Proofgold Asset

Param int^int : ι
Param add_SNo^add_SNo : ι → ι → ι
Param mul_SNo^mul_SNo : ι → ι → ι
Param ordsucc^ordsucc : ι → ι
Param minus_SNo^minus_SNo : ι → ι
Param If_i^If_i : ο → ι → ι → ι
Param SNoLe^SNoLe : ι → ι → ο
Conjecture 97664..^A20871 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x0 x18 x19 = add_SNo (mul_SNo 2 (add_SNo x18 x18)) (minus_SNo x19)) ⟶ (∀ x18 . x18 ∈ int ⟶ x1 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x2 x18 = x18) ⟶ x3 = 1 ⟶ x4 = 2 ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x5 x18 x19 x20 = If_i (SNoLe x18 0) x19 (x0 (x5 (add_SNo x18 (minus_SNo 1)) x19 x20) (x6 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x6 x18 x19 x20 = If_i (SNoLe x18 0) x20 (x1 (x5 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ x7 x18 = x5 (x2 x18) x3 x4) ⟶ (∀ x18 . x18 ∈ int ⟶ x8 x18 = add_SNo (mul_SNo x18 (x7 x18)) x18) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x9 x18 x19 = add_SNo (mul_SNo 2 (add_SNo x18 x18)) (minus_SNo x19)) ⟶ (∀ x18 . x18 ∈ int ⟶ x10 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x11 x18 = add_SNo x18 (minus_SNo 1)) ⟶ x12 = 2 ⟶ x13 = 1 ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x14 x18 x19 x20 = If_i (SNoLe x18 0) x19 (x9 (x14 (add_SNo x18 (minus_SNo 1)) x19 x20) (x15 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x15 x18 x19 x20 = If_i (SNoLe x18 0) x20 (x10 (x14 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ x16 x18 = x14 (x11 x18) x12 x13) ⟶ (∀ x18 . x18 ∈ int ⟶ x17 x18 = add_SNo (mul_SNo x18 (x16 x18)) x18) ⟶ ∀ x18 . x18 ∈ int ⟶ SNoLe 0 x18 ⟶ x8 x18 = x17 x18
Conjecture 155ce..^A20766 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 . 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 . (∀ 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 . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ 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 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x36 x37 x38 x39 ∈ int) ⟶ ∀ x37 : ι → ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x37 x38 x39 x40 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ ∀ x40 . x40 ∈ int ⟶ ∀ x41 : ι → ι → ι . (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x41 x42 x43 ∈ int) ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι → ι . (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x43 x44 x45 ∈ int) ⟶ ∀ x44 : ι → ι → ι . (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x44 x45 x46 ∈ int) ⟶ ∀ x45 : ι → ι . (∀ x46 . x46 ∈ int ⟶ x45 x46 ∈ int) ⟶ ∀ x46 . x46 ∈ 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 : ι → ι . (∀ x50 . x50 ∈ int ⟶ x49 x50 ∈ int) ⟶ (∀ x50 . x50 ∈ int ⟶ x0 x50 = mul_SNo 2 (add_SNo (add_SNo x50 x50) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x1 x50 = x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x2 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x3 x50 = x50) ⟶ x4 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x5 x50 x51 = If_i (SNoLe x50 0) x51 (x2 (x5 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x6 x50 = x5 (x3 x50) x4) ⟶ (∀ x50 . x50 ∈ int ⟶ x7 x50 = add_SNo (x6 x50) (minus_SNo 1)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x8 x50 x51 = If_i (SNoLe x50 0) x51 (x0 (x8 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x9 x50 = x8 (x1 x50) (x7 x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x10 x50 = x9 x50) ⟶ x11 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x12 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x13 x50 x51 = If_i (SNoLe x50 0) x51 (x10 (x13 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x14 x50 x51 = x13 x11 (x12 x50 x51)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x15 x50 x51 = mul_SNo (add_SNo 2 x51) x50) ⟶ x16 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ x17 x50 = x50) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x18 x50 x51 = If_i (SNoLe x50 0) x51 (x15 (x18 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x19 x50 = x18 x16 (x17 x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x20 x50 x51 = add_SNo (x14 x50 x51) (add_SNo (x19 x50) (minus_SNo x50))) ⟶ (∀ x50 . x50 ∈ int ⟶ x21 x50 = x50) ⟶ x22 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x23 x50 x51 = If_i (SNoLe x50 0) x51 (x20 (x23 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x24 x50 = x23 (x21 x50) x22) ⟶ (∀ x50 . x50 ∈ int ⟶ x25 x50 = x24 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x26 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x27 x50 = x50) ⟶ x28 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x29 x50 x51 = If_i (SNoLe x50 0) x51 (x26 (x29 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x30 x50 = x29 (x27 x50) x28) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x31 x50 x51 = mul_SNo x50 x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x32 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ x33 x50 = x50) ⟶ x34 = 1 ⟶ x35 = add_SNo 2 (add_SNo 2 2) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x36 x50 x51 x52 = If_i (SNoLe x50 0) x51 (x31 (x36 (add_SNo x50 (minus_SNo 1)) x51 x52) (x37 (add_SNo x50 (minus_SNo 1)) x51 x52))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x37 x50 x51 x52 = If_i (SNoLe x50 0) x52 (x32 (x36 (add_SNo x50 (minus_SNo 1)) x51 x52) (x37 (add_SNo x50 (minus_SNo 1)) x51 x52))) ⟶ (∀ x50 . x50 ∈ int ⟶ x38 x50 = x36 (x33 x50) x34 x35) ⟶ (∀ x50 . x50 ∈ int ⟶ x39 x50 = mul_SNo (add_SNo (x30 x50) (minus_SNo 1)) (x38 x50)) ⟶ x40 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x41 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x42 x50 x51 = If_i (SNoLe x50 0) x51 (x39 (x42 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x43 x50 x51 = x42 x40 (x41 x50 x51)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x44 x50 x51 = add_SNo (add_SNo (x43 x50 x51) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x50 x50)) x50))) x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x45 x50 = x50) ⟶ x46 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x47 x50 x51 = If_i (SNoLe x50 0) x51 (x44 (x47 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x48 x50 = x47 (x45 x50) x46) ⟶ (∀ x50 . x50 ∈ int ⟶ x49 x50 = x48 x50) ⟶ ∀ x50 . x50 ∈ int ⟶ SNoLe 0 x50 ⟶ x25 x50 = x49 x50
