Proofgold Address

Param int^int : ι
Param mul_SNo^mul_SNo : ι → ι → 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
Conjecture 8b4a3..^A21614 : ∀ 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 (add_SNo (x9 x40 x41) (mul_SNo 2 (add_SNo (add_SNo x40 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 (add_SNo (x14 x40 x41) 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 (add_SNo (mul_SNo 2 (add_SNo (add_SNo x40 x40) x40)) x40) x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x22 x40 x41 = add_SNo 1 (add_SNo (add_SNo x41 x41) x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x40) ⟶ x24 = 1 ⟶ x25 = 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 66baf..^A21524 : ∀ 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 (add_SNo (add_SNo (x14 x40 x41) 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 (add_SNo x40 x40) x40)) x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x22 x40 x41 = add_SNo 1 (add_SNo (add_SNo x41 x41) x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x40) ⟶ x24 = 1 ⟶ x25 = 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 820e6..^A214885 : ∀ 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 . 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ 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 → 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 ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι → ι → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x28 x29 x30 x31 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 : ι → ι . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ int) ⟶ ∀ x31 . x31 ∈ 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 → ι . (∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x35 x36 x37 ∈ int) ⟶ ∀ x36 : ι → ι . (∀ x37 . x37 ∈ int ⟶ x36 x37 ∈ int) ⟶ ∀ x37 . x37 ∈ int ⟶ ∀ x38 : ι → ι → ι . (∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x38 x39 x40 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ ∀ x40 : ι → ι . (∀ x41 . x41 ∈ int ⟶ x40 x41 ∈ int) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x0 x41 x42 = add_SNo 1 (minus_SNo (add_SNo (add_SNo (add_SNo x41 x41) x41) x42))) ⟶ (∀ x41 . x41 ∈ int ⟶ x1 x41 = x41) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x2 x41 x42 = x42) ⟶ x3 = 1 ⟶ x4 = 0 ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x5 x41 x42 x43 = If_i (SNoLe x41 0) x42 (x0 (x5 (add_SNo x41 (minus_SNo 1)) x42 x43) (x6 (add_SNo x41 (minus_SNo 1)) x42 x43))) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x6 x41 x42 x43 = If_i (SNoLe x41 0) x43 (x1 (x5 (add_SNo x41 (minus_SNo 1)) x42 x43))) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x7 x41 x42 = x5 (x2 x41 x42) x3 x4) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x8 x41 x42 = add_SNo (x7 x41 x42) x41) ⟶ (∀ x41 . x41 ∈ int ⟶ x9 x41 = x41) ⟶ x10 = 0 ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x11 x41 x42 = If_i (SNoLe x41 0) x42 (x8 (x11 (add_SNo x41 (minus_SNo 1)) x42) x41)) ⟶ (∀ x41 . x41 ∈ int ⟶ x12 x41 = x11 (x9 x41) x10) ⟶ (∀ x41 . x41 ∈ int ⟶ x13 x41 = add_SNo (x12 x41) (minus_SNo x41)) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x14 x41 x42 = add_SNo x41 x42) ⟶ (∀ x41 . x41 ∈ int ⟶ x15 x41 = x41) ⟶ (∀ x41 . x41 ∈ int ⟶ x16 x41 = add_SNo x41 (minus_SNo 1)) ⟶ x17 = 2 ⟶ x18 = 1 ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x19 x41 x42 x43 = If_i (SNoLe x41 0) x42 (x14 (x19 (add_SNo x41 (minus_SNo 1)) x42 x43) (x20 (add_SNo x41 (minus_SNo 1)) x42 x43))) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x20 x41 x42 x43 = If_i (SNoLe x41 0) x43 (x15 (x19 (add_SNo x41 (minus_SNo 1)) x42 x43))) ⟶ (∀ x41 . x41 ∈ int ⟶ x21 x41 = x19 (x16 x41) x17 x18) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x22 x41 x42 = add_SNo x42 (minus_SNo x41)) ⟶ (∀ x41 . x41 ∈ int ⟶ x23 x41 = x41) ⟶ (∀ x41 . x41 ∈ int ⟶ x24 x41 = x41) ⟶ x25 = 1 ⟶ x26 = 0 ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x27 x41 x42 x43 = If_i (SNoLe x41 0) x42 (x22 (x27 (add_SNo x41 (minus_SNo 1)) x42 x43) (x28 (add_SNo x41 (minus_SNo 1)) x42 x43))) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x28 x41 x42 x43 = If_i (SNoLe x41 0) x43 (x23 (x27 (add_SNo x41 (minus_SNo 1)) x42 x43))) ⟶ (∀ x41 . x41 ∈ int ⟶ x29 x41 = x27 (x24 x41) x25 x26) ⟶ (∀ x41 . x41 ∈ int ⟶ x30 x41 = mul_SNo (x21 x41) (x29 x41)) ⟶ x31 = 1 ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x32 x41 x42 = x42) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x33 x41 x42 = If_i (SNoLe x41 0) x42 (x30 (x33 (add_SNo x41 (minus_SNo 1)) x42))) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x34 x41 x42 = x33 x31 (x32 x41 x42)) ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x35 x41 x42 = add_SNo (x34 x41 x42) x41) ⟶ (∀ x41 . x41 ∈ int ⟶ x36 x41 = x41) ⟶ x37 = 0 ⟶ (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x38 x41 x42 = If_i (SNoLe x41 0) x42 (x35 (x38 (add_SNo x41 (minus_SNo 1)) x42) x41)) ⟶ (∀ x41 . x41 ∈ int ⟶ x39 x41 = x38 (x36 x41) x37) ⟶ (∀ x41 . x41 ∈ int ⟶ x40 x41 = add_SNo (x39 x41) (minus_SNo x41)) ⟶ ∀ x41 . x41 ∈ int ⟶ SNoLe 0 x41 ⟶ x13 x41 = x40 x41
