Proofgold Asset

Param int^int : ι
Param add_SNo^add_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
Param mul_SNo^mul_SNo : ι → ι → ι
Conjecture 6b84f..^A2446 : ∀ 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 x17 x17) ⟶ x2 = 2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x4 x17 = x3 (x1 x17) x2) ⟶ (∀ x17 . x17 ∈ int ⟶ x5 x17 = add_SNo (x4 x17) (minus_SNo 2)) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = mul_SNo x17 x17) ⟶ x7 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ x8 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x9 x17 = x17) ⟶ x10 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = If_i (SNoLe x17 0) x18 (x8 (x11 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x11 (x9 x17) x10) ⟶ (∀ x17 . x17 ∈ int ⟶ x13 x17 = x12 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x6 (x14 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 x7 (x13 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = add_SNo (mul_SNo 2 (x15 x17)) (minus_SNo 2)) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture 64401..^A24444 : ∀ 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 → 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 → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 . x12 ∈ 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 . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ 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 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ 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 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι → ι . (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x33 x34 x35 ∈ int) ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι . (∀ x36 . x36 ∈ int ⟶ x35 x36 ∈ int) ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x0 x40 x41 = mul_SNo (add_SNo 2 x41) x40) ⟶ x1 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ x2 x40 = x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x3 x40 x41 = If_i (SNoLe x40 0) x41 (x0 (x3 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x4 x40 = x3 x1 (x2 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x5 x40 = add_SNo 1 (add_SNo (x4 x40) (minus_SNo x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x6 x40 x41 = x41) ⟶ x7 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x8 x40 x41 = If_i (SNoLe x40 0) x41 (x5 (x8 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x9 x40 x41 = x8 (x6 x40 x41) x7) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x10 x40 x41 = add_SNo (x9 x40 x41) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x11 x40 x41 = x41) ⟶ x12 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x13 x40 x41 = If_i (SNoLe x40 0) x41 (x10 (x13 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x14 x40 x41 = x13 (x11 x40 x41) x12) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x15 x40 x41 = add_SNo (add_SNo (x14 x40 x41) (mul_SNo 2 (add_SNo (add_SNo x40 x40) x40))) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x16 x40 = x40) ⟶ x17 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x18 x40 x41 = If_i (SNoLe x40 0) x41 (x15 (x18 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x19 x40 = x18 (x16 x40) x17) ⟶ (∀ x40 . x40 ∈ int ⟶ x20 x40 = x19 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x21 x40 x41 = add_SNo (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x40)) x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x22 x40 x41 = add_SNo 1 (add_SNo (mul_SNo 2 (add_SNo (add_SNo x41 x41) x41)) x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x40) ⟶ x24 = 1 ⟶ x25 = mul_SNo 2 (add_SNo 2 2) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x26 x40 x41 x42 = If_i (SNoLe x40 0) x41 (x21 (x26 (add_SNo x40 (minus_SNo 1)) x41 x42) (x27 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x27 x40 x41 x42 = If_i (SNoLe x40 0) x42 (x22 (x26 (add_SNo x40 (minus_SNo 1)) x41 x42) (x27 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ x28 x40 = x26 (x23 x40) x24 x25) ⟶ (∀ x40 . x40 ∈ int ⟶ x29 x40 = x28 x40) ⟶ x30 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x31 x40 x41 = x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x32 x40 x41 = If_i (SNoLe x40 0) x41 (x29 (x32 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x33 x40 x41 = x32 x30 (x31 x40 x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x34 x40 x41 = add_SNo (add_SNo (x33 x40 x41) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x40))) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x35 x40 = x40) ⟶ x36 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x37 x40 x41 = If_i (SNoLe x40 0) x41 (x34 (x37 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x38 x40 = x37 (x35 x40) x36) ⟶ (∀ x40 . x40 ∈ int ⟶ x39 x40 = x38 x40) ⟶ ∀ x40 . x40 ∈ int ⟶ SNoLe 0 x40 ⟶ x20 x40 = x39 x40
