x32 x33 ∈ int) ⟶ ∀ x31 : ι → ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x31 x32 x33 x34 ∈ int) ⟶ ∀ x32 : ι → ι . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 . x34 ∈ 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 → ι . (∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x38 x39 x40 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ ∀ x40 . x40 ∈ int ⟶ ∀ x41 : ι → ι → ι . (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x41 x42 x43 ∈ int) ⟶ ∀ x42 : ι → ι . (∀ x43 . x43 ∈ int ⟶ x42 x43 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x0 x44 x45 = mul_SNo x44 x45) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x1 x44 x45 = x45) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x2 x44 x45 = x45) ⟶ x3 = 1 ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x4 x44 x45 = x45) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x5 x44 x45 x46 = If_i (SNoLe x44 0) x45 (x0 (x5 (add_SNo x44 (minus_SNo 1)) x45 x46) (x6 (add_SNo x44 (minus_SNo 1)) x45 x46))) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x6 x44 x45 x46 = If_i (SNoLe x44 0) x46 (x1 (x5 (add_SNo x44 (minus_SNo 1)) x45 x46) (x6 (add_SNo x44 (minus_SNo 1)) x45 x46))) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x7 x44 x45 = x5 (x2 x44 x45) x3 (x4 x44 x45)) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x8 x44 x45 = add_SNo (x7 x44 x45) x44) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x9 x44 x45 = add_SNo 2 x45) ⟶ (∀ x44 . x44 ∈ int ⟶ x10 x44 = x44) ⟶ x11 = 1 ⟶ x12 = add_SNo 1 2 ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x13 x44 x45 x46 = If_i (SNoLe x44 0) x45 (x8 (x13 (add_SNo x44 (minus_SNo 1)) x45 x46) (x14 (add_SNo x44 (minus_SNo 1)) x45 x46))) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x14 x44 x45 x46 = If_i (SNoLe x44 0) x46 (x9 (x13 (add_SNo x44 (minus_SNo 1)) x45 x46) (x14 (add_SNo x44 (minus_SNo 1)) x45 x46))) ⟶ (∀ x44 . x44 ∈ int ⟶ x15 x44 = x13 (x10 x44) x11 x12) ⟶ (∀ x44 . x44 ∈ int ⟶ x16 x44 = x15 x44) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x17 x44 x45 = mul_SNo x44 x45) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x18 x44 x45 = x45) ⟶ (∀ x44 . x44 ∈ int ⟶ x19 x44 = add_SNo 1 x44) ⟶ x20 = 1 ⟶ (∀ x44 . x44 ∈ int ⟶ x21 x44 = add_SNo 1 (add_SNo x44 x44)) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x22 x44 x45 x46 = If_i (SNoLe x44 0) x45 (x17 (x22 (add_SNo x44 (minus_SNo 1)) x45 x46) (x23 (add_SNo x44 (minus_SNo 1)) x45 x46))) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x23 x44 x45 x46 = If_i (SNoLe x44 0) x46 (x18 (x22 (add_SNo x44 (minus_SNo 1)) x45 x46) (x23 (add_SNo x44 (minus_SNo 1)) x45 x46))) ⟶ (∀ x44 . x44 ∈ int ⟶ x24 x44 = x22 (x19 x44) x20 (x21 x44)) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x25 x44 x45 = mul_SNo x44 x45) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x26 x44 x45 = x45) ⟶ (∀ x44 . x44 ∈ int ⟶ x27 x44 = x44) ⟶ x28 = 1 ⟶ (∀ x44 . x44 ∈ int ⟶ x29 x44 = add_SNo 1 (add_SNo x44 x44)) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x30 x44 x45 x46 = If_i (SNoLe x44 0) x45 (x25 (x30 (add_SNo x44 (minus_SNo 1)) x45 x46) (x31 (add_SNo x44 (minus_SNo 1)) x45 x46))) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x31 x44 x45 x46 = If_i (SNoLe x44 0) x46 (x26 (x30 (add_SNo x44 (minus_SNo 1)) x45 x46) (x31 (add_SNo x44 (minus_SNo 1)) x45 x46))) ⟶ (∀ x44 . x44 ∈ int ⟶ x32 x44 = x30 (x27 x44) x28 (x29 x44)) ⟶ (∀ x44 . x44 ∈ int ⟶ x33 x44 = mul_SNo (x24 x44) (x32 x44)) ⟶ x34 = 1 ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x35 x44 x45 = x45) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x36 x44 x45 = If_i (SNoLe x44 0) x45 (x33 (x36 (add_SNo x44 (minus_SNo 1)) x45))) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x37 x44 x45 = x36 x34 (x35 x44 x45)) ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x38 x44 x45 = add_SNo (x37 x44 x45) x44) ⟶ (∀ x44 . x44 ∈ int ⟶ x39 x44 = x44) ⟶ x40 = 1 ⟶ (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x41 x44 x45 = If_i (SNoLe x44 0) x45 (x38 (x41 (add_SNo x44 (minus_SNo 1)) x45) x44)) ⟶ (∀ x44 . x44 ∈ int ⟶ x42 x44 = x41 (x39 x44) x40) ⟶ (∀ x44 . x44 ∈ int ⟶ x43 x44 = x42 x44) ⟶ ∀ x44 . x44 ∈ int ⟶ SNoLe 0 x44 ⟶ x16 x44 = x43 x44
Conjecture 22bc7..^A61705 : ∀ 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 . x3 ∈ 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 . x13 ∈ 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 ⟶ x1 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x2 x18 = add_SNo 1 x18) ⟶ x3 = 2 ⟶ (∀ 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 (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 2 x18) ⟶ x13 = 2 ⟶ (∀ 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 ∈ int ⟶ x17 x18 = x16 x18) ⟶ ∀ x18 . x18 ∈ int ⟶ SNoLe 0 x18 ⟶ x8 x18 = x17 x18