Conjecture ea50f..^A21484 : ∀ 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 (x4 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 (add_SNo (x9 x40 x41) (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 (add_SNo (x14 x40 x41) 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 (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 (add_SNo x41 x41) x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x40) ⟶ x24 = 1 ⟶ x25 = 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 (x33 x40 x41) (mul_SNo 2 (mul_SNo 2 (add_SNo (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 885b3..^A21474 : ∀ 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 (add_SNo (x9 x40 x41) (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 (add_SNo (x14 x40 x41) 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 (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 (add_SNo x41 x41) x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x40) ⟶ x24 = 1 ⟶ x25 = 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 5d86e..^A21454 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ 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 ⟶ x0 x40 = add_SNo (add_SNo x40 x40) 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 ∈ int ⟶ x4 x40 = x3 x1 (x2 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x5 x40 = add_SNo 1 (x4 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 (add_SNo (x9 x40 x41) (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 (add_SNo (x14 x40 x41) 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 (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 (add_SNo x41 x41) x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x40) ⟶ x24 = 1 ⟶ x25 = 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 f8eb5..^A213770 : ∀ 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 . 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ 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 → 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 . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 : ι → ι → ι . (∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x35 x36 x37 ∈ int) ⟶ ∀ x36 : ι → ι . (∀ x37 . x37 ∈ int ⟶ x36 x37 ∈ int) ⟶ ∀ x37 : ι → ι . (∀ x38 . x38 ∈ int ⟶ x37 x38 ∈ int) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x0 x38 x39 = add_SNo 2 (add_SNo 2 (add_SNo x38 x39))) ⟶ (∀ x38 . x38 ∈ int ⟶ x1 x38 = x38) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x2 x38 x39 = x39) ⟶ x3 = 1 ⟶ x4 = 0 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x5 x38 x39 x40 = If_i (SNoLe x38 0) x39 (x0 (x5 (add_SNo x38 (minus_SNo 1)) x39 x40) (x6 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x6 x38 x39 x40 = If_i (SNoLe x38 0) x40 (x1 (x5 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x7 x38 x39 = x5 (x2 x38 x39) x3 x4) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x8 x38 x39 = add_SNo (x7 x38 x39) x38) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x9 x38 x39 = x39) ⟶ (∀ x38 . x38 ∈ int ⟶ x10 x38 = x38) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x11 x38 x39 = If_i (SNoLe x38 0) x39 (x8 (x11 (add_SNo x38 (minus_SNo 1)) x39) x38)) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x12 x38 x39 = x11 (x9 x38 x39) (x10 x38)) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x13 x38 x39 = x12 x38 x39) ⟶ (∀ 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 . x38 ∈ int ⟶ x17 x38 = x16 (x14 x38) x15) ⟶ (∀ x38 . x38 ∈ int ⟶ x18 x38 = add_SNo (x17 x38) x38) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x19 x38 x39 = add_SNo x38 x39) ⟶ (∀ x38 . x38 ∈ int ⟶ x20 x38 = x38) ⟶ (∀ x38 . x38 ∈ int ⟶ x21 x38 = x38) ⟶ x22 = add_SNo 1 (add_SNo 2 2) ⟶ x23 = add_SNo 2 2 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x24 x38 x39 x40 = If_i (SNoLe x38 0) x39 (x19 (x24 (add_SNo x38 (minus_SNo 1)) x39 x40) (x25 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x25 x38 x39 x40 = If_i (SNoLe x38 0) x40 (x20 (x24 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ x26 x38 = x24 (x21 x38) x22 x23) ⟶ (∀ x38 . x38 ∈ int ⟶ x27 x38 = add_SNo (add_SNo (add_SNo (add_SNo (x26 x38) (minus_SNo 1)) (minus_SNo (mul_SNo 2 (add_SNo 2 x38)))) (minus_SNo x38)) (minus_SNo x38)) ⟶ x28 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x29 x38 x39 = add_SNo 2 x39) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x30 x38 x39 = If_i (SNoLe x38 0) x39 (x27 (x30 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x31 x38 x39 = x30 x28 (x29 x38 x39)) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x32 x38 x39 = add_SNo (x31 x38 x39) x38) ⟶ (∀ x38 . x38 ∈ int ⟶ x33 x38 = x38) ⟶ x34 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x35 x38 x39 = If_i (SNoLe x38 0) x39 (x32 (x35 (add_SNo x38 (minus_SNo 1)) x39) x38)) ⟶ (∀ x38 . x38 ∈ int ⟶ x36 x38 = x35 (x33 x38) x34) ⟶ (∀ x38 . x38 ∈ int ⟶ x37 x38 = x36 x38) ⟶ ∀ x38 . x38 ∈ int ⟶ SNoLe 0 x38 ⟶ x18 x38 = x37 x38
