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 b7c78..^A90313 : ∀ 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 . 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 . (∀ 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 (mul_SNo (add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) (add_SNo (If_i (SNoLe (mul_SNo x18 x19) 0) x19 x18) x18)) x19) ⟶ (∀ x18 . x18 ∈ int ⟶ x1 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x2 x18 = x18) ⟶ x3 = 2 ⟶ x4 = 0 ⟶ (∀ 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 ∈ int ⟶ x8 x18 = x7 x18) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x9 x18 x19 = add_SNo (mul_SNo (add_SNo 2 (mul_SNo 2 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))))) x18) x19) ⟶ (∀ x18 . x18 ∈ int ⟶ x10 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x11 x18 = add_SNo x18 (minus_SNo 1)) ⟶ (∀ x18 . x18 ∈ int ⟶ x12 x18 = add_SNo (If_i (SNoLe x18 0) 0 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) 1) ⟶ x13 = 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 ∈ int ⟶ x17 x18 = mul_SNo (x16 x18) 2) ⟶ ∀ x18 . x18 ∈ int ⟶ SNoLe 0 x18 ⟶ x8 x18 = x17 x18
Conjecture f6e59..^A90306 : ∀ 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 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ 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 → 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 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ 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 . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ (∀ x23 . x23 ∈ int ⟶ x0 x23 = mul_SNo x23 x23) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x3 x23 x24 = If_i (SNoLe x23 0) x24 (x0 (x3 (add_SNo x23 (minus_SNo 1)) x24))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x5 x23 x24 = add_SNo (add_SNo (mul_SNo x4 x23) x23) x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x6 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = add_SNo x23 (minus_SNo 1)) ⟶ (∀ x23 . x23 ∈ int ⟶ x8 x23 = add_SNo (If_i (SNoLe x23 0) 1 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) 1) ⟶ x9 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x10 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x5 (x10 (add_SNo x23 (minus_SNo 1)) x24 x25) (x11 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x11 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x6 (x10 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x12 x23 = x10 (x7 x23) (x8 x23) x9) ⟶ (∀ x23 . x23 ∈ int ⟶ x13 x23 = x12 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x14 x23 x24 = add_SNo (mul_SNo (add_SNo 1 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) x23) x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x15 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x16 x23 = add_SNo x23 (minus_SNo 1)) ⟶ (∀ x23 . x23 ∈ int ⟶ x17 x23 = add_SNo (If_i (SNoLe x23 0) 1 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) 1) ⟶ x18 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x19 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x14 (x19 (add_SNo x23 (minus_SNo 1)) x24 x25) (x20 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x20 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x15 (x19 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x21 x23 = x19 (x16 x23) (x17 x23) x18) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = x21 x23) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x13 x23 = x22 x23
Conjecture b103b..^A89252 : ∀ 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 . x14 ∈ int ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ 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 → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ 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 . 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 . (∀ 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 2 (add_SNo (mul_SNo 2 (mul_SNo x30 x31)) (minus_SNo x30)))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x1 x30 x31 = x31) ⟶ 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) (mul_SNo 2 (mul_SNo x30 x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x6 x30 = x30) ⟶ x7 = 1 ⟶ (∀ 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 ⟶ x9 x30 = x8 (x6 x30) x7) ⟶ (∀ x30 . x30 ∈ int ⟶ x10 x30 = x9 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x11 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x12 x30 x31 = add_SNo 1 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x13 x30 x31 = x31) ⟶ x14 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x15 x30 x31 = add_SNo 1 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x16 x30 x31 x32 = If_i (SNoLe x30 0) x31 (x11 (x16 (add_SNo x30 (minus_SNo 1)) x31 x32) (x17 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x17 x30 x31 x32 = If_i (SNoLe x30 0) x32 (x12 (x16 (add_SNo x30 (minus_SNo 1)) x31 x32) (x17 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x18 x30 x31 = x16 (x13 x30 x31) x14 (x15 x30 x31)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x19 x30 x31 = add_SNo (x18 x30 x31) (mul_SNo x30 x31)) ⟶ (∀ 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 . x30 ∈ int ⟶ x23 x30 = x22 (x20 x30) x21) ⟶ (∀ x30 . x30 ∈ int ⟶ x24 x30 = add_SNo x30 x30) ⟶ (∀ 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 ∈ int ⟶ x28 x30 = x27 (x25 x30) x26) ⟶ (∀ x30 . x30 ∈ int ⟶ x29 x30 = mul_SNo (x23 x30) (x28 x30)) ⟶ ∀ x30 . x30 ∈ int ⟶ SNoLe 0 x30 ⟶ x10 x30 = x29 x30