Conjecture 19b53..^A20758 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ 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 . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 : ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ int) ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x31 x32 x33 x34 ∈ int) ⟶ ∀ x32 : ι → ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x32 x33 x34 x35 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 : ι → ι . (∀ x35 . x35 ∈ int ⟶ x34 x35 ∈ int) ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x36 x37 x38 ∈ int) ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι → ι . (∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x38 x39 x40 ∈ int) ⟶ ∀ x39 : ι → ι → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x39 x40 x41 ∈ int) ⟶ ∀ x40 : ι → ι . (∀ x41 . x41 ∈ int ⟶ x40 x41 ∈ int) ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ ∀ x44 : ι → ι . (∀ x45 . x45 ∈ int ⟶ x44 x45 ∈ int) ⟶ ∀ x45 : ι → ι . (∀ x46 . x46 ∈ int ⟶ x45 x46 ∈ int) ⟶ ∀ x46 . x46 ∈ 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 : ι → ι . (∀ x50 . x50 ∈ int ⟶ x49 x50 ∈ int) ⟶ (∀ x50 . x50 ∈ int ⟶ x0 x50 = mul_SNo 2 (add_SNo (add_SNo x50 x50) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x1 x50 = x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x2 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x3 x50 = x50) ⟶ x4 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x5 x50 x51 = If_i (SNoLe x50 0) x51 (x2 (x5 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x6 x50 = x5 (x3 x50) x4) ⟶ (∀ x50 . x50 ∈ int ⟶ x7 x50 = add_SNo (x6 x50) (minus_SNo 1)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x8 x50 x51 = If_i (SNoLe x50 0) x51 (x0 (x8 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x9 x50 = x8 (x1 x50) (x7 x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x10 x50 = x9 x50) ⟶ x11 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x12 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x13 x50 x51 = If_i (SNoLe x50 0) x51 (x10 (x13 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x14 x50 x51 = x13 x11 (x12 x50 x51)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x15 x50 x51 = add_SNo (x14 x50 x51) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x50 x50)) x50))) ⟶ (∀ x50 . x50 ∈ int ⟶ x16 x50 = x50) ⟶ x17 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x18 x50 x51 = If_i (SNoLe x50 0) x51 (x15 (x18 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x19 x50 = x18 (x16 x50) x17) ⟶ (∀ x50 . x50 ∈ int ⟶ x20 x50 = x19 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x21 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x22 x50 = x50) ⟶ x23 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x24 x50 x51 = If_i (SNoLe x50 0) x51 (x21 (x24 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x25 x50 = x24 (x22 x50) x23) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x26 x50 x51 = mul_SNo x50 x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x27 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ x28 x50 = x50) ⟶ x29 = 1 ⟶ x30 = add_SNo 1 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x31 x50 x51 x52 = If_i (SNoLe x50 0) x51 (x26 (x31 (add_SNo x50 (minus_SNo 1)) x51 x52) (x32 (add_SNo x50 (minus_SNo 1)) x51 x52))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x32 x50 x51 x52 = If_i (SNoLe x50 0) x52 (x27 (x31 (add_SNo x50 (minus_SNo 1)) x51 x52) (x32 (add_SNo x50 (minus_SNo 1)) x51 x52))) ⟶ (∀ x50 . x50 ∈ int ⟶ x33 x50 = x31 (x28 x50) x29 x30) ⟶ (∀ x50 . x50 ∈ int ⟶ x34 x50 = mul_SNo (add_SNo (x25 x50) (minus_SNo 1)) (x33 x50)) ⟶ x35 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x36 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x37 x50 x51 = If_i (SNoLe x50 0) x51 (x34 (x37 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x38 x50 x51 = x37 x35 (x36 x50 x51)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x39 x50 x51 = add_SNo (add_SNo (x38 x50 x51) (mul_SNo 2 (add_SNo x50 x50))) x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x40 x50 = x50) ⟶ x41 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x42 x50 x51 = If_i (SNoLe x50 0) x51 (x39 (x42 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x43 x50 = x42 (x40 x50) x41) ⟶ (∀ x50 . x50 ∈ int ⟶ x44 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x45 x50 = x50) ⟶ x46 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x47 x50 x51 = If_i (SNoLe x50 0) x51 (x44 (x47 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x48 x50 = x47 (x45 x50) x46) ⟶ (∀ x50 . x50 ∈ int ⟶ x49 x50 = mul_SNo (x43 x50) (x48 x50)) ⟶ ∀ x50 . x50 ∈ int ⟶ SNoLe 0 x50 ⟶ x20 x50 = x49 x50
Conjecture efa92..^A20726 : ∀ 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 : 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 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x36 x37 x38 ∈ int) ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι → ι . (∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x38 x39 x40 ∈ int) ⟶ ∀ x39 : ι → ι → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x39 x40 x41 ∈ int) ⟶ ∀ x40 : ι → ι . (∀ x41 . x41 ∈ int ⟶ x40 x41 ∈ int) ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ ∀ x44 : ι → ι . (∀ x45 . x45 ∈ int ⟶ x44 x45 ∈ int) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x0 x45 x46 = mul_SNo (add_SNo 2 x46) x45) ⟶ x1 = 2 ⟶ (∀ x45 . x45 ∈ int ⟶ x2 x45 = x45) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x3 x45 x46 = If_i (SNoLe x45 0) x46 (x0 (x3 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x4 x45 = x3 x1 (x2 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x5 x45 = add_SNo (x4 x45) (minus_SNo x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x6 x45 x46 = x46) ⟶ x7 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x8 x45 x46 = If_i (SNoLe x45 0) x46 (x5 (x8 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x9 x45 x46 = x8 (x6 x45 x46) x7) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x10 x45 x46 = add_SNo (x9 x45 x46) (mul_SNo 2 (add_SNo (add_SNo x45 x45) x45))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x11 x45 x46 = x46) ⟶ x12 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x13 x45 x46 = If_i (SNoLe x45 0) x46 (x10 (x13 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x14 x45 x46 = x13 (x11 x45 x46) x12) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x15 x45 x46 = add_SNo (x14 x45 x46) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x45 x45)) x45))) ⟶ (∀ x45 . x45 ∈ int ⟶ x16 x45 = x45) ⟶ x17 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x18 x45 x46 = If_i (SNoLe x45 0) x46 (x15 (x18 