Conjecture 5ffc7..^A21334 : ∀ 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 . 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 → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 : ι → ι → 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 → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x28 x29 x30 ∈ 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 → 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 = mul_SNo (add_SNo 2 x41) 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 . 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 ⟶ ∀ x41 . x41 ∈ int ⟶ x16 x40 x41 = x41) ⟶ 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 ⟶ ∀ x41 . x41 ∈ int ⟶ x19 x40 x41 = x18 (x16 x40 x41) x17) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x20 x40 x41 = add_SNo (add_SNo (x19 x40 x41) x40) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x21 x40 = x40) ⟶ x22 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x23 x40 x41 = If_i (SNoLe x40 0) x41 (x20 (x23 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x24 x40 = x23 (x21 x40) x22) ⟶ (∀ x40 . x40 ∈ int ⟶ x25 x40 = x24 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x26 x40 x41 = add_SNo (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo (add_SNo x40 x40) x40)) x41)) (minus_SNo 1)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x27 x40 x41 = add_SNo x41 x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x28 x40 x41 = x41) ⟶ x29 = 1 ⟶ x30 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x31 x40 x41 x42 = If_i (SNoLe x40 0) x41 (x26 (x31 (add_SNo x40 (minus_SNo 1)) x41 x42) (x32 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x32 x40 x41 x42 = If_i (SNoLe x40 0) x42 (x27 (x31 (add_SNo x40 (minus_SNo 1)) x41 x42) (x32 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x33 x40 x41 = x31 (x28 x40 x41) x29 x30) ⟶ (∀ 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 ⟶ x25 x40 = x39 x40
Conjecture bcbbe..^A21294 : ∀ 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 . (∀ 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 → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 : ι → ι → 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 → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x28 x29 x30 ∈ 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 → 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 ⟶ 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 ⟶ ∀ x41 . x41 ∈ int ⟶ x16 x40 x41 = x41) ⟶ 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 ⟶ ∀ x41 . x41 ∈ int ⟶ x19 x40 x41 = x18 (x16 x40 x41) x17) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x20 x40 x41 = add_SNo (add_SNo (x19 x40 x41) x40) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x21 x40 = x40) ⟶ x22 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x23 x40 x41 = If_i (SNoLe x40 0) x41 (x20 (x23 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x24 x40 = x23 (x21 x40) x22) ⟶ (∀ x40 . x40 ∈ int ⟶ x25 x40 = x24 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x26 x40 x41 = add_SNo (add_SNo (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x41)) (minus_SNo 1)) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x27 x40 x41 = add_SNo x41 x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x28 x40 x41 = x41) ⟶ x29 = 1 ⟶ x30 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x31 x40 x41 x42 = If_i (SNoLe x40 0) x41 (x26 (x31 (add_SNo x40 (minus_SNo 1)) x41 x42) (x32 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x32 x40 x41 x42 = If_i (SNoLe x40 0) x42 (x27 (x31 (add_SNo x40 (minus_SNo 1)) x41 x42) (x32 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x33 x40 x41 = x31 (x28 x40 x41) x29 x30) ⟶ (∀ 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 ⟶ x25 x40 = x39 x40