Conjecture e876e..^A24439 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ 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 . x6 ∈ 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 → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 . x12 ∈ 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 . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ 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 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ 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 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι → ι . (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x33 x34 x35 ∈ int) ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι . (∀ x36 . x36 ∈ int ⟶ x35 x36 ∈ int) ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ (∀ x40 . x40 ∈ int ⟶ x0 x40 = add_SNo 1 (mul_SNo 2 (mul_SNo 2 (add_SNo x40 x40)))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x1 x40 x41 = x41) ⟶ x2 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x3 x40 x41 = If_i (SNoLe x40 0) x41 (x0 (x3 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x4 x40 x41 = x3 (x1 x40 x41) x2) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x5 x40 x41 = mul_SNo (add_SNo 2 x41) x40) ⟶ x6 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ x7 x40 = x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x8 x40 x41 = If_i (SNoLe x40 0) x41 (x5 (x8 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x9 x40 = x8 x6 (x7 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x10 x40 x41 = add_SNo (add_SNo (x4 x40 x41) (minus_SNo x40)) (x9 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x11 x40 x41 = x41) ⟶ x12 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x13 x40 x41 = If_i (SNoLe x40 0) x41 (x10 (x13 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x14 x40 x41 = x13 (x11 x40 x41) x12) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x15 x40 x41 = add_SNo (add_SNo (x14 x40 x41) (mul_SNo 2 (add_SNo (add_SNo x40 x40) x40))) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x16 x40 = x40) ⟶ x17 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x18 x40 x41 = If_i (SNoLe x40 0) x41 (x15 (x18 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x19 x40 = x18 (x16 x40) x17) ⟶ (∀ x40 . x40 ∈ int ⟶ x20 x40 = x19 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x21 x40 x41 = add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo x40 x40))) x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x22 x40 x41 = add_SNo 1 (add_SNo (mul_SNo 2 (add_SNo (add_SNo x41 x41) x41)) x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x40) ⟶ x24 = 1 ⟶ x25 = mul_SNo 2 (add_SNo 2 2) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x26 x40 x41 x42 = If_i (SNoLe x40 0) x41 (x21 (x26 (add_SNo x40 (minus_SNo 1)) x41 x42) (x27 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x27 x40 x41 x42 = If_i (SNoLe x40 0) x42 (x22 (x26 (add_SNo x40 (minus_SNo 1)) x41 x42) (x27 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ x28 x40 = x26 (x23 x40) x24 x25) ⟶ (∀ x40 . x40 ∈ int ⟶ x29 x40 = x28 x40) ⟶ x30 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x31 x40 x41 = x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x32 x40 x41 = If_i (SNoLe x40 0) x41 (x29 (x32 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x33 x40 x41 = x32 x30 (x31 x40 x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x34 x40 x41 = add_SNo (add_SNo (x33 x40 x41) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x40))) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x35 x40 = x40) ⟶ x36 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x37 x40 x41 = If_i (SNoLe x40 0) x41 (x34 (x37 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x38 x40 = x37 (x35 x40) x36) ⟶ (∀ x40 . x40 ∈ int ⟶ x39 x40 = x38 x40) ⟶ ∀ x40 . x40 ∈ int ⟶ SNoLe 0 x40 ⟶ x20 x40 = x39 x40
Conjecture 0270a..^A24434 : ∀ 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 → 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 → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 . x12 ∈ 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 . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ 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 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ 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 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι → ι . (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x33 x34 x35 ∈ int) ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι . (∀ x36 . x36 ∈ int ⟶ x35 x36 ∈ int) ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x0 x40 x41 = mul_SNo (add_SNo 2 x41) x40) ⟶ x1 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ x2 x40 = x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x3 x40 x41 = If_i (SNoLe x40 0) x41 (x0 (x3 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x4 x40 = x3 x1 (x2 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x5 x40 = add_SNo 1 (add_SNo (x4 x40) (minus_SNo x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x6 x40 x41 = x41) ⟶ x7 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x8 x40 x41 = If_i (SNoLe x40 0) x41 (x5 (x8 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x9 x40 x41 = x8 (x6 x40 x41) x7) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x10 x40 x41 = add_SNo (x9 x40 x41) (mul_SNo 2 (add_SNo (add_SNo x40 x40) x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x11 x40 x41 = x41) ⟶ x12 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x13 x40 x41 = If_i (SNoLe x40 0) x41 (x10 (x13 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x14 x40 x41 = x13 (x11 x40 x41) x12) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x15 