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x19 x45 = x18 (x16 x45) x17) ⟶ (∀ x45 . x45 ∈ int ⟶ x20 x45 = x19 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x21 x45 x46 = add_SNo (add_SNo (mul_SNo 2 (add_SNo x45 x45)) x45) x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x22 x45 x46 = add_SNo (add_SNo x46 x46) x46) ⟶ (∀ x45 . x45 ∈ int ⟶ x23 x45 = x45) ⟶ x24 = 1 ⟶ x25 = add_SNo 1 2 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x26 x45 x46 x47 = If_i (SNoLe x45 0) x46 (x21 (x26 (add_SNo x45 (minus_SNo 1)) x46 x47) (x27 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x27 x45 x46 x47 = If_i (SNoLe x45 0) x47 (x22 (x26 (add_SNo x45 (minus_SNo 1)) x46 x47) (x27 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ x28 x45 = x26 (x23 x45) x24 x25) ⟶ (∀ x45 . x45 ∈ int ⟶ x29 x45 = add_SNo x45 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x30 x45 = x45) ⟶ x31 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x32 x45 x46 = If_i (SNoLe x45 0) x46 (x29 (x32 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ x33 x45 = x32 (x30 x45) x31) ⟶ (∀ x45 . x45 ∈ int ⟶ x34 x45 = mul_SNo (x28 x45) (x33 x45)) ⟶ x35 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x36 x45 x46 = x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x37 x45 x46 = If_i (SNoLe x45 0) x46 (x34 (x37 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x38 x45 x46 = x37 x35 (x36 x45 x46)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x39 x45 x46 = add_SNo (add_SNo (x38 x45 x46) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x45 x45)) x45))) x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x40 x45 = x45) ⟶ x41 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x42 x45 x46 = If_i (SNoLe x45 0) x46 (x39 (x42 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x43 x45 = x42 (x40 x45) x41) ⟶ (∀ x45 . x45 ∈ int ⟶ x44 x45 = x43 x45) ⟶ ∀ x45 . x45 ∈ int ⟶ SNoLe 0 x45 ⟶ x20 x45 = x44 x45
Conjecture 32a47..^A2066 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ x0 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x1 x17 = add_SNo x17 x17) ⟶ x2 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x4 x17 = x3 (x1 x17) x2) ⟶ (∀ x17 . x17 ∈ int ⟶ x5 x17 = mul_SNo 2 (x4 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = mul_SNo x17 x17) ⟶ x7 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ x8 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x9 x17 = x17) ⟶ x10 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = If_i (SNoLe x17 0) x18 (x8 (x11 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x11 (x9 x17) x10) ⟶ (∀ x17 . x17 ∈ int ⟶ x13 x17 = x12 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x6 (x14 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 x7 (x13 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = mul_SNo 2 (mul_SNo (add_SNo 1 (add_SNo 2 2)) (x15 x17))) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture c9987..^A20606 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι → ι . (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x29 x30 x31 ∈ int) ⟶ ∀ x30 : ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x30 x31 x32 ∈ int) ⟶ ∀ x31 : ι → ι . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 : ι → ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x34 x35 x36 x37 ∈ int) ⟶ ∀ x35 : ι → ι → ι → ι . (∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x35 x36 x37 x38 ∈ int) ⟶ ∀ x36 : ι → ι . (∀ x37 . x37 ∈ int ⟶ x36 x37 ∈ int) ⟶ ∀ x37 : ι → ι . (∀ x38 . x38 ∈ int ⟶ x37 x38 ∈ int) ⟶ ∀ x38 . x38 ∈ int ⟶ ∀ 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 ⟶ x0 x48 = add_SNo (add_SNo x48 x48) x48) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x1 x48 x49 = add_SNo x49 x49) ⟶ x2 = 1 ⟶ (∀ 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 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x4 x48 x49 = x3 (x1 x48 x49) x2) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x5 x48 x49 = mul_SNo (add_SNo 2 x49) x48) ⟶ x6 = 2 ⟶ (∀ x48 . x48 ∈ int ⟶ x7 x48 = x48) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x8 x48 x49 = If_i (SNoLe x48 0) x49 (x5 (x8 (add_SNo x48 (minus_SNo 1)) x49) x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ x9 x48 = x8 x6 (x7 x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x10 x48 x49 = add_SNo (x4 x48 x49) (add_SNo (x9 x48) (minus_SNo x48))) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x11 x48 x49 = x49) ⟶ x12 = 1 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x13 x48 x49 = If_i (SNoLe x48 0) x49 (x10 (x13 (add_SNo x48 (minus_SNo 1)) x49) x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x14 x48 x49 = x13 (x11 x48 x49) x12) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x15 x48 x49 = add_SNo (x14 x48 x49) (mul_SNo 2 (add_SNo (add_SNo x48 x48) x48))) ⟶ (∀ x48 . x48 ∈ int ⟶ x16 x48 = x48) ⟶ x17 = 1 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x18 x48 x49 = If_i (SNoLe x48 0) x49 (x15 (x18 (add_SNo x48 (minus_SNo 1)) x49) x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ x19 x48 = x18 (x16 x48) x17) ⟶ (∀ x48 . x48 ∈ int ⟶ x20 x48 = x19 x48) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x21 x48 x49 = add_SNo (add_SNo (add_SNo x48 x48) x48) x49) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x22 x48 x49 = add_SNo x49 x49) ⟶ (∀ x48 . x48 ∈ int ⟶ x23 x48 = x48) ⟶ x24 = 1 ⟶ x25 = 2 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x26 x48 x49 x50 = If_i (SNoLe x48 0) x49 (x21 (x26 (add_SNo x48 (minus_SNo 1)) x49 x50) (x27 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x27 x48 x49 x50 = If_i (SNoLe x48 0) x50 (x22 (x26 (add_SNo x48 (minus_SNo 1)) x49 x50) (x27 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ x28 x48 = x26 (x23 x48) x24 x25) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x29 x48 x49 = mul_SNo x48 x49) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x30 x48 x49 = x49) ⟶ (∀ x48 . x48 ∈ int ⟶ x31 x48 = x48) ⟶ x32 = 1 ⟶ x33 = add_SNo 1 2 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x34 x48 x49 x50 = If_i (SNoLe x48 0) x49 (x29 (x34 (add_SNo x48 (minus_SNo 1)) x49 x50) (x35 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x35 x48 x49 x50 = If_i (SNoLe x48 0) x50 (x30 (x34 (add_SNo x48 (minus_SNo 1)) x49 x50) (x35 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ x36 x48 = x34 (x31 x48) x32 x33) ⟶ (∀ x48 . x48 ∈ int ⟶ x37 x48 = mul_SNo (x28 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 (mul_SNo 2 (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 ⟶ x20 x48 = x47 x48