Conjecture f7420..^A88920 : ∀ 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 . 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 . 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 . (∀ 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 : 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 1 (add_SNo (add_SNo x24 (minus_SNo x23)) (minus_SNo x23))) ⟶ (∀ x23 . x23 ∈ int ⟶ x1 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x2 x23 = mul_SNo 2 (add_SNo x23 x23)) ⟶ x3 = 2 ⟶ x4 = 0 ⟶ (∀ 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))) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x5 (x2 x23) x3 x4) ⟶ (∀ x23 . x23 ∈ int ⟶ x8 x23 = x7 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x9 x23 = mul_SNo (add_SNo x23 x23) x23) ⟶ x10 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x11 x23 x24 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x23 x23) x23)) (minus_SNo x24)) ⟶ (∀ x23 . x23 ∈ int ⟶ x12 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x13 x23 = add_SNo x23 (minus_SNo 1)) ⟶ (∀ x23 . x23 ∈ int ⟶ x14 x23 = add_SNo (If_i (SNoLe x23 0) 0 (add_SNo 2 2)) 1) ⟶ x15 = 1 ⟶ (∀ 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 x23) x15) ⟶ (∀ x23 . x23 ∈ int ⟶ x19 x23 = 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 (x19 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = x21 x23) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x8 x23 = x22 x23
Conjecture 8576d..^A8845 : ∀ 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 . 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 . 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 . (∀ 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 : 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 1 (add_SNo (add_SNo x23 x23) x24)) ⟶ (∀ x23 . x23 ∈ int ⟶ x1 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x2 x23 = mul_SNo 2 (add_SNo x23 x23)) ⟶ x3 = 1 ⟶ x4 = 0 ⟶ (∀ 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))) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x5 (x2 x23) x3 x4) ⟶ (∀ x23 . x23 ∈ int ⟶ x8 x23 = add_SNo (x7 x23) (minus_SNo 1)) ⟶ (∀ x23 . x23 ∈ int ⟶ x9 x23 = mul_SNo (add_SNo x23 x23) x23) ⟶ x10 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x11 x23 x24 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x23 x23) x23)) (minus_SNo x24)) ⟶ (∀ x23 . x23 ∈ int ⟶ x12 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x13 x23 = add_SNo x23 (minus_SNo 1)) ⟶ (∀ x23 . x23 ∈ int ⟶ x14 x23 = add_SNo (If_i (SNoLe x23 0) 0 (add_SNo 2 2)) 1) ⟶ x15 = 1 ⟶ (∀ 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 x23) x15) ⟶ (∀ x23 . x23 ∈ int ⟶ x19 x23 = 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 (x19 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = add_SNo (x21 x23) (minus_SNo 2)) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x8 x23 = x22 x23
Conjecture 7543f..^A8843 : ∀ 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 . 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 . 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 . (∀ 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 : 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 1 (add_SNo (add_SNo x23 x23) x24)) ⟶ (∀ x23 . x23 ∈ int ⟶ x1 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x2 x23 = mul_SNo 2 (add_SNo x23 x23)) ⟶ x3 = 1 ⟶ x4 = 0 ⟶ (∀ 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))) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x5 (x2 x23) x3 x4) ⟶ (∀ x23 . x23 ∈ int ⟶ x8 x23 = x7 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x9 x23 = mul_SNo x23 x23) ⟶ x10 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x11 x23 x24 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x23 x23) x23)) (minus_SNo x24)) ⟶ (∀ x23 . x23 ∈ int ⟶ x12 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x13 x23 = add_SNo x23 (minus_SNo 1)) ⟶ (∀ x23 . x23 ∈ int ⟶ x14 x23 = add_SNo (mul_SNo (If_i (SNoLe x23 0) 0 (add_SNo 1 2)) 2) 1) ⟶ x15 = 1 ⟶ (∀ 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 x23) x15) ⟶ (∀ x23 . x23 ∈ int ⟶ x19 x23 = 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 (x19 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = x21 x23) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x8 x23 = x22 x23
Conjecture 1d9d9..^A88229 : ∀ 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 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ 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 → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ 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 → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ 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 : 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 . x34 ∈ int ⟶ x0 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x1 x33 x34 = add_SNo x34 (minus_SNo 1)) ⟶ (∀ x33 . x33 ∈ int ⟶ x2 x33 = x33) ⟶ x3 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ x4 x33 = add_SNo x33 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = x33) ⟶ x6 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x7 x33 x34 = If_i (SNoLe x33 0) x34 (x4 (x7 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x8 x33 = x7 (x5 x33) x6) ⟶ (∀ x33 . x33 ∈ int ⟶ x9 x33 = x8 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x10 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x0 (x10 (add_SNo x33 (minus_SNo 1)) x34 x35) (x11 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x11 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x1 (x10 (add_SNo x33 (minus_SNo 1)) x34 x35) (x11 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x12 x33 = x10 (x2 x33) x3 (x9 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x13 x33 = x12 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x15 x33 x34 = add_SNo x34 (minus_SNo 1)) ⟶ (∀ x33 . x33 ∈ int ⟶ x16 x33 = add_SNo x33 (minus_SNo 1)) ⟶ x17 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ x18 x33 = add_SNo x33 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x19 x33 = add_SNo x33 (minus_SNo 1)) ⟶ x20 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x21 x33 x34 = If_i (SNoLe x33 0) x34 (x18 (x21 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x22 x33 = x21 (x19 x33) x20) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = add_SNo (x22 x33) (minus_SNo 1)) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x24 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x14 (x24 (add_SNo x33 (minus_SNo 1)) x34 x35) (x25 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x25 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x15 (x24 (add_SNo x33 (minus_SNo 1)) x34 x35) (x25 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x26 x33 = x24 (x16 x33) x17 (x23 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x27 x33 = add_SNo x33 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x28 x33 = x33) ⟶ x29 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x30 x33 x34 = If_i (SNoLe x33 0) x34 (x27 (x30 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x31 x33 = x30 (x28 x33) x29) ⟶ (∀ x33 . x33 ∈ int ⟶ x32 x33 = mul_SNo (x26 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x13 x33 = x32 x33