x40 x41 = add_SNo (x14 x40 x41) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ x16 x40 = x40) ⟶ x17 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x18 x40 x41 = If_i (SNoLe x40 0) x41 (x15 (x18 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x19 x40 = x18 (x16 x40) x17) ⟶ (∀ x40 . x40 ∈ int ⟶ x20 x40 = x19 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x21 x40 x41 = add_SNo (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x40)) x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x22 x40 x41 = add_SNo 1 (mul_SNo 2 (add_SNo (add_SNo x41 x41) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x40) ⟶ x24 = 1 ⟶ x25 = add_SNo 1 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x26 x40 x41 x42 = If_i (SNoLe x40 0) x41 (x21 (x26 (add_SNo x40 (minus_SNo 1)) x41 x42) (x27 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x27 x40 x41 x42 = If_i (SNoLe x40 0) x42 (x22 (x26 (add_SNo x40 (minus_SNo 1)) x41 x42) (x27 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ x28 x40 = x26 (x23 x40) x24 x25) ⟶ (∀ x40 . x40 ∈ int ⟶ x29 x40 = x28 x40) ⟶ x30 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x31 x40 x41 = x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x32 x40 x41 = If_i (SNoLe x40 0) x41 (x29 (x32 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x33 x40 x41 = x32 x30 (x31 x40 x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x34 x40 x41 = add_SNo (add_SNo (x33 x40 x41) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x40))) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x35 x40 = x40) ⟶ x36 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x37 x40 x41 = If_i (SNoLe x40 0) x41 (x34 (x37 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x38 x40 = x37 (x35 x40) x36) ⟶ (∀ x40 . x40 ∈ int ⟶ x39 x40 = x38 x40) ⟶ ∀ x40 . x40 ∈ int ⟶ SNoLe 0 x40 ⟶ x20 x40 = x39 x40
Conjecture 6a36f..^A24346 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ 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 . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 . x6 ∈ 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 → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 . x12 ∈ 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 . x16 ∈ int ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ 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 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 : ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x23 x24 x25 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 : ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ 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 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x31 x32 x33 x34 ∈ int) ⟶ ∀ x32 : ι → ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x32 x33 x34 x35 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 : ι → ι . (∀ x35 . x35 ∈ int ⟶ x34 x35 ∈ int) ⟶ ∀ x35 . x35 ∈ 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 → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x39 x40 x41 ∈ int) ⟶ ∀ x40 : ι → ι . (∀ x41 . x41 ∈ int ⟶ x40 x41 ∈ int) ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ ∀ x44 : ι → ι . (∀ x45 . x45 ∈ int ⟶ x44 x45 ∈ int) ⟶ (∀ x45 . x45 ∈ int ⟶ x0 x45 = add_SNo 1 (mul_SNo 2 (add_SNo (add_SNo x45 x45) x45))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x1 x45 x46 = x46) ⟶ x2 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x3 x45 x46 = If_i (SNoLe x45 0) x46 (x0 (x3 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x4 x45 x46 = x3 (x1 x45 x46) x2) ⟶ (∀ x45 . x45 ∈ int ⟶ x5 x45 = add_SNo (add_SNo x45 x45) x45) ⟶ x6 = 2 ⟶ (∀ x45 . x45 ∈ int ⟶ x7 x45 = x45) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x8 x45 x46 = If_i (SNoLe x45 0) x46 (x5 (x8 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ x9 x45 = x8 x6 (x7 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x10 x45 x46 = add_SNo (x4 x45 x46) (x9 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x11 x45 x46 = x46) ⟶ x12 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x13 x45 x46 = If_i (SNoLe x45 0) x46 (x10 (x13 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x14 x45 x46 = x13 (x11 x45 x46) x12) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x15 x45 x46 = mul_SNo (add_SNo 2 x46) x45) ⟶ x16 = 2 ⟶ (∀ x45 . x45 ∈ int ⟶ x17 x45 = x45) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x18 x45 x46 = If_i (SNoLe x45 0) x46 (x15 (x18 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x19 x45 = x18 x16 (x17 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x20 x45 x46 = add_SNo (add_SNo (x14 x45 x46) (minus_SNo x45)) (x19 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x21 x45 = x45) ⟶ x22 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x23 x45 x46 = If_i (SNoLe x45 0) x46 (x20 (x23 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x24 x45 = x23 (x21 x45) x22) ⟶ (∀ x45 . x45 ∈ int ⟶ x25 x45 = x24 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x26 x45 x46 = add_SNo (add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo x45 x45))) x45) x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x27 x45 x46 = add_SNo 1 (mul_SNo 2 (add_SNo (add_SNo x46 x46) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ x28 x45 = x45) ⟶ x29 = 1 ⟶ x30 = add_SNo 1 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x31 x45 x46 x47 = If_i (SNoLe x45 0) x46 (x26 (x31 (add_SNo x45 (minus_SNo 1)) x46 x47) (x32 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x32 x45 x46 x47 = If_i (SNoLe x45 0) x47 (x27 (x31 (add_SNo x45 (minus_SNo 1)) x46 x47) (x32 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ x33 x45 = x31 (x28 x45) x29 x30) ⟶ (∀ x45 . x45 ∈ int ⟶ x34 x45 = x33 x45) ⟶ x35 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x36 x45 x46 = x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x37 x45 x46 = If_i (SNoLe x45 0) x46 (x34 (x37 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x38 x45 x46 = x37 x35 (x36 x45 x46)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x39 x45 x46 = add_SNo (add_SNo (x38 x45 x46) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x45 x45)) x45))) x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x40 x45 = x45) ⟶ x41 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x42 x45 x46 = If_i (SNoLe x45 0) x46 (x39 (x42 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x43 x45 = x42 (x40 x45) x41) ⟶ (∀ x45 . x45 ∈ int ⟶ x44 x45 = x43 x45) ⟶ ∀ x45 . x45 ∈ int ⟶ SNoLe 0 x45 ⟶ x25 x45 = x44 x45
Conjecture 86d70..^A24170 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . 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 . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ 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 → 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 → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ 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 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι → ι . (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x33 x34 x35 ∈ int) ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι . (∀ x36 . x36 ∈ int ⟶ x35 x36 ∈ int) ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ (∀ x40 . x40 ∈ int ⟶ x0 x40 = add_SNo 1 (mul_SNo 2 (add_SNo (add_SNo x40 x40) x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x1 x40 x41 = x41) ⟶ x2 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x3 x40 x41 = If_i (SNoLe x40 0) x41 (x0 (x3 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x4 x40 x41 = x3 (x1 x40 x41) x2) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x5 x40 x41 = add_SNo (x4 x40 x41) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x6 x40 x41 = x41) ⟶ x7 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x8 x40 x41 = If_i (SNoLe x40 0) x41 (x5 (x8 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x9 x40 x41 = x8 (x6 x40 x41) x7) ⟶ (∀ x40 . x40 ∈ int ⟶ x10 x40 = add_SNo (add_SNo x40 x40) x40) ⟶ x11 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ x12 x40 = x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x13 x40 x41 = If_i (SNoLe x40 0) x41 (x10 (x13 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ x14 x40 = x13 x11 (x12 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x15 x40 x41 = add_SNo (x9 x40 x41) (x14 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x16 x40 = x40) ⟶ x17 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x18 x40 x41 = If_i (SNoLe x40 0) x41 (x15 (x18 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x19 x40 = x18 (x16 x40) x17) ⟶ (∀ x40 . x40 ∈ int ⟶ x20 x40 = x19 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x21 x40 x41 = add_SNo (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x40)) x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x22 x40 x41 = add_SNo 1 (mul_SNo 2 (add_SNo (add_SNo x41 x41) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x40) ⟶ x24 = 1 ⟶ x25 = add_SNo 1 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x26 x40 x41 x42 = If_i (SNoLe x40 0) x41 (x21 (x26 (add_SNo x40 (minus_SNo 1)) x41 x42) (x27 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x27 x40 x41 x42 = If_i (SNoLe x40 0) x42 (x22 (x26 (add_SNo x40 (minus_SNo 1)) x41 x42) (x27 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ x28 x40 = x26 (x23 x40) x24 x25) ⟶ (∀ x40 . x40 ∈ int ⟶ x29 x40 = x28 x40) ⟶ x30 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x31 x40 x41 = x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x32 x40 x41 = If_i (SNoLe x40 0) x41 (x29 (x32 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x33 x40 x41 = x32 x30 (x31 x40 x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x34 x40 x41 = add_SNo (add_SNo (x33 x40 x41) (mul_SNo 2 (mul_SNo 2 (add_SNo x40 x40)))) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x35 x40 = x40) ⟶ x36 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x37 x40 x41 = If_i (SNoLe x40 0) x41 (x34 (x37 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x38 x40 = x37 (x35 x40) x36) ⟶ (∀ x40 . x40 ∈ int ⟶ x39 x40 = x38 x40) ⟶ ∀ x40 . x40 ∈ int ⟶ SNoLe 0 x40 ⟶ x20 x40 = x39 x40