Conjecture 04070..^A20595 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x25 x26 x27 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 : ι → ι → ι → ι . (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x29 x30 x31 x32 ∈ int) ⟶ ∀ x30 : ι → ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x30 x31 x32 x33 ∈ int) ⟶ ∀ x31 : ι → ι . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ ∀ x32 : ι → ι . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ int) ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι → ι . (∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x35 x36 x37 ∈ int) ⟶ ∀ x36 : ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x36 x37 x38 ∈ int) ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 : ι → ι → ι . (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x40 x41 x42 ∈ int) ⟶ ∀ x41 : ι → ι . (∀ x42 . x42 ∈ int ⟶ x41 x42 ∈ int) ⟶ ∀ x42 : ι → ι . (∀ x43 . x43 ∈ int ⟶ x42 x43 ∈ int) ⟶ (∀ x43 . x43 ∈ int ⟶ x0 x43 = add_SNo (add_SNo x43 x43) x43) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x1 x43 x44 = add_SNo x44 x44) ⟶ x2 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x3 x43 x44 = If_i (SNoLe x43 0) x44 (x0 (x3 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x4 x43 x44 = x3 (x1 x43 x44) x2) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x5 x43 x44 = add_SNo (x4 x43 x44) (mul_SNo 2 (add_SNo (add_SNo x43 x43) x43))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x6 x43 x44 = x44) ⟶ x7 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x8 x43 x44 = If_i (SNoLe x43 0) x44 (x5 (x8 (add_SNo x43 (minus_SNo 1)) x44) x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x9 x43 x44 = x8 (x6 x43 x44) x7) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x10 x43 x44 = add_SNo (x9 x43 x44) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x43 x43)) x43))) ⟶ (∀ x43 . x43 ∈ int ⟶ x11 x43 = x43) ⟶ x12 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x13 x43 x44 = If_i (SNoLe x43 0) x44 (x10 (x13 (add_SNo x43 (minus_SNo 1)) x44) x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x14 x43 = x13 (x11 x43) x12) ⟶ (∀ x43 . x43 ∈ int ⟶ x15 x43 = x14 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x16 x43 x44 = add_SNo (add_SNo (add_SNo x43 x43) x43) x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x17 x43 x44 = add_SNo x44 x44) ⟶ (∀ x43 . x43 ∈ int ⟶ x18 x43 = x43) ⟶ x19 = 1 ⟶ x20 = 2 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x21 x43 x44 x45 = If_i (SNoLe x43 0) x44 (x16 (x21 (add_SNo x43 (minus_SNo 1)) x44 x45) (x22 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x22 x43 x44 x45 = If_i (SNoLe x43 0) x45 (x17 (x21 (add_SNo x43 (minus_SNo 1)) x44 x45) (x22 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ x23 x43 = x21 (x18 x43) x19 x20) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x24 x43 x44 = mul_SNo x43 x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x25 x43 x44 = x44) ⟶ (∀ x43 . x43 ∈ int ⟶ x26 x43 = x43) ⟶ x27 = 1 ⟶ x28 = add_SNo 1 2 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x29 x43 x44 x45 = If_i (SNoLe x43 0) x44 (x24 (x29 (add_SNo x43 (minus_SNo 1)) x44 x45) (x30 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x30 x43 x44 x45 = If_i (SNoLe x43 0) x45 (x25 (x29 (add_SNo x43 (minus_SNo 1)) x44 x45) (x30 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ x31 x43 = x29 (x26 x43) x27 x28) ⟶ (∀ x43 . x43 ∈ int ⟶ x32 x43 = mul_SNo (x23 x43) (x31 x43)) ⟶ x33 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x34 x43 x44 = x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x35 x43 x44 = If_i (SNoLe x43 0) x44 (x32 (x35 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x36 x43 x44 = x35 x33 (x34 x43 x44)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x37 x43 x44 = add_SNo (x36 x43 x44) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x43 x43)) x43))) ⟶ (∀ x43 . x43 ∈ int ⟶ x38 x43 = x43) ⟶ x39 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x40 x43 x44 = If_i (SNoLe x43 0) x44 (x37 (x40 (add_SNo x43 (minus_SNo 1)) x44) x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x41 x43 = x40 (x38 x43) x39) ⟶ (∀ x43 . x43 ∈ int ⟶ x42 x43 = x41 x43) ⟶ ∀ x43 . x43 ∈ int ⟶ SNoLe 0 x43 ⟶ x15 x43 = x42 x43
Conjecture fa1f9..^A20594 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ 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 . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 : ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ int) ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x31 x32 x33 x34 ∈ int) ⟶ ∀ x32 : ι → ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x32 x33 x34 x35 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 : ι → ι . (∀ x35 . x35 ∈ int ⟶ x34 x35 ∈ int) ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x36 x37 x38 ∈ int) ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι → ι . (∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x38 x39 x40 ∈ int) ⟶ ∀ x39 : ι → ι → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x39 x40 x41 ∈ int) ⟶ ∀ x40 : ι → ι . (∀ x41 . x41 ∈ int ⟶ x40 x41 ∈ int) ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ ∀ x44 : ι → ι . (∀ x45 . x45 ∈ int ⟶ x44 x45 ∈ int) ⟶ ∀ x45 : ι → ι . (∀ x46 . x46 ∈ int ⟶ x45 x46 ∈ int) ⟶ ∀ x46 . x46 ∈ 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 : ι → ι . (∀ x50 . x50 ∈ int ⟶ x49 x50 ∈ int) ⟶ (∀ x50 . x50 ∈ int ⟶ x0 x50 = mul_SNo 2 (add_SNo (add_SNo x50 x50) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x1 x50 = x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x2 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x3 x50 = x50) ⟶ x4 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x5 x50 x51 = If_i (SNoLe x50 0) x51 (x2 (x5 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x6 x50 = x5 (x3 x50) x4) ⟶ (∀ x50 . x50 ∈ int ⟶ x7 x50 = add_SNo (x6 x50) (minus_SNo 1)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x8 x50 x51 = If_i (SNoLe x50 0) x51 (x0 (x8 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x9 x50 = x8 (x1 x50) (x7 x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x10 x50 = x9 x50) ⟶ x11 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x12 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x13 x50 x51 = If_i (SNoLe x50 0) x51 (x10 (x13 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x14 