Conjecture f8b37..^A212850 : ∀ 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 . x6 ∈ int ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ 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 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ x0 x28 = add_SNo x28 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x1 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x2 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x3 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x3 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x4 x28 x29 = x3 (x1 x28 x29) (x2 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x5 x28 x29 = add_SNo (x4 x28 x29) (minus_SNo x28)) ⟶ x6 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ x7 x28 = add_SNo 2 x28) ⟶ x8 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x10 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x5 (x10 (add_SNo x28 (minus_SNo 1)) x29 x30) (x11 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x11 x28 x29 x30 = If_i (SNoLe x28 0) x30 x6) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x10 (x7 x28) x8 (x9 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = add_SNo (x12 x28) 1) ⟶ (∀ x28 . x28 ∈ int ⟶ x14 x28 = add_SNo x28 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x28) ⟶ x16 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x17 x28 x29 = If_i (SNoLe x28 0) x29 (x14 (x17 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x18 x28 = x17 (x15 x28) x16) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x19 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x20 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x28) ⟶ x22 = add_SNo 1 2 ⟶ x23 = add_SNo 1 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x24 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x19 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30) (x25 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x25 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x20 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30) (x25 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x24 (x21 x28) x22 x23) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = add_SNo 1 (mul_SNo (add_SNo (x18 x28) (minus_SNo 2)) (x26 x28))) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture 58adf..^A212699 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι → 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 . 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 (mul_SNo 2 (add_SNo x15 x15)) x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x2 x15 = add_SNo 1 x15) ⟶ (∀ 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 . x15 ∈ int ⟶ x5 x15 = mul_SNo 2 (mul_SNo 2 (x4 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) ⟶ (∀ x15 . x15 ∈ int ⟶ x9 x15 = add_SNo 1 x15) ⟶ 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 x15) x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = mul_SNo 2 (mul_SNo 2 (x13 x15))) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture a521f..^A212133 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x0 x7 x8 = add_SNo (add_SNo x7 (minus_SNo 2)) x8) ⟶ (∀ x7 . x7 ∈ int ⟶ x1 x7 = add_SNo x7 x7) ⟶ x2 = 2 ⟶ (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x3 x7 x8 = If_i (SNoLe x7 0) x8 (x0 (x3 (add_SNo x7 (minus_SNo 1)) x8) x7)) ⟶ (∀ x7 . x7 ∈ int ⟶ x4 x7 = x3 (x1 x7) x2) ⟶ (∀ x7 . x7 ∈ int ⟶ x5 x7 = mul_SNo (x4 x7) x7) ⟶ (∀ x7 . x7 ∈ int ⟶ x6 x7 = add_SNo (mul_SNo (add_SNo (add_SNo x7 (minus_SNo 1)) x7) (add_SNo (mul_SNo x7 x7) (minus_SNo x7))) x7) ⟶ ∀ x7 . x7 ∈ int ⟶ SNoLe 0 x7 ⟶ x5 x7 = x6 x7
Conjecture 70d71..^A21204 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 . x9 ∈ 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 → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ 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 : 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 = add_SNo (mul_SNo 2 (add_SNo (add_SNo (add_SNo x40 x40) x40) x41)) (minus_SNo 1)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x1 x40 x41 = add_SNo x41 x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x2 x40 x41 = x41) ⟶ x3 = 1 ⟶ x4 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x5 x40 x41 x42 = If_i (SNoLe x40 0) x41 (x0 (x5 (add_SNo x40 (minus_SNo 1)) x41 x42) (x6 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x6 x40 x41 x42 = If_i (SNoLe x40 0) x42 (x1 (x5 (add_SNo x40 (minus_SNo 1)) x41 x42) (x6 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x7 x40 x41 = x5 (x2 x40 x41) x3 x4) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x8 x40 x41 = mul_SNo (add_SNo 2 x41) x40) ⟶ x9 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ x10 x40 = x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x11 x40 x41 = If_i (SNoLe x40 0) x41 (x8 (x11 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x12 x40 = x11 x9 (x10 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x13 x40 x41 = add_SNo (x7 x40 x41) (add_SNo (x12 x40) (minus_SNo x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ x14 x40 = x40) ⟶ x15 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x16 x40 x41 = If_i (SNoLe x40 0) x41 (x13 (x16 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x17 x40 = x16 (x14 x40) x15) ⟶ (∀ x40 . x40 ∈ int ⟶ x18 x40 = x17 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x19 x40 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x40 x40) x40)) (minus_SNo 1)) ⟶ (∀ x40 . x40 ∈ int ⟶ x20 x40 = x40) ⟶ x21 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x22 x40 x41 = If_i (SNoLe x40 0) x41 (x19 (x22 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x22 (x20 x40) x21) ⟶ (∀ x40 . x40 ∈ int ⟶ x24 x40 = add_SNo x40 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x25 x40 = x40) ⟶ x26 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x27 x40 x41 = If_i (SNoLe x40 0) x41 (x24 (x27 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ x28 x40 = x27 (x25 x40) x26) ⟶ (∀ x40 . x40 ∈ int ⟶ x29 x40 = add_SNo (x23 x40) (minus_SNo (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) x40) (mul_SNo (add_SNo (mul_SNo (mul_SNo x40 2) 2) x40) 2)) ⟶ (∀ 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 ⟶ x18 x40 = x39 x40