Conjecture 60e8e..^A61572 : ∀ 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 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ 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 = mul_SNo x22 x23) ⟶ (∀ 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 (mul_SNo (add_SNo 2 x23) (mul_SNo x22 x23)) (x4 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 = mul_SNo x22 x23) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x12 x22 x23 = add_SNo x23 (minus_SNo 1)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x13 x22 x23 = x23) ⟶ (∀ 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 x23)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x16 x22 x23 = add_SNo (x15 x22 x23) (mul_SNo (mul_SNo (add_SNo 1 x23) (add_SNo 1 x23)) 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 69259..^A6125 : ∀ 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 : 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 . x13 ∈ 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 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ 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 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x0 x23 x24 = mul_SNo x23 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x1 x23 x24 = add_SNo x24 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x2 x23 = x23) ⟶ x3 = 1 ⟶ x4 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x5 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x0 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x6 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x1 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x5 (x2 x23) x3 x4) ⟶ (∀ x23 . x23 ∈ int ⟶ x8 x23 = x7 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x9 x23 x24 = mul_SNo x23 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x10 x23 x24 = add_SNo x24 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x11 x23 = add_SNo x23 (minus_SNo 2)) ⟶ x12 = 1 ⟶ x13 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x14 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x9 (x14 (add_SNo x23 (minus_SNo 1)) x24 x25) (x15 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x15 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x10 (x14 (add_SNo x23 (minus_SNo 1)) x24 x25) (x15 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x16 x23 = x14 (x11 x23) x12 x13) ⟶ (∀ x23 . x23 ∈ int ⟶ x17 x23 = add_SNo x23 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x18 x23 = add_SNo (add_SNo (add_SNo x23 (minus_SNo 1)) x23) (minus_SNo 2)) ⟶ x19 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x20 x23 x24 = If_i (SNoLe x23 0) x24 (x17 (x20 (add_SNo x23 (minus_SNo 1)) x24))) ⟶ (∀ x23 . x23 ∈ int ⟶ x21 x23 = x20 (x18 x23) x19) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = mul_SNo (x16 x23) (x21 x23)) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x8 x23 = x22 x23
Conjecture 69b3c..^A61062 : ∀ 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 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ 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 = mul_SNo (mul_SNo x20 x21) x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x1 x20 x21 = x21) ⟶ x2 = 1 ⟶ (∀ 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 x20 x21) x2) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x5 x20 x21 = add_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 = add_SNo 1 (mul_SNo (mul_SNo x21 x21) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = add_SNo x21 (minus_SNo 1)) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = add_SNo x20 (minus_SNo 1)) ⟶ x14 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ x15 x20 = x20) ⟶ (∀ 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 . x20 ∈ int ⟶ x19 x20 = add_SNo (x18 x20) (If_i (SNoLe x20 0) 0 1)) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture d22da..^A6105 : ∀ 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 → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . x7 ∈ 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 . x20 ∈ 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 ⟶ x0 x25 = mul_SNo x25 x25) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x3 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x3 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x25 . x25 ∈ int ⟶ x5 x25 = add_SNo 1 (mul_SNo 2 (add_SNo x25 x25))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x6 x25 x26 = x26) ⟶ x7 = 1 ⟶ (∀ 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 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x9 x25 x26 = x8 (x6 x25 x26) x7) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x10 x25 x26 = add_SNo (mul_SNo x4 x25) (x9 x25 x26)) ⟶ (∀ x25 . x25 ∈ int ⟶ x11 x25 = x25) ⟶ x12 = 1 ⟶ (∀ 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 (mul_SNo 2 (mul_SNo 2 (mul_SNo 2 (add_SNo x25 x25)))) x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x17 x25 x26 = add_SNo 1 (mul_SNo 2 (add_SNo x26 x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x18 x25 = x25) ⟶ x19 = 1 ⟶ x20 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ 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 ∈ int ⟶ x24 x25 = x23 x25) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x15 x25 = x24 x25