x50 x51 = x13 x11 (x12 x50 x51)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x15 x50 x51 = add_SNo (x14 x50 x51) (mul_SNo 2 (mul_SNo 2 (add_SNo x50 x50)))) ⟶ (∀ x50 . x50 ∈ int ⟶ x16 x50 = x50) ⟶ x17 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x18 x50 x51 = If_i (SNoLe x50 0) x51 (x15 (x18 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x19 x50 = x18 (x16 x50) x17) ⟶ (∀ x50 . x50 ∈ int ⟶ x20 x50 = x19 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x21 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x22 x50 = x50) ⟶ x23 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x24 x50 x51 = If_i (SNoLe x50 0) x51 (x21 (x24 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x25 x50 = x24 (x22 x50) x23) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x26 x50 x51 = mul_SNo x50 x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x27 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ x28 x50 = x50) ⟶ x29 = 1 ⟶ x30 = add_SNo 1 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x31 x50 x51 x52 = If_i (SNoLe x50 0) x51 (x26 (x31 (add_SNo x50 (minus_SNo 1)) x51 x52) (x32 (add_SNo x50 (minus_SNo 1)) x51 x52))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x32 x50 x51 x52 = If_i (SNoLe x50 0) x52 (x27 (x31 (add_SNo x50 (minus_SNo 1)) x51 x52) (x32 (add_SNo x50 (minus_SNo 1)) x51 x52))) ⟶ (∀ x50 . x50 ∈ int ⟶ x33 x50 = x31 (x28 x50) x29 x30) ⟶ (∀ x50 . x50 ∈ int ⟶ x34 x50 = mul_SNo (add_SNo (x25 x50) (minus_SNo 1)) (x33 x50)) ⟶ x35 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x36 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x37 x50 x51 = If_i (SNoLe x50 0) x51 (x34 (x37 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x38 x50 x51 = x37 x35 (x36 x50 x51)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x39 x50 x51 = add_SNo (x38 x50 x51) (mul_SNo 2 (add_SNo x50 x50))) ⟶ (∀ x50 . x50 ∈ int ⟶ x40 x50 = x50) ⟶ x41 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x42 x50 x51 = If_i (SNoLe x50 0) x51 (x39 (x42 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x43 x50 = x42 (x40 x50) x41) ⟶ (∀ x50 . x50 ∈ int ⟶ x44 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x45 x50 = x50) ⟶ x46 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x47 x50 x51 = If_i (SNoLe x50 0) x51 (x44 (x47 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x48 x50 = x47 (x45 x50) x46) ⟶ (∀ x50 . x50 ∈ int ⟶ x49 x50 = mul_SNo (x43 x50) (x48 x50)) ⟶ ∀ x50 . x50 ∈ int ⟶ SNoLe 0 x50 ⟶ x20 x50 = x49 x50
Conjecture ec029..^A20593 : ∀ 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 . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 : ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x30 x31 x32 ∈ int) ⟶ ∀ x31 : ι → ι . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ ∀ x32 : ι → ι . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ int) ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι → ι . (∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x35 x36 x37 ∈ int) ⟶ ∀ x36 : ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x36 x37 x38 ∈ int) ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 : ι → ι → ι . (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x40 x41 x42 ∈ int) ⟶ ∀ x41 : ι → ι . (∀ x42 . x42 ∈ int ⟶ x41 x42 ∈ int) ⟶ ∀ x42 : ι → ι . (∀ x43 . x43 ∈ int ⟶ x42 x43 ∈ int) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x0 x43 x44 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x43 x43) x43)) (mul_SNo (mul_SNo x44 x44) x44)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x1 x43 x44 = add_SNo x44 x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x2 x43 x44 = x44) ⟶ x3 = 1 ⟶ x4 = 2 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x5 x43 x44 x45 = If_i (SNoLe x43 0) x44 (x0 (x5 (add_SNo x43 (minus_SNo 1)) x44 x45) (x6 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x6 x43 x44 x45 = If_i (SNoLe x43 0) x45 (x1 (x5 (add_SNo x43 (minus_SNo 1)) x44 x45) (x6 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x7 x43 x44 = x5 (x2 x43 x44) x3 x4) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x8 x43 x44 = mul_SNo (add_SNo 2 x44) x43) ⟶ x9 = 2 ⟶ (∀ x43 . x43 ∈ int ⟶ x10 x43 = x43) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x11 x43 x44 = If_i (SNoLe x43 0) x44 (x8 (x11 (add_SNo x43 (minus_SNo 1)) x44) x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x12 x43 = x11 x9 (x10 x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x13 x43 x44 = add_SNo (add_SNo (x7 x43 x44) (minus_SNo x43)) (x12 x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x14 x43 = x43) ⟶ x15 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x16 x43 x44 = If_i (SNoLe x43 0) x44 (x13 (x16 (add_SNo x43 (minus_SNo 1)) x44) x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x17 x43 = x16 (x14 x43) x15) ⟶ (∀ x43 . x43 ∈ int ⟶ x18 x43 = x17 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x19 x43 x44 = add_SNo (add_SNo (add_SNo (mul_SNo x44 x44) x43) x43) x43) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x20 x43 x44 = add_SNo x44 x44) ⟶ (∀ x43 . x43 ∈ int ⟶ x21 x43 = x43) ⟶ x22 = 1 ⟶ x23 = 2 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x24 x43 x44 x45 = If_i (SNoLe x43 0) x44 (x19 (x24 (add_SNo x43 (minus_SNo 1)) x44 x45) (x25 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x25 x43 x44 x45 = If_i (SNoLe x43 0) x45 (x20 (x24 (add_SNo x43 (minus_SNo 1)) x44 x45) (x25 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ x26 x43 = x24 (x21 x43) x22 x23) ⟶ (∀ x43 . x43 ∈ int ⟶ x27 x43 = add_SNo x43 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x28 x43 = add_SNo x43 (minus_SNo 1)) ⟶ x29 = 2 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x30 x43 x44 = If_i (SNoLe x43 0) x44 (x27 (x30 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ x31 x43 = x30 (x28 x43) x29) ⟶ (∀ x43 . x43 ∈ int ⟶ x32 x43 = mul_SNo (x26 x43) (x31 x43)) ⟶ x33 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x34 x43 x44 = x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x35 x43 x44 = If_i (SNoLe x43 0) x44 (x32 (x35 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x36 x43 x44 = x35 x33 (x34 x43 x44)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x37 x43 x44 = add_SNo (add_SNo (x36 x43 x44) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x43 x43)) x43))) x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x38 x43 = x43) ⟶ x39 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x40 x43 x44 = If_i (SNoLe x43 0) x44 (x37 (x40 (add_SNo x43 (minus_SNo 1)) x44) x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x41 x43 = x40 (x38 x43) x39) ⟶ (∀ x43 . x43 ∈ int ⟶ x42 x43 = x41 x43) ⟶ ∀ x43 . x43 ∈ int ⟶ SNoLe 0 x43 ⟶ x18 x43 = x42 x43