Conjecture ca41e..^A24167 : ∀ 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 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x0 x27 x28 = add_SNo 0 (minus_SNo (mul_SNo x27 x28))) ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x1 x27 x28 = x28) ⟶ x2 = 1 ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x3 x27 x28 = If_i (SNoLe x27 0) x28 (x0 (x3 (add_SNo x27 (minus_SNo 1)) x28) x27)) ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x4 x27 x28 = x3 (x1 x27 x28) x2) ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x5 x27 x28 = add_SNo (add_SNo (mul_SNo x27 x28) (x4 x27 x28)) x27) ⟶ (∀ x27 . x27 ∈ int ⟶ x6 x27 = x27) ⟶ x7 = 1 ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x8 x27 x28 = If_i (SNoLe x27 0) x28 (x5 (x8 (add_SNo x27 (minus_SNo 1)) x28) x27)) ⟶ (∀ x27 . x27 ∈ int ⟶ x9 x27 = x8 (x6 x27) x7) ⟶ (∀ x27 . x27 ∈ int ⟶ x10 x27 = x9 x27) ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x11 x27 x28 = mul_SNo x27 x28) ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x12 x27 x28 = x28) ⟶ x13 = 1 ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x14 x27 x28 = If_i (SNoLe x27 0) x28 (x11 (x14 (add_SNo x27 (minus_SNo 1)) x28) x27)) ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x15 x27 x28 = x14 (x12 x27 x28) x13) ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x16 x27 x28 = add_SNo (x15 x27 x28) (minus_SNo (mul_SNo (add_SNo 1 x28) x27))) ⟶ (∀ x27 . x27 ∈ int ⟶ x17 x27 = x27) ⟶ x18 = 1 ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x19 x27 x28 = If_i (SNoLe x27 0) x28 (x16 (x19 (add_SNo x27 (minus_SNo 1)) x28) x27)) ⟶ (∀ x27 . x27 ∈ int ⟶ x20 x27 = x19 (x17 x27) x18) ⟶ (∀ x27 . x27 ∈ int ⟶ x21 x27 = add_SNo 0 (minus_SNo x27)) ⟶ (∀ x27 . x27 ∈ int ⟶ x22 x27 = x27) ⟶ x23 = 1 ⟶ (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x24 x27 x28 = If_i (SNoLe x27 0) x28 (x21 (x24 (add_SNo x27 (minus_SNo 1)) x28))) ⟶ (∀ x27 . x27 ∈ int ⟶ x25 x27 = x24 (x22 x27) x23) ⟶ (∀ x27 . x27 ∈ int ⟶ x26 x27 = mul_SNo (x20 x27) (x25 x27)) ⟶ ∀ x27 . x27 ∈ int ⟶ SNoLe 0 x27 ⟶ x10 x27 = x26 x27
Conjecture 67d0f..^A24148 : ∀ 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 . 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 . x11 ∈ int ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ 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 ⟶ ∀ 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 . (∀ 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 (add_SNo 2 x31) x30) ⟶ x1 = 2 ⟶ (∀ x30 . x30 ∈ int ⟶ x2 x30 = x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x3 x30 x31 = If_i (SNoLe x30 0) x31 (x0 (x3 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x4 x30 = x3 x1 (x2 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x5 x30 = x4 x30) ⟶ (∀ 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 ∈ int ⟶ x9 x30 = x8 (x6 x30) x7) ⟶ (∀ x30 . x30 ∈ int ⟶ x10 x30 = mul_SNo x30 x30) ⟶ x11 = 2 ⟶ (∀ x30 . x30 ∈ int ⟶ x12 x30 = mul_SNo x30 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x13 x30 x31 = If_i (SNoLe x30 0) x31 (x10 (x13 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x14 x30 = x13 x11 (x12 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x15 x30 = add_SNo (x9 x30) (minus_SNo (x14 x30))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x16 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x17 x30 x31 = x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x18 x30 = x30) ⟶ x19 = 1 ⟶ x20 = mul_SNo 2 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x21 x30 x31 x32 = If_i (SNoLe x30 0) x31 (x16 (x21 (add_SNo x30 (minus_SNo 1)) x31 x32) (x22 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x22 x30 x31 x32 = If_i (SNoLe x30 0) x32 (x17 (x21 (add_SNo x30 (minus_SNo 1)) x31 x32) (x22 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ x23 x30 = x21 (x18 x30) x19 x20) ⟶ (∀ x30 . x30 ∈ int ⟶ x24 x30 = mul_SNo x30 x30) ⟶ x25 = 2 ⟶ (∀ x30 . x30 ∈ int ⟶ x26 x30 = mul_SNo x30 x30) ⟶ (∀ 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 (x26 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x29 x30 = add_SNo (x23 x30) (minus_SNo (x28 x30))) ⟶ ∀ x30 . x30 ∈ int ⟶ SNoLe 0 x30 ⟶ x15 x30 = x29 x30
Conjecture a26c3..^A24141 : ∀ 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 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x0 x20 x21 = 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 = x4 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 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = add_SNo (x9 x20) (minus_SNo 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 = mul_SNo 2 (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 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = add_SNo (x18 x20) (minus_SNo x20)) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture 068bd..^A24139 : ∀ 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 . 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 . x11 ∈ int ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ 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 ⟶ ∀ 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 . (∀ 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 (add_SNo 2 x31) x30) ⟶ x1 = 2 ⟶ (∀ x30 . x30 ∈ int ⟶ x2 x30 = x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x3 x30 x31 = If_i (SNoLe x30 0) x31 (x0 (x3 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x4 x30 = x3 x1 (x2 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x5 x30 = add_SNo (x4 x30) (minus_SNo x30)) ⟶ (∀ 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 ∈ int ⟶ x9 x30 = x8 (x6 x30) x7) ⟶ (∀ x30 . x30 ∈ int ⟶ x10 x30 = mul_SNo x30 x30) ⟶ x11 = 2 ⟶ (∀ x30 . x30 ∈ int ⟶ x12 x30 = mul_SNo (mul_SNo x30 