Conjecture 6ab1c..^A21194 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ 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 → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ 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 : 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 = add_SNo (mul_SNo 2 (add_SNo (add_SNo (add_SNo x40 x40) x40) x41)) (minus_SNo 1)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x1 x40 x41 = add_SNo x41 x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x2 x40 x41 = x41) ⟶ x3 = 1 ⟶ x4 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x5 x40 x41 x42 = If_i (SNoLe x40 0) x41 (x0 (x5 (add_SNo x40 (minus_SNo 1)) x41 x42) (x6 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x6 x40 x41 x42 = If_i (SNoLe x40 0) x42 (x1 (x5 (add_SNo x40 (minus_SNo 1)) x41 x42) (x6 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x7 x40 x41 = x5 (x2 x40 x41) x3 x4) ⟶ (∀ x40 . x40 ∈ int ⟶ x8 x40 = add_SNo (add_SNo x40 x40) x40) ⟶ x9 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ x10 x40 = x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x11 x40 x41 = If_i (SNoLe x40 0) x41 (x8 (x11 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ x12 x40 = x11 x9 (x10 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x13 x40 x41 = add_SNo (x7 x40 x41) (x12 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x14 x40 = x40) ⟶ x15 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x16 x40 x41 = If_i (SNoLe x40 0) x41 (x13 (x16 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x17 x40 = x16 (x14 x40) x15) ⟶ (∀ x40 . x40 ∈ int ⟶ x18 x40 = x17 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x19 x40 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x40 x40) x40)) (minus_SNo 1)) ⟶ (∀ x40 . x40 ∈ int ⟶ x20 x40 = x40) ⟶ x21 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x22 x40 x41 = If_i (SNoLe x40 0) x41 (x19 (x22 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x22 (x20 x40) x21) ⟶ (∀ x40 . x40 ∈ int ⟶ x24 x40 = add_SNo x40 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x25 x40 = x40) ⟶ x26 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x27 x40 x41 = If_i (SNoLe x40 0) x41 (x24 (x27 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ x28 x40 = x27 (x25 x40) x26) ⟶ (∀ x40 . x40 ∈ int ⟶ x29 x40 = add_SNo (x23 x40) (minus_SNo (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 ⟶ x18 x40 = x39 x40
Conjecture d3ef0..^A21064 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 . x9 ∈ 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 → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ 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 → 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 : 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 = add_SNo (add_SNo (mul_SNo 2 (add_SNo x33 x34)) (minus_SNo 1)) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x1 x33 x34 = add_SNo x34 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x2 x33 x34 = x34) ⟶ x3 = 1 ⟶ x4 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x5 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x0 (x5 (add_SNo x33 (minus_SNo 1)) x34 x35) (x6 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x6 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x1 (x5 (add_SNo x33 (minus_SNo 1)) x34 x35) (x6 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x7 x33 x34 = x5 (x2 x33 x34) x3 x4) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x8 x33 x34 = mul_SNo (add_SNo 2 x34) x33) ⟶ x9 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ x10 x33 = x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x11 x33 x34 = If_i (SNoLe x33 0) x34 (x8 (x11 (add_SNo x33 (minus_SNo 1)) x34) x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x12 x33 = x11 x9 (x10 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = add_SNo (x7 x33 x34) (x12 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x14 x33 = x33) ⟶ x15 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x16 x33 x34 = If_i (SNoLe x33 0) x34 (x13 (x16 (add_SNo x33 (minus_SNo 1)) x34) x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x17 