Conjecture 836e9..^A20579 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ 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 . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ int) ⟶ ∀ x31 : ι → ι . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ 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 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x36 x37 x38 ∈ int) ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι → ι . (∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x38 x39 x40 ∈ int) ⟶ ∀ x39 : ι → ι → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x39 x40 x41 ∈ int) ⟶ ∀ x40 : ι → ι . (∀ x41 . x41 ∈ int ⟶ x40 x41 ∈ int) ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ ∀ x44 : ι → ι . (∀ x45 . x45 ∈ int ⟶ x44 x45 ∈ int) ⟶ (∀ x45 . x45 ∈ int ⟶ x0 x45 = add_SNo (add_SNo x45 x45) x45) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x1 x45 x46 = add_SNo x46 x46) ⟶ x2 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x3 x45 x46 = If_i (SNoLe x45 0) x46 (x0 (x3 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x4 x45 x46 = x3 (x1 x45 x46) x2) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x5 x45 x46 = add_SNo (x4 x45 x46) (mul_SNo 2 (add_SNo (add_SNo x45 x45) x45))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x6 x45 x46 = x46) ⟶ x7 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x8 x45 x46 = If_i (SNoLe x45 0) x46 (x5 (x8 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x9 x45 x46 = x8 (x6 x45 x46) x7) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x10 x45 x46 = add_SNo (x9 x45 x46) (mul_SNo 2 (mul_SNo 2 (add_SNo x45 x45)))) ⟶ (∀ x45 . x45 ∈ int ⟶ x11 x45 = x45) ⟶ x12 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x13 x45 x46 = If_i (SNoLe x45 0) x46 (x10 (x13 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x14 x45 = x13 (x11 x45) x12) ⟶ (∀ x45 . x45 ∈ int ⟶ x15 x45 = x14 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x16 x45 x46 = mul_SNo x45 x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x17 x45 x46 = x46) ⟶ (∀ x45 . x45 ∈ int ⟶ x18 x45 = add_SNo 1 x45) ⟶ x19 = 1 ⟶ x20 = add_SNo 1 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x21 x45 x46 x47 = If_i (SNoLe x45 0) x46 (x16 (x21 (add_SNo x45 (minus_SNo 1)) x46 x47) (x22 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x22 x45 x46 x47 = If_i (SNoLe x45 0) x47 (x17 (x21 (add_SNo x45 (minus_SNo 1)) x46 x47) (x22 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ x23 x45 = x21 (x18 x45) x19 x20) ⟶ (∀ x45 . x45 ∈ int ⟶ x24 x45 = mul_SNo (mul_SNo x45 x45) x45) ⟶ x25 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ x26 x45 = add_SNo x45 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x27 x45 = x45) ⟶ x28 = 2 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x29 x45 x46 = If_i (SNoLe x45 0) x46 (x26 (x29 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ x30 x45 = x29 (x27 x45) x28) ⟶ (∀ x45 . x45 ∈ int ⟶ x31 x45 = x30 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x32 x45 x46 = If_i (SNoLe x45 0) x46 (x24 (x32 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ x33 x45 = x32 x25 (x31 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x34 x45 = add_SNo (x23 x45) (minus_SNo (x33 x45))) ⟶ x35 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x36 x45 x46 = x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x37 x45 x46 = If_i (SNoLe x45 0) x46 (x34 (x37 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x38 x45 x46 = x37 x35 (x36 x45 x46)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x39 x45 x46 = add_SNo (add_SNo (add_SNo (add_SNo (add_SNo (add_SNo (x38 x45 x46) x45) x45) x45) x45) x45) x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x40 x45 = x45) ⟶ x41 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x42 x45 x46 = If_i (SNoLe x45 0) x46 (x39 (x42 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x43 x45 = x42 (x40 x45) x41) ⟶ (∀ x45 . x45 ∈ int ⟶ x44 x45 = x43 x45) ⟶ ∀ x45 . x45 ∈ int ⟶ SNoLe 0 x45 ⟶ x15 x45 = x44 x45
Conjecture 39c5e..^A20577 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ 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 . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 : ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ int) ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x31 x32 x33 x34 ∈ int) ⟶ ∀ x32 : ι → ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x32 x33 x34 x35 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 : ι → ι . (∀ x35 . x35 ∈ int ⟶ x34 x35 ∈ int) ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x36 x37 x38 ∈ int) ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι → ι . (∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x38 x39 x40 ∈ int) ⟶ ∀ x39 : ι → ι → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x39 x40 x41 ∈ int) ⟶ ∀ x40 : ι → ι . (∀ x41 . x41 ∈ int ⟶ x40 x41 ∈ int) ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ ∀ x44 : ι → ι . (∀ x45 . x45 ∈ int ⟶ x44 x45 ∈ int) ⟶ (∀ x45 . x45 ∈ int ⟶ x0 x45 = mul_SNo 2 (add_SNo (add_SNo x45 x45) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x1 x45 = x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x2 x45 = add_SNo x45 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x3 x45 = x45) ⟶ x4 = 2 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x5 x45 x46 = If_i (SNoLe x45 0) x46 (x2 (x5 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ x6 x45 = x5 (x3 x45) x4) ⟶ (∀ x45 . x45 ∈ int ⟶ x7 x45 = add_SNo (x6 x45) (minus_SNo 1)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x8 x45 x46 = If_i (SNoLe x45 0) x46 (x0 (x8 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ x9 x45 = x8 (x1 x45) (x7 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x10 x45 = x9 x45) ⟶ x11 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x12 x45 x46 = x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x13 x45 x46 = If_i (SNoLe x45 0) x46 (x10 (x13 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x14 x45 x46 = x13 x11 (x12 x45 x46)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x15 x45 x46 = add_SNo (add_SNo (x14 x45 x46) (mul_SNo 2 (add_SNo (add_SNo x45 