Conjecture 6ebc6..^A60946 : ∀ 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 → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ 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 . 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 → 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 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ 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 . x24 ∈ int ⟶ ∀ x25 : ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x25 x26 x27 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x0 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x1 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x2 x28 x29 = x29) ⟶ x3 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x4 x28 x29 = add_SNo 1 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x5 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x0 (x5 (add_SNo x28 (minus_SNo 1)) x29 x30) (x6 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x6 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x1 (x5 (add_SNo x28 (minus_SNo 1)) x29 x30) (x6 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x7 x28 x29 = x5 (x2 x28 x29) x3 (x4 x28 x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x8 x28 x29 = add_SNo x28 (x7 x28 x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x28) ⟶ x10 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = If_i (SNoLe x28 0) x29 (x8 (x11 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x11 (x9 x28) x10) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x14 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x15 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x16 x28 x29 = add_SNo x29 (minus_SNo 1)) ⟶ x17 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x18 x28 x29 = add_SNo 1 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x19 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x14 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30) (x20 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x20 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x15 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30) (x20 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x21 x28 x29 = x19 (x16 x28 x29) x17 (x18 x28 x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x22 x28 x29 = add_SNo (mul_SNo (x21 x28 x29) (add_SNo 1 x29)) x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x23 x28 = x28) ⟶ x24 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x25 x28 x29 = If_i (SNoLe x28 0) x29 (x22 (x25 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x25 (x23 x28) x24) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = x26 x28) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture a36e2..^A6088 : ∀ 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 : 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 . x13 ∈ 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 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ 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 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x0 x23 x24 = mul_SNo (add_SNo 2 x24) x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x1 x23 x24 = add_SNo x24 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x2 x23 = x23) ⟶ x3 = 1 ⟶ x4 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x5 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x0 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x6 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x1 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x5 (x2 x23) x3 x4) ⟶ (∀ x23 . x23 ∈ int ⟶ x8 x23 = x7 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x9 x23 x24 = mul_SNo (add_SNo 1 x24) x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x10 x23 x24 = add_SNo x24 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x11 x23 = add_SNo x23 (minus_SNo 1)) ⟶ (∀ x23 . x23 ∈ int ⟶ x12 x23 = If_i (SNoLe x23 0) 1 2) ⟶ x13 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x14 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x9 (x14 (add_SNo x23 (minus_SNo 1)) x24 x25) (x15 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x15 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x10 (x14 (add_SNo x23 (minus_SNo 1)) x24 x25) (x15 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x16 x23 = x14 (x11 x23) (x12 x23) x13) ⟶ (∀ x23 . x23 ∈ int ⟶ x17 x23 = add_SNo x23 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x18 x23 = x23) ⟶ x19 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x20 x23 x24 = If_i (SNoLe x23 0) x24 (x17 (x20 (add_SNo x23 (minus_SNo 1)) x24))) ⟶ (∀ x23 . x23 ∈ int ⟶ x21 x23 = x20 (x18 x23) x19) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = mul_SNo (x16 x23) (x21 x23)) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x8 x23 = x22 x23