x33 = x16 (x14 x33) x15) ⟶ (∀ x33 . x33 ∈ int ⟶ x18 x33 = x17 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x19 x33 x34 = add_SNo (add_SNo (mul_SNo 2 (add_SNo x33 x34)) (minus_SNo 1)) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x20 x33 x34 = add_SNo x34 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x21 x33 x34 = x34) ⟶ x22 = 1 ⟶ x23 = 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 ⟶ ∀ x34 . x34 ∈ int ⟶ x26 x33 x34 = x24 (x21 x33 x34) x22 x23) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x27 x33 x34 = add_SNo (x26 x33 x34) (mul_SNo 2 (mul_SNo 2 (add_SNo (add_SNo x33 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 . x33 ∈ int ⟶ x31 x33 = x30 (x28 x33) x29) ⟶ (∀ x33 . x33 ∈ int ⟶ x32 x33 = x31 x33) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x18 x33 = x32 x33
Conjecture 7441d..^A20984 : ∀ 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 . 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 → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι → ι . (∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x35 x36 x37 ∈ int) ⟶ ∀ x36 : ι → ι . (∀ x37 . x37 ∈ int ⟶ x36 x37 ∈ int) ⟶ ∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ ∀ x39 : ι → ι → ι → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x39 x40 x41 x42 ∈ int) ⟶ ∀ x40 : ι → ι → ι → ι . (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x40 x41 x42 x43 ∈ int) ⟶ ∀ x41 : ι → ι . (∀ x42 . x42 ∈ int ⟶ x41 x42 ∈ int) ⟶ ∀ x42 : ι → ι . (∀ x43 . x43 ∈ int ⟶ x42 x43 ∈ int) ⟶ ∀ x43 . x43 ∈ int ⟶ ∀ x44 : ι → ι → ι . (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x44 x45 x46 ∈ int) ⟶ ∀ x45 : ι → ι → ι . (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x45 x46 x47 ∈ int) ⟶ ∀ x46 : ι → ι → ι . (∀ x47 . x47 ∈ int ⟶ ∀ x48 . x48 ∈ int ⟶ x46 x47 x48 ∈ int) ⟶ ∀ x47 : ι → ι → ι . (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x47 x48 x49 ∈ int) ⟶ ∀ x48 : ι → ι . (∀ x49 . x49 ∈ int ⟶ x48 x49 ∈ int) ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 : ι → ι → ι . (∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x50 x51 x52 ∈ int) ⟶ ∀ x51 : ι → ι . (∀ x52 . x52 ∈ int ⟶ x51 x52 ∈ int) ⟶ ∀ x52 : ι → ι . (∀ x53 . x53 ∈ int ⟶ x52 x53 ∈ int) ⟶ (∀ x53 . x53 ∈ int ⟶ x0 x53 = add_SNo (add_SNo x53 x53) x53) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x1 x53 x54 = add_SNo x54 x54) ⟶ x2 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x3 x53 x54 = If_i (SNoLe x53 0) x54 (x0 (x3 (add_SNo x53 (minus_SNo 1)) x54))) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x4 x53 x54 = x3 (x1 x53 x54) x2) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x5 x53 x54 = mul_SNo (add_SNo 2 x54) x53) ⟶ x6 = 2 ⟶ (∀ x53 . x53 ∈ int ⟶ x7 x53 = x53) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x8 x53 x54 = If_i (SNoLe x53 0) x54 (x5 (x8 (add_SNo x53 (minus_SNo 1)) x54) x53)) ⟶ (∀ x53 . x53 ∈ int ⟶ x9 x53 = x8 x6 (x7 x53)) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x10 x53 x54 = add_SNo (x4 x53 x54) (x9 x53)) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x11 x53 x54 = x54) ⟶ x12 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x13 x53 x54 = If_i (SNoLe x53 0) x54 (x10 (x13 (add_SNo x53 (minus_SNo 1)) x54) x53)) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x14 x53 x54 = x13 (x11 x53 x54) x12) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x15 x53 x54 = mul_SNo (add_SNo 2 x54) x53) ⟶ x16 = 2 ⟶ (∀ x53 . x53 ∈ int ⟶ x17 x53 = x53) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x18 x53 x54 = If_i (SNoLe x53 0) x54 (x15 (x18 (add_SNo x53 (minus_SNo 1)) x54) x53)) ⟶ (∀ x53 . x53 ∈ int ⟶ x19 x53 = x18 x16 (x17 x53)) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x20 x53 x54 = add_SNo (add_SNo (x14 x53 x54) (minus_SNo x53)) (x19 x53)) ⟶ (∀ x53 . x53 ∈ int ⟶ x21 x53 = x53) ⟶ x22 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x23 x53 x54 = If_i (SNoLe x53 0) x54 (x20 (x23 (add_SNo x53 (minus_SNo 1)) x54) x53)) ⟶ (∀ x53 . x53 ∈ int ⟶ x24 x53 = x23 (x21 x53) x22) ⟶ (∀ x53 . x53 ∈ int ⟶ x25 x53 = x24 x53) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x26 x53 x54 = add_SNo (add_SNo (add_SNo (mul_SNo x54 x54) x53) x53) x53) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x27 x53 x54 = add_SNo x54 x54) ⟶ (∀ x53 . x53 ∈ int ⟶ x28 x53 = x53) ⟶ x29 = 1 ⟶ x30 = 2 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x31 x53 x54 x55 = If_i (SNoLe x53 0) x54 (x26 (x31 (add_SNo x53 (minus_SNo 1)) x54 x55) (x32 (add_SNo x53 (minus_SNo 1)) x54 x55))) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x32 x53 x54 x55 = If_i (SNoLe x53 0) x55 (x27 (x31 (add_SNo x53 (minus_SNo 1)) x54 x55) (x32 (add_SNo x53 (minus_SNo 1)) x54 x55))) ⟶ (∀ x53 . x53 ∈ int ⟶ x33 x53 = x31 (x28 x53) x29 x30) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x34 