x30) x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x13 x30 x31 = If_i (SNoLe x30 0) x31 (x10 (x13 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x14 x30 = x13 x11 (x12 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x15 x30 = add_SNo (x9 x30) (minus_SNo (x14 x30))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x16 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x17 x30 x31 = x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x18 x30 = x30) ⟶ x19 = 1 ⟶ x20 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x21 x30 x31 x32 = If_i (SNoLe x30 0) x31 (x16 (x21 (add_SNo x30 (minus_SNo 1)) x31 x32) (x22 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x22 x30 x31 x32 = If_i (SNoLe x30 0) x32 (x17 (x21 (add_SNo x30 (minus_SNo 1)) x31 x32) (x22 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ x23 x30 = x21 (x18 x30) x19 x20) ⟶ (∀ x30 . x30 ∈ int ⟶ x24 x30 = mul_SNo x30 x30) ⟶ x25 = 2 ⟶ (∀ x30 . x30 ∈ int ⟶ x26 x30 = mul_SNo (mul_SNo x30 x30) x30) ⟶ (∀ 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 (x26 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x29 x30 = add_SNo (x23 x30) (minus_SNo (x28 x30))) ⟶ ∀ x30 . x30 ∈ int ⟶ SNoLe 0 x30 ⟶ x15 x30 = x29 x30
Conjecture b3ba9..^A24134 : ∀ 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 . 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 → 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 . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ 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 (add_SNo 2 x34) x33) ⟶ x1 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ x2 x33 = x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x3 x33 x34 = If_i (SNoLe x33 0) x34 (x0 (x3 (add_SNo x33 (minus_SNo 1)) x34) x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x4 x33 = x3 x1 (x2 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = add_SNo (x4 x33) (minus_SNo x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = x33) ⟶ x7 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x8 x33 x34 = If_i (SNoLe x33 0) x34 (x5 (x8 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x9 x33 = x8 (x6 x33) x7) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x10 x33 x34 = mul_SNo (mul_SNo x33 x33) x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = x33) ⟶ x12 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ x13 x33 = x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x14 x33 = x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x15 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x10 (x15 (add_SNo x33 (minus_SNo 1)) x34 x35) (x16 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x16 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x11 (x15 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x17 x33 = x15 x12 (x13 x33) (x14 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x18 x33 = add_SNo (x9 x33) (minus_SNo (x17 x33))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x19 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x20 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x33) ⟶ x22 = 1 ⟶ x23 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x24 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x19 (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 (x20 (x24 (add_SNo x33 (minus_SNo 1)) x34 x35) (x25 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x26 x33 = x24 (x21 x33) x22 x23) ⟶ (∀ x33 . x33 ∈ int ⟶ x27 x33 = mul_SNo (mul_SNo x33 x33) x33) ⟶ x28 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ x29 x33 = mul_SNo x33 x33) ⟶ (∀ 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 (x29 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x32 x33 = add_SNo (x26 x33) (minus_SNo (mul_SNo (x31 x33) x33))) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x18 x33 = x32 x33
Conjecture ffe94..^A24133 : ∀ 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 . 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 . x11 ∈ int ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ 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 ⟶ ∀ 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 . (∀ 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 (add_SNo 2 x31) x30) ⟶ x1 = 2 ⟶ (∀ x30 . x30 ∈ int ⟶ x2 x30 = x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x3 x30 x31 = If_i (SNoLe x30 0) x31 (x0 (x3 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x4 x30 = x3 x1 (x2 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x5 x30 = add_SNo (x4 x30) (minus_SNo x30)) ⟶ (∀ 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 ∈ int ⟶ x9 x30 = x8 (x6 x30) x7) ⟶ (∀ x30 . x30 ∈ int ⟶ x10 x30 = mul_SNo x30 x30) ⟶ x11 = 2 ⟶ (∀ x30 . x30 ∈ int ⟶ x12 x30 = x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x13 x30 x31 = If_i (SNoLe x30 0) x31 (x10 (x13 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x14 x30 = x13 x11 (x12 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x15 x30 = add_SNo (x9 x30) (minus_SNo (mul_SNo (mul_SNo (x14 x30) x30) x30))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x16 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x17 x30 x31 = x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x18 x30 = x30) ⟶ x19 = 1 ⟶ x20 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x21 x30 x31 x32 = If_i (SNoLe x30 0) x31 (x16 (x21 (add_SNo x30 (minus_SNo 1)) x31 x32) (x22 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x22 x30 x31 x32 = If_i (SNoLe x30 0) x32 (x17 (x21 (add_SNo x30 (minus_SNo 1)) x31 x32) (x22 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ x23 x30 = x21 (x18 x30) x19 x20) ⟶ (∀ x30 . x30 ∈ int ⟶ x24 x30 = mul_SNo (mul_SNo x30 x30) x30) ⟶ x25 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ x26 x30 = mul_SNo x30 x30) ⟶ (∀ 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 (x26 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x29 x30 = add_SNo (x23 x30) (minus_SNo (x28 x30))) ⟶ ∀ x30 . x30 ∈ int ⟶ SNoLe 0 x30 ⟶ x15 x30 = x29 x30