Conjecture 1bd58..^A87547 : ∀ 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 = mul_SNo x22 x23) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x1 x22 x23 = add_SNo x23 (minus_SNo 1)) ⟶ 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 2 (mul_SNo x22 x23)) (minus_SNo x22)) (x4 x22 x23)) ⟶ (∀ 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 = 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 (x15 x22 x23) (mul_SNo (add_SNo (add_SNo x23 (minus_SNo 1)) 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 ac981..^A87287 : ∀ 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 : 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 . 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 → 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 . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ 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 . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x0 x23 x24 = x24) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x1 x23 x24 = add_SNo x23 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x2 x23 = add_SNo (add_SNo x23 x23) x23) ⟶ x3 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ x4 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x5 x23 x24 = If_i (SNoLe x23 0) x24 (x2 (x5 (add_SNo x23 (minus_SNo 1)) x24))) ⟶ (∀ x23 . x23 ∈ int ⟶ x6 x23 = x5 x3 (x4 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x6 x23) ⟶ x8 = 2 ⟶ x9 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x10 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x0 (x10 (add_SNo x23 (minus_SNo 1)) x24 x25) (x11 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x11 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x1 (x10 (add_SNo x23 (minus_SNo 1)) x24 x25) (x11 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x12 x23 = x10 (x7 x23) x8 x9) ⟶ (∀ x23 . x23 ∈ int ⟶ x13 x23 = x12 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x14 x23 x24 = x24) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x15 x23 x24 = add_SNo (mul_SNo (add_SNo 2 2) x24) x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x16 x23 = add_SNo (add_SNo x23 x23) x23) ⟶ x17 = 1 ⟶ x18 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x19 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x14 (x19 (add_SNo x23 (minus_SNo 1)) x24 x25) (x20 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x20 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x15 (x19 (add_SNo x23 (minus_SNo 1)) x24 x25) (x20 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x21 x23 = x19 (x16 x23) x17 x18) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = mul_SNo 2 (x21 x23)) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x13 x23 = x22 x23
Conjecture 920fc..^A86984 : ∀ 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 → 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 : 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 . (∀ 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 ⟶ ∀ x26 . x26 ∈ int ⟶ x0 x25 x26 = add_SNo (mul_SNo x25 x26) x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x1 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x2 x25 x26 = add_SNo (add_SNo x25 x25) x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x3 x25 x26 = x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x4 x25 = x25) ⟶ x5 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ x6 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x7 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x2 (x7 (add_SNo x25 (minus_SNo 1)) x26 x27) (x8 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x8 x25 x26 x27 = If_i (SNoLe x25 0) x27 (x3 (x7 (add_SNo x25 (minus_SNo 1)) x26 x27) (x8 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x9 x25 = x7 (x4 x25) x5 (x6 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x10 x25 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x11 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x11 (add_SNo x25 (minus_SNo 1)) x26) x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x12 x25 = x11 (x1 x25) (x10 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x13 x25 = x12 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x14 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x15 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x16 x25 = add_SNo 1 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x17 x25 x26 = If_i (SNoLe x25 0) x26 (x14 (x17 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x18 x25 = x17 (x15 x25) (x16 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x19 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x20 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 (add_SNo (x18 x25) (minus_SNo x25)) (x23 x25)) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x13 x25 = x24 x25