x53 x54 = mul_SNo x53 x54) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x35 x53 x54 = x54) ⟶ (∀ x53 . x53 ∈ int ⟶ x36 x53 = x53) ⟶ x37 = 1 ⟶ x38 = add_SNo 1 2 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x39 x53 x54 x55 = If_i (SNoLe x53 0) x54 (x34 (x39 (add_SNo x53 (minus_SNo 1)) x54 x55) (x40 (add_SNo x53 (minus_SNo 1)) x54 x55))) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x40 x53 x54 x55 = If_i (SNoLe x53 0) x55 (x35 (x39 (add_SNo x53 (minus_SNo 1)) x54 x55) (x40 (add_SNo x53 (minus_SNo 1)) x54 x55))) ⟶ (∀ x53 . x53 ∈ int ⟶ x41 x53 = x39 (x36 x53) x37 x38) ⟶ (∀ x53 . x53 ∈ int ⟶ x42 x53 = mul_SNo (x33 x53) (x41 x53)) ⟶ x43 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x44 x53 x54 = x54) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x45 x53 x54 = If_i (SNoLe x53 0) x54 (x42 (x45 (add_SNo x53 (minus_SNo 1)) x54))) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x46 x53 x54 = x45 x43 (x44 x53 x54)) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x47 x53 x54 = add_SNo (add_SNo (x46 x53 x54) x53) (mul_SNo (add_SNo (mul_SNo (mul_SNo x53 2) 2) x53) 2)) ⟶ (∀ x53 . x53 ∈ int ⟶ x48 x53 = x53) ⟶ x49 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x50 x53 x54 = If_i (SNoLe x53 0) x54 (x47 (x50 (add_SNo x53 (minus_SNo 1)) x54) x53)) ⟶ (∀ x53 . x53 ∈ int ⟶ x51 x53 = x50 (x48 x53) x49) ⟶ (∀ x53 . x53 ∈ int ⟶ x52 x53 = x51 x53) ⟶ ∀ x53 . x53 ∈ int ⟶ SNoLe 0 x53 ⟶ x25 x53 = x52 x53
Conjecture e2105..^A20973 : ∀ 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 (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 (add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo x40 x40))) x40) x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x22 x40 x41 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x41 x41)) x40)) ⟶ (∀ 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) x40) (mul_SNo (add_SNo (mul_SNo (add_SNo x40 x40) 2) x40) 2)) ⟶ (∀ 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 295f3..^A20969 : ∀ 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 → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ 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 → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 : ι → ι . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ int) ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 : ι → ι . (∀ x35 . x35 ∈ int ⟶ x34 x35 ∈ int) ⟶ ∀ x35 : ι → ι → ι . (∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x35 x36 x37 ∈ int) ⟶ ∀ x36 : ι → ι . (∀ x37 . x37 ∈ int ⟶ x36 x37 ∈ int) ⟶ ∀ x37 : ι → ι . (∀ x38 . x38 ∈ int ⟶ x37 x38 ∈ int) ⟶ ∀ x38 . x38 ∈ int ⟶ ∀ x39 : ι → ι → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x39 x40 x41 ∈ int) ⟶ ∀ x40 : ι → ι → ι . (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x40 x41 x42 ∈ int) ⟶ ∀ x41 : ι → ι → ι . (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x41 x42 x43 ∈ 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 . x44 ∈ int ⟶ ∀ x45 : ι → ι → ι . (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x45 x46 x47 ∈ int) ⟶ ∀ x46 : ι → ι . (∀ x47 . x47 ∈ int ⟶ x46 x47 ∈ int) ⟶ ∀ x47 : ι → ι . (∀ x48 . x48 ∈ int ⟶ x47 x48 ∈ int) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x0 x48 x49 = mul_SNo (add_SNo 2 x49) x48) ⟶ x1 = 2 ⟶ (∀ x48 . x48 ∈ int ⟶ x2 x48 = x48) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x3 x48 x49 = If_i (SNoLe x48 0) x49 (x0 (x3 (add_SNo x48 (minus_SNo 1)) x49) x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ x4 x48 = x3 x1 (x2 x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x5 x48 x49 = add_SNo (x4 x48) (mul_SNo (mul_SNo x49 x49) x49)) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x6 x48 x49 = add_SNo x49 x49) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x7 x48 x49 = x49) ⟶ x8 = 1 ⟶ x9 = 2 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x10 x48 x49 x50 = If_i (SNoLe x48 0) x49 (x5 (x10 (add_SNo x48 (minus_SNo 1)) x49 x50) (x11 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x11 x48 x49 x50 = If_i (SNoLe x48 0) x50 (x6 (x10 (add_SNo x48 (minus_SNo 1)) x49 x50) (x11 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x12 x48 x49 = x10 (x7 x48 x49) x8 x9) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x13 x48 x49 = add_SNo (add_SNo (x12 x48 x49) (mul_SNo 2 (add_SNo (add_SNo x48 x48) x48))) x48) ⟶ (∀ x48 . x48 ∈ int ⟶ x14 x48 = x48) ⟶ x15 = 1 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x16 x48 x49 = If_i (SNoLe x48 0) x49 (x13 (x16 (add_SNo x48 (minus_SNo 1)) x49) x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ x17 x48 = x16 (x14 x48) x15) ⟶ (∀ x48 . x48 ∈ int ⟶ x18 x48 = x17 x48) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x19 x48 x49 = add_SNo (add_SNo (add_SNo x48 x48) x48) x49) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x20 x48 x49 = add_SNo