Conjecture ae856..^A24118 : ∀ 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 . x6 ∈ 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 ⟶ x0 x20 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x20 x20)) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x1 x20 = x20) ⟶ 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 ∈ int ⟶ x4 x20 = x3 (x1 x20) x2) ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = mul_SNo x20 x20) ⟶ x6 = 2 ⟶ (∀ 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 (x7 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = add_SNo (x4 x20) (minus_SNo (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 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 (x18 x20) (minus_SNo (mul_SNo (mul_SNo (mul_SNo x20 x20) x20) x20))) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture 592a1..^A24116 : ∀ 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 = 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 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = add_SNo (x4 x15) (minus_SNo (mul_SNo x15 x15))) ⟶ (∀ 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 = 1 ⟶ 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 (x13 x15) (minus_SNo (mul_SNo x15 x15))) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture 26eb2..^A241031 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x10 x11 x12 x13 ∈ int) ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ 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 . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : 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 → ι . (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x29 x30 x31 ∈ 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 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 : ι → ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x34 x35 x36 x37 ∈ int) ⟶ ∀ x35 : ι → ι → ι → ι . (∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x35 x36 x37 x38 ∈ int) ⟶ ∀ x36 : ι → ι . (∀ x37 . x37 ∈ int ⟶ x36 x37 ∈ int) ⟶ ∀ x37 : ι → ι . (∀ x38 . x38 ∈ int ⟶ x37 x38 ∈ int) ⟶ (∀ x38 . x38 ∈ int ⟶ x0 x38 = add_SNo x38 x38) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x1 x38 x39 = x39) ⟶ (∀ x38 . x38 ∈ int ⟶ x2 x38 = x38) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x3 x38 x39 = If_i (SNoLe x38 0) x39 (x0 (x3 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x4 x38 x39 = x3 (x1 x38 x39) (x2 x38)) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x5 x38 x39 = add_SNo 1 (x4 x38 x39)) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x6 x38 x39 = x39) ⟶ x7 = 2 ⟶ x8 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ x9 x38 = x38) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x10 x38 x39 x40 = If_i (SNoLe x38 0) x39 (x5 (x10 (add_SNo x38 (minus_SNo 1)) x39 x40) (x11 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x11 x38 x39 x40 = If_i (SNoLe x38 0) x40 (x6 (x10 (add_SNo x38 (minus_SNo 1)) x39 x40) (x11 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ x12 x38 = x10 x7 x8 (x9 x38)) ⟶ (∀ x38 . x38 ∈ int ⟶ x13 x38 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x38 x38) x38)) x38) ⟶ (∀ x38 . x38 ∈ int ⟶ x14 x38 = x38) ⟶ x15 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x16 x38 x39 = If_i (SNoLe x38 0) x39 (x13 (x16 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ (∀ x38 . x38 ∈ int ⟶ x17 x38 = x16 (x14 x38) x15) ⟶ (∀ x38 . x38 ∈ int ⟶ x18 x38 = mul_SNo (x12 x38) (add_SNo 1 (x17 x38))) ⟶ (∀ x38 . x38 ∈ int ⟶ x19 x38 = add_SNo (mul_SNo x38 x38) x38) ⟶ x20 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ x21 x38 = add_SNo x38 x38) ⟶ (∀ x38 . x38 ∈ int ⟶ x22 x38 = x38) ⟶ x23 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x24 x38 x39 = If_i (SNoLe x38 0) x39 (x21 (x24 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ (∀ x38 . x38 ∈ int ⟶ x25 x38 = x24 (x22 x38) x23) ⟶ (∀ x38 . x38 ∈ int ⟶ x26 x38 = x25 x38) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x27 x38 x39 = If_i (SNoLe x38 0) x39 (x19 (x27 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ (∀ x38 . x38 ∈ int ⟶ x28 x38 = x27 x20 (x26 x38)) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x29 x38 x39 = mul_SNo x38 x39) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x30 x38 x39 = x39) ⟶ (∀ x38 . x38 ∈ int ⟶ x31 x38 = x38) ⟶ x32 = 1 ⟶ x33 = add_SNo 1 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x34 x38 x39 x40 = If_i (SNoLe x38 0) x39 (x29 (x34 (add_SNo x38 (minus_SNo 1)) x39 x40) (x35 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x35 x38 x39 x40 = If_i (SNoLe x38 0) x40 (x30 (x34 (add_SNo x38 (minus_SNo 1)) x39 x40) (x35 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ x36 x38 = x34 (x31 x38) x32 x33) ⟶ (∀ x38 . x38 ∈ int ⟶ x37 x38 = mul_SNo (add_SNo 1 (x28 x38)) (add_SNo 1 (x36 x38))) ⟶ ∀ x38 . x38 ∈ int ⟶ SNoLe 0 x38 ⟶ x18 x38 = x37 x38