Conjecture 03070..^A86948 : ∀ 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 → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x12 x13 x14 x15 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ (∀ x15 . x15 ∈ int ⟶ x0 x15 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x15 x15)) x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = add_SNo 1 x15) ⟶ x2 = 2 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = add_SNo (x4 x15) (minus_SNo (mul_SNo 2 (add_SNo 2 2)))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x6 x15 x16 = mul_SNo x15 x16) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x7 x15 x16 = x16) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = x15) ⟶ x9 = add_SNo 1 (add_SNo 2 2) ⟶ x10 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x11 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x6 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x12 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x7 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x11 (x8 x15) x9 x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = mul_SNo 2 (mul_SNo 2 (add_SNo (x13 x15) (minus_SNo 2)))) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture 9cd9e..^A86942 : ∀ 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 → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x12 x13 x14 x15 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ (∀ x15 . x15 ∈ int ⟶ x0 x15 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x15 x15)) x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = add_SNo 1 x15) ⟶ x2 = 2 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = mul_SNo (add_SNo (add_SNo (x4 x15) (minus_SNo 2)) (minus_SNo 2)) 2) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x6 x15 x16 = mul_SNo x15 x16) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x7 x15 x16 = x16) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = x15) ⟶ x9 = add_SNo 2 2 ⟶ x10 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x11 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x6 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x12 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x7 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x11 (x8 x15) x9 x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = add_SNo (mul_SNo (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))) (add_SNo (x13 x15) (minus_SNo 1))) 2) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture 95a1d..^A8548 : ∀ 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x12 x13 x14 x15 ∈ 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 ⟶ x0 x15 x16 = mul_SNo (add_SNo (mul_SNo 2 (add_SNo (add_SNo x16 (minus_SNo 2)) x16)) x16) x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = x15) ⟶ x2 = 1 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16) x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = x4 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x6 x15 x16 = mul_SNo x15 x16) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x7 x15 x16 = add_SNo 1 (add_SNo 2 (add_SNo 2 x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = add_SNo x15 (minus_SNo 1)) ⟶ x9 = 1 ⟶ x10 = add_SNo 2 (add_SNo 2 2) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x11 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x6 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x12 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x7 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x11 (x8 x15) x9 x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = x13 x15) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture 685c7..^A8546 : ∀ 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x12 x13 x14 x15 ∈ 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 ⟶ x0 x15 x16 = add_SNo (mul_SNo (add_SNo 1 (add_SNo 2 2)) (mul_SNo x15 x16)) (minus_SNo x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = x15) ⟶ x2 = 1 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16) x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = x4 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x6 x15 x16 = mul_SNo x15 x16) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x7 x15 x16 = add_SNo 1 (add_SNo 2 (add_SNo 2 x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = x15) ⟶ x9 = 1 ⟶ x10 = add_SNo 2 2 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x11 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x6 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x12 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x7 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x11 (x8 x15) x9 x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = x13 x15) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture 62b4b..^A8545 : ∀ 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x12 x13 x14 x15 ∈ 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 ⟶ x0 x15 x16 = add_SNo (mul_SNo 2 (mul_SNo 2 (mul_SNo x15 x16))) (minus_SNo x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = x15) ⟶ x2 = 1 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16) x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = x4 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x6 x15 x16 = mul_SNo x15 x16) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x7 x15 x16 = add_SNo 2 (add_SNo 2 x16)) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = add_SNo x15 (minus_SNo 1)) ⟶ x9 = 1 ⟶ x10 = add_SNo 1 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x11 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x6 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x12 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x7 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x11 (x8 x15) x9 x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = mul_SNo (x13 x15) (If_i (SNoLe x15 0) 1 (add_SNo 1 2))) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture 5dad7..