x49 x49) ⟶ (∀ x48 . x48 ∈ int ⟶ x21 x48 = x48) ⟶ x22 = 1 ⟶ x23 = 2 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x24 x48 x49 x50 = If_i (SNoLe x48 0) x49 (x19 (x24 (add_SNo x48 (minus_SNo 1)) x49 x50) (x25 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x25 x48 x49 x50 = If_i (SNoLe x48 0) x50 (x20 (x24 (add_SNo x48 (minus_SNo 1)) x49 x50) (x25 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ x26 x48 = x24 (x21 x48) x22 x23) ⟶ (∀ x48 . x48 ∈ int ⟶ x27 x48 = mul_SNo x48 x48) ⟶ x28 = 1 ⟶ (∀ x48 . x48 ∈ int ⟶ x29 x48 = add_SNo x48 x48) ⟶ (∀ x48 . x48 ∈ int ⟶ x30 x48 = add_SNo x48 (minus_SNo 1)) ⟶ x31 = 2 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x32 x48 x49 = If_i (SNoLe x48 0) x49 (x29 (x32 (add_SNo x48 (minus_SNo 1)) x49))) ⟶ (∀ x48 . x48 ∈ int ⟶ x33 x48 = x32 (x30 x48) x31) ⟶ (∀ x48 . x48 ∈ int ⟶ x34 x48 = x33 x48) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x35 x48 x49 = If_i (SNoLe x48 0) x49 (x27 (x35 (add_SNo x48 (minus_SNo 1)) x49))) ⟶ (∀ x48 . x48 ∈ int ⟶ x36 x48 = x35 x28 (x34 x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ x37 x48 = mul_SNo (x26 x48) (x36 x48)) ⟶ x38 = 1 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x39 x48 x49 = x49) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x40 x48 x49 = If_i (SNoLe x48 0) x49 (x37 (x40 (add_SNo x48 (minus_SNo 1)) x49))) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x41 x48 x49 = x40 x38 (x39 x48 x49)) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x42 x48 x49 = add_SNo (add_SNo (x41 x48 x49) (mul_SNo 2 (add_SNo (add_SNo x48 x48) x48))) x48) ⟶ (∀ x48 . x48 ∈ int ⟶ x43 x48 = x48) ⟶ x44 = 1 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x45 x48 x49 = If_i (SNoLe x48 0) x49 (x42 (x45 (add_SNo x48 (minus_SNo 1)) x49) x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ x46 x48 = x45 (x43 x48) x44) ⟶ (∀ x48 . x48 ∈ int ⟶ x47 x48 = x46 x48) ⟶ ∀ x48 . x48 ∈ int ⟶ SNoLe 0 x48 ⟶ x18 x48 = x47 x48
Conjecture 4f6d9..^A2089 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ 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 . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ (∀ x22 . x22 ∈ int ⟶ x0 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x1 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x2 x22 = add_SNo 1 (add_SNo x22 x22)) ⟶ x3 = 2 ⟶ x4 = 2 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x5 x22 x23 = If_i (SNoLe x22 0) x23 (x2 (x5 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ x6 = x5 x3 x4 ⟶ x7 = x6 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x8 x22 x23 = If_i (SNoLe x22 0) x23 (x0 (x8 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x9 x22 = x8 (x1 x22) x7) ⟶ (∀ x22 . x22 ∈ int ⟶ x10 x22 = x9 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x11 x22 = mul_SNo x22 x22) ⟶ x12 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ x13 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x14 x22 = x22) ⟶ x15 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x16 x22 x23 = If_i (SNoLe x22 0) x23 (x13 (x16 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x17 x22 = x16 (x14 x22) x15) ⟶ (∀ x22 . x22 ∈ int ⟶ x18 x22 = x17 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x19 x22 x23 = If_i (SNoLe x22 0) x23 (x11 (x19 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x20 x22 = x19 x12 (x18 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x21 x22 = mul_SNo (add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) (x20 x22)) ⟶ ∀ x22 . x22 ∈ int ⟶ SNoLe 0 x22 ⟶ x10 x22 = x21 x22
Conjecture 09af3..^A20874 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x0 x17 x18 = add_SNo x17 x18) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x1 x17 x18 = x18) ⟶ (∀ x17 . x17 ∈ int ⟶ x2 x17 = x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x4 x17 x18 = x3 (x1 x17 x18) (x2 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x5 x17 x18 = mul_SNo 2 (x4 x17 x18)) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = x17) ⟶ x7 = 2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x8 x17 x18 = If_i (SNoLe x17 0) x18 (x5 (x8 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x9 x17 = x8 (x6 x17) x7) ⟶ (∀ x17 . x17 ∈ int ⟶ x10 x17 = add_SNo (mul_SNo (add_SNo (x9 x17) (minus_SNo 2)) x17) (minus_SNo x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x11 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x17) ⟶ x13 = 2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x11 (x14 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 (x12 x17) x13) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = mul_SNo (add_SNo (add_SNo (mul_SNo (add_SNo (add_SNo (x15 x17) (minus_SNo 2)) (minus_SNo x17)) (add_SNo 1 (add_SNo 2 2))) (minus_SNo 1)) (minus_SNo (mul_SNo x17 x17))) x17) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x10 x17 = x16 x17