Conjecture a1b36..^A24102 : ∀ 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 = add_SNo (add_SNo x15 x15) x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = add_SNo 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 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = add_SNo (x4 x15) (minus_SNo x15)) ⟶ (∀ 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 = 1 ⟶ x10 = add_SNo 1 (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 (x13 x15) (minus_SNo x15)) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture 315e2..^A241029 : ∀ 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 → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 . x6 ∈ 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 . 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 . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι → 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 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ (∀ x30 . x30 ∈ int ⟶ x0 x30 = add_SNo x30 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x1 x30 = x30) ⟶ 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 ∈ int ⟶ x4 x30 = x3 (x1 x30) x2) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x5 x30 x31 = mul_SNo (add_SNo 2 x31) x30) ⟶ x6 = 2 ⟶ (∀ x30 . x30 ∈ int ⟶ x7 x30 = x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x8 x30 x31 = If_i (SNoLe x30 0) x31 (x5 (x8 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x9 x30 = x8 x6 (x7 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x10 x30 = add_SNo (x9 x30) (minus_SNo x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x11 x30 = x30) ⟶ x12 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x13 x30 x31 = If_i (SNoLe x30 0) x31 (x10 (x13 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x14 x30 = x13 (x11 x30) x12) ⟶ (∀ x30 . x30 ∈ int ⟶ x15 x30 = mul_SNo (add_SNo 1 (x4 x30)) (add_SNo 1 (x14 x30))) ⟶ (∀ x30 . x30 ∈ int ⟶ x16 x30 = add_SNo x30 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x17 x30 = x30) ⟶ x18 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x19 x30 x31 = If_i (SNoLe x30 0) x31 (x16 (x19 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x20 x30 = x19 (x17 x30) x18) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x21 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x22 x30 x31 = x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x23 x30 = x30) ⟶ x24 = 1 ⟶ x25 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x26 x30 x31 x32 = If_i (SNoLe x30 0) x31 (x21 (x26 (add_SNo x30 (minus_SNo 1)) x31 x32) (x27 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x27 x30 x31 x32 = If_i (SNoLe x30 0) x32 (x22 (x26 (add_SNo x30 (minus_SNo 1)) x31 x32) (x27 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ x28 x30 = x26 (x23 x30) x24 x25) ⟶ (∀ x30 . x30 ∈ int ⟶ x29 x30 = mul_SNo (add_SNo 1 (x20 x30)) (add_SNo 1 (x28 x30))) ⟶ ∀ x30 . x30 ∈ int ⟶ SNoLe 0 x30 ⟶ x15 x30 = x29 x30
Conjecture 6e435..^A24091 : ∀ 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 (x4 x17) (minus_SNo (mul_SNo (mul_SNo x17 x17) 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 (x15 x17) (minus_SNo (mul_SNo (mul_SNo x17 x17) x17))) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture 1ceae..^A24088 : ∀ 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 (x4 x17) (minus_SNo 1)) ⟶ (∀ 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 (x15 x17) (minus_SNo 1)) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture e986f..^A24086 : ∀ 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 . x6 ∈ 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 : 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 (mul_SNo 2 (add_SNo (add_SNo x25 x25) x25)) x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x1 x25 = x25) ⟶ x2 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x3 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x3 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x4 x25 = x3 (x1 x25) x2) ⟶ (∀ x25 . x25 ∈ int ⟶ x5 x25 = mul_SNo (mul_SNo x25 x25) x25) ⟶ x6 = 2 ⟶ (∀ x25 . x25 ∈ int ⟶ x7 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x8 x25 x26 = If_i (SNoLe x25 0) x26 (x5 (x8 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x9 x25 = x8 x6 (x7 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x10 x25 = add_SNo (x4 x25) (minus_SNo (mul_SNo (mul_SNo (x9 x25) x25) x25))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x11 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x12 x25 x26 = x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x13 x25 = x25) ⟶ x14 = 1 ⟶ x15 = add_SNo 1 (add_SNo 2 (add_SNo 2 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 (mul_SNo x25 x25) x25) ⟶ x20 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ x21 x25 = mul_SNo (mul_SNo x25 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 = add_SNo (x18 x25) (minus_SNo (mul_SNo (mul_SNo (x23 x25) x25) x25))) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25