^A8544 : ∀ 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x12 x13 x14 x15 ∈ 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 ⟶ x0 x15 x16 = add_SNo (mul_SNo (add_SNo 1 2) (mul_SNo x15 x16)) (minus_SNo x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = x15) ⟶ x2 = 1 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16) x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = x4 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x6 x15 x16 = mul_SNo x15 x16) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x7 x15 x16 = add_SNo 1 (add_SNo 2 x16)) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = add_SNo x15 (minus_SNo 1)) ⟶ x9 = 1 ⟶ x10 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x11 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x6 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x12 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x7 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x11 (x8 x15) x9 x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = mul_SNo (x13 x15) (If_i (SNoLe x15 0) 1 2)) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture 29860..^A85449 : ∀ 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 = x24) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x1 x23 x24 = mul_SNo 2 (add_SNo (add_SNo x23 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 = 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 = 1 ⟶ x15 = 1 ⟶ (∀ 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 = x21 x23) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x8 x23 = x22 x23
Conjecture f0d04..^A8543 : ∀ 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x12 x13 x14 x15 ∈ 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 ⟶ x0 x15 x16 = add_SNo (mul_SNo 2 (mul_SNo (add_SNo 1 2) (mul_SNo x15 x16))) (minus_SNo x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = x15) ⟶ x2 = 1 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16) x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = x4 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x6 x15 x16 = mul_SNo x15 x16) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x7 x15 x16 = add_SNo 2 (add_SNo 2 (add_SNo 2 x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = x15) ⟶ x9 = 1 ⟶ x10 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x11 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x6 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x12 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x7 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x11 (x8 x15) x9 x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = x13 x15) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture df487..^A8542 : ∀ 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 . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ 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 . x16 ∈ int ⟶ x0 x15 x16 = mul_SNo x15 x16) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x1 x15 x16 = add_SNo 2 (add_SNo 2 (add_SNo 2 x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x2 x15 = x15) ⟶ x3 = 1 ⟶ x4 = 1 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x5 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x0 (x5 (add_SNo x15 (minus_SNo 1)) x16 x17) (x6 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x6 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x1 (x5 (add_SNo x15 (minus_SNo 1)) x16 x17) (x6 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x7 x15 = x5 (x2 x15) x3 x4) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = x7 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x9 x15 x16 = mul_SNo (add_SNo 1 (mul_SNo 2 (add_SNo (add_SNo x16 x16) x16))) x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x10 x15 = add_SNo x15 (minus_SNo 1)) ⟶ x11 = 1 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x12 x15 x16 = If_i (SNoLe x15 0) x16 (x9 (x12 (add_SNo x15 (minus_SNo 1)) x16) x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x12 (x10 x15) x11) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = x13 x15) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x8 x15 = x14 x15
Conjecture 7175a..^A85353 : ∀ 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 → 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 . x21 ∈ 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 . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x0 x26 x27 = add_SNo (add_SNo (mul_SNo 2 (add_SNo (add_SNo x26 x26) x26)) x26) x27) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x1 x26 x27 = mul_SNo 2 (add_SNo (add_SNo x27 x27) x27)) ⟶ (∀ x26 . x26 ∈ int ⟶ x2 x26 = x26) ⟶ x3 = 1 ⟶ x4 = 1 ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x5 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x0 (x5 (add_SNo x26 (minus_SNo 1)) x27 x28) (x6 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x6 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x1 (x5 (add_SNo x26 (minus_SNo 1)) x27 x28) (x6 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x7 x26 = x5 (x2 x26) x3 x4) ⟶ (∀ x26 . x26 ∈ int ⟶ x8 x26 = x7 x26) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x9 x26 x27 = mul_SNo x26 x27) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x10 x26 x27 = x27) ⟶ (∀ x26 . x26 ∈ int ⟶ x11 x26 = x26) ⟶ x12 = 2 ⟶ x13 = add_SNo 1 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x14 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x9 (x14 (add_SNo x26 (minus_SNo 1)) x27 x28) (x15 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x15 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x10 (x14 (add_SNo x26 (minus_SNo 1)) x27 x28) (x15 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x16 x26 = x14 (x11 x26) x12 x13) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x17 x26 x27 = mul_SNo x26 x27) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x18 x26 x27 = x27) ⟶ (∀ x26 . x26 ∈ int ⟶ x19 x26 = x26) ⟶ x20 = 1 ⟶ x21 = add_SNo 2 (add_SNo 2 2) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x22 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x17 (x22 (add_SNo x26 (minus_SNo 1)) x27 x28) (x23 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x23 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x18 (x22 (add_SNo x26 (minus_SNo 1)) x27 x28) (x23 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x24 x26 = x22 (x19 x26) x20 x21) ⟶ (∀ x26 . x26 ∈ int ⟶ x25 x26 = add_SNo (x16 x26) (minus_SNo (x24 x26))) ⟶ ∀ x26 . x26 ∈ int ⟶ SNoLe 0 x26 ⟶ x8 x26 = x25 x26