x45) x45))) x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x16 x45 = x45) ⟶ x17 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x18 x45 x46 = If_i (SNoLe x45 0) x46 (x15 (x18 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x19 x45 = x18 (x16 x45) x17) ⟶ (∀ x45 . x45 ∈ int ⟶ x20 x45 = x19 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x21 x45 = add_SNo x45 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x22 x45 = x45) ⟶ x23 = 2 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x24 x45 x46 = If_i (SNoLe x45 0) x46 (x21 (x24 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ x25 x45 = x24 (x22 x45) x23) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x26 x45 x46 = mul_SNo x45 x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x27 x45 x46 = x46) ⟶ (∀ x45 . x45 ∈ int ⟶ x28 x45 = x45) ⟶ x29 = 1 ⟶ x30 = add_SNo 2 (add_SNo 2 2) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x31 x45 x46 x47 = If_i (SNoLe x45 0) x46 (x26 (x31 (add_SNo x45 (minus_SNo 1)) x46 x47) (x32 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x32 x45 x46 x47 = If_i (SNoLe x45 0) x47 (x27 (x31 (add_SNo x45 (minus_SNo 1)) x46 x47) (x32 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ x33 x45 = x31 (x28 x45) x29 x30) ⟶ (∀ x45 . x45 ∈ int ⟶ x34 x45 = mul_SNo (add_SNo (x25 x45) (minus_SNo 1)) (x33 x45)) ⟶ x35 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x36 x45 x46 = x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x37 x45 x46 = If_i (SNoLe x45 0) x46 (x34 (x37 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x38 x45 x46 = x37 x35 (x36 x45 x46)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x39 x45 x46 = add_SNo (add_SNo (x38 x45 x46) (mul_SNo 2 (add_SNo (add_SNo x45 x45) x45))) x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x40 x45 = x45) ⟶ x41 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x42 x45 x46 = If_i (SNoLe x45 0) x46 (x39 (x42 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x43 x45 = x42 (x40 x45) x41) ⟶ (∀ x45 . x45 ∈ int ⟶ x44 x45 = x43 x45) ⟶ ∀ x45 . x45 ∈ int ⟶ SNoLe 0 x45 ⟶ x20 x45 = x44 x45
Conjecture e9936..^A20573 : ∀ 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 (add_SNo x40 x40) x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x11 x40 x41 = x41) ⟶ x12 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x13 x40 x41 = If_i (SNoLe x40 0) x41 (x10 (x13 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x14 x40 x41 = x13 (x11 x40 x41) x12) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x15 x40 x41 = add_SNo (add_SNo (x14 x40 x41) (mul_SNo 2 (add_SNo (add_SNo x40 x40) x40))) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x16 x40 = x40) ⟶ x17 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x18 x40 x41 = If_i (SNoLe x40 0) x41 (x15 (x18 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x19 x40 = x18 (x16 x40) x17) ⟶ (∀ x40 . x40 ∈ int ⟶ x20 x40 = x19 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x21 x40 x41 = add_SNo (mul_SNo (add_SNo 1 2) (add_SNo (add_SNo x40 x40) x41)) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x22 x40 x41 = mul_SNo 2 (add_SNo (add_SNo x41 x41) x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x40) ⟶ x24 = 1 ⟶ x25 = 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 95615..^A20572 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : 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 ⟶ x0 x40 = mul_SNo 2 (add_SNo (add_SNo x40 x40) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x1 x40 x41 = x41) ⟶ x2 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x3 x40 x41 = If_i (SNoLe x40 0) x41 (x0 (x3 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x4 x40 x41 = x3 (x1 x40 x41) x2) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x5 x40 x41 = add_SNo (x4 x40 x41) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x6 x40 x41 = x41) ⟶ x7 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x8 x40 x41 = If_i (SNoLe x40 0) x41 (x5 (x8 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x9 x40 x41 = x8 (x6 x40 x41) x7) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ 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 ⟶ x11 x40 = x40) ⟶ 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 ⟶ x14 x40 = x13 (x11 x40) x12) ⟶ (∀ x40 . x40 ∈ int ⟶ x15 x40 = x14 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x16 x40 x41 = add_SNo (add_SNo (mul_SNo 2 (add_SNo x40 x40)) x40) x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x17 x40 x41 = add_SNo (add_SNo x41 x41) x41) ⟶ (∀ x40 . x40 ∈ int ⟶ x18 x40 = x40) ⟶ x19 = 1 ⟶ x20 = add_SNo 1 2 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x21 x40 x41 x42 = If_i (SNoLe x40 0) x41 (x16 (x21 (add_SNo x40 (minus_SNo 1)) x41 x42) (x22 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x22 x40 x41 x42 = If_i (SNoLe x40 0) x42 (x17 (x21 (add_SNo x40 (minus_SNo 1)) x41 x42) (x22 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x21 (x18 x40) x19 x20) ⟶ (∀ 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 = mul_SNo (x23 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 (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 ⟶ x15 x40 = x39 x40
Conjecture 38b42..^A20571 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x25 x26 x27 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 : ι → ι → ι → ι . (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x29 x30 x31 x32 ∈ int) ⟶ ∀ x30 : ι → ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x30 x31 x32 x33 ∈ int) ⟶ ∀ x31 : ι → ι . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ ∀ x32 : ι → ι . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ int) ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι → ι . (∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x35 x36 x37 ∈ int) ⟶ ∀ x36 : ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x36 x37 x38 ∈ int) ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 : ι → ι → ι . (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x40 x41 x42 ∈ int) ⟶ ∀ x41 : ι → ι . (∀ x42 . x42 ∈ int ⟶ x41 x42 ∈ int) ⟶ ∀ x42 : ι → ι . (∀ x43 . x43 ∈ int ⟶ x42 x43 ∈ int) ⟶ (∀ x43 . x43 ∈ int ⟶ x0 x43 = add_SNo (add_SNo x43 x43) x43) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x1 x43 x44 = add_SNo x44 x44) ⟶ x2 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x3 x43 x44 = If_i (SNoLe x43 0) x44 (x0 (x3 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x4 x43 x44 = x3 (x1 x43 x44) x2) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x5 x43 x44 = add_SNo (x4 x43 x44) (mul_SNo 2 (add_SNo (add_SNo x43 x43) x43))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x6 x43 x44 = x44) ⟶ x7 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x8 x43 x44 = If_i (SNoLe x43 0) x44 (x5 (x8 (add_SNo x43 (minus_SNo 1)) x44) x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x9 x43 x44 = x8 (x6 x43 x44) x7) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x10 x43 x44 = add_SNo (add_SNo (x9 x43 x44) (mul_SNo 2 (add_SNo (add_SNo x43 x43) x43))) x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x11 x43 = x43) ⟶ x12 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x13 x43 x44 = If_i (SNoLe x43 0) x44 (x10 (x13 (add_SNo x43 (minus_SNo 1)) x44) x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x14 x43 = x13 (x11 x43) x12) ⟶ (∀ x43 . x43 ∈ int ⟶ x15 x43 = x14 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x16 x43 x44 = add_SNo (add_SNo (add_SNo x43 x43) x43) x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x17 x43 x44 = add_SNo x44 x44) ⟶ (∀ x43 . x43 ∈ int ⟶ x18 x43 = x43) ⟶ x19 = 1 ⟶ x20 = 2 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x21 x43 x44 x45 = If_i (SNoLe x43 0) x44 (x16 (x21 (add_SNo x43 (minus_SNo 1)) x44 x45) (x22 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x22 x43 x44 x45 = If_i (SNoLe x43 0) x45 (x17 (x21 (add_SNo x43 (minus_SNo 1)) x44 x45) (x22 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ x23 x43 = x21 (x18 x43) x19 x20) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x24 x43 x44 = mul_SNo x43 x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x25 x43 x44 = x44) ⟶ (∀ x43 . x43 ∈ int ⟶ x26 x43 = x43) ⟶ x27 = 1 ⟶ x28 = add_SNo 1 2 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x29 x43 x44 x45 = If_i (SNoLe x43 0) x44 (x24 (x29 (add_SNo x43 (minus_SNo 1)) x44 x45) (x30 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x30 x43 x44 x45 = If_i (SNoLe x43 0) x45 (x25 (x29 (add_SNo x43 (minus_SNo 1)) x44 x45) (x30 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ x31 x43 = x29 (x26 x43) x27 x28) ⟶ (∀ x43 . x43 ∈ int ⟶ x32 x43 = mul_SNo (x23 x43) (x31 x43)) ⟶ x33 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x34 x43 x44 = x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x35 x43 x44 = If_i (SNoLe x43 0) x44 (x32 (x35 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x36 x43 x44 = x35 x33 (x34 x43 x44)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x37 x43 x44 = add_SNo (add_SNo (x36 x43 x44) (mul_SNo 2 (add_SNo (add_SNo x43 x43) x43))) x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x38 x43 = x43) ⟶ x39 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x40 x43 x44 = If_i (SNoLe x43 0) x44 (x37 (x40 (add_SNo x43 (minus_SNo 1)) x44) x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x41 x43 = x40 (x38 x43) x39) ⟶ (∀ x43 . x43 ∈ int ⟶ x42 x43 = x41 x43) ⟶ ∀ x43 . x43 ∈ int ⟶ SNoLe 0 x43 ⟶ x15 x43 = x42 x43
Conjecture 518fc..^A20569 : ∀ 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 . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x31 x32 x33 x34 ∈ int) ⟶ ∀ x32 : ι → ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x32 x33 x34 x35 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 : ι → ι . (∀ x35 . x35 ∈ int ⟶ x34 x35 ∈ int) ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x36 x37 x38 ∈ int) ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι → ι . (∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x38 x39 x40 ∈ int) ⟶ ∀ x39 : ι → ι → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x39 x40 x41 ∈ int) ⟶ ∀ x40 : ι → ι . (∀ x41 . x41 ∈ int ⟶ x40 x41 ∈ int) ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ ∀ x44 : ι → ι . (∀ x45 . x45 ∈ int ⟶ x44 x45 ∈ int) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x0 x45 x46 = mul_SNo (add_SNo 2 x46) x45) ⟶ x1 = 2 ⟶ (∀ x45 . x45 ∈ int ⟶ x2 x45 = x45) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x3 x45 x46 = If_i (SNoLe x45 0) x46 (x0 (x3 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x4 x45 = x3 x1 (x2 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x5 x45 = add_SNo (x4 x45) (minus_SNo x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x6 x45 x46 = x46) ⟶ x7 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x8 x45 x46 = If_i (SNoLe x45 0) x46 (x5 (x8 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x9 x45 x46 = x8 (x6 x45 x46) x7) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x10 x45 x46 = mul_SNo (add_SNo 2 x46) x45) ⟶ x11 = 2 ⟶ (∀ x45 . x45 ∈ int ⟶ x12 x45 = x45) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x13 x45 x46 = If_i (SNoLe x45 0) x46 (x10 (x13 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x14 x45 = x13 x11 (x12 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x15 x45 x46 = add_SNo (x9 x45 x46) (x14 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x16 x45 x46 = x46) ⟶ x17 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x18 x45 x46 = If_i (SNoLe x45 0) x46 (x15 (x18 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x19 x45 x46 = x18 (x16 x45 x46) x17) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x20 x45 x46 = add_SNo (add_SNo (x19 x45 x46) (mul_SNo 2 (add_SNo x45 x45))) x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x21 x45 = x45) ⟶ x22 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x23 x45 x46 = If_i (SNoLe x45 0) x46 (x20 (x23 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x24 x45 = x23 (x21 x45) x22) ⟶ (∀ x45 . x45 ∈ int ⟶ x25 x45 = x24 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x26 x45 x46 = add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo (add_SNo x45 x45) x45))) x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x27 x45 x46 = add_SNo (mul_SNo 2 (add_SNo x46 x46)) x46) ⟶ (∀ x45 . x45 ∈ int ⟶ x28 x45 = x45) ⟶ x29 = 1 ⟶ x30 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x31 x45 x46 x47 = If_i (SNoLe x45 0) x46 (x26 (x31 (add_SNo x45 (minus_SNo 1)) x46 x47) (x32 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x32 x45 x46 x47 = If_i (SNoLe x45 0) x47 (x27 (x31 (add_SNo x45 (minus_SNo 1)) x46 x47) (x32 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ x33 x45 = x31 (x28 x45) x29 x30) ⟶ (∀ x45 . x45 ∈ int ⟶ x34 x45 = x33 x45) ⟶ x35 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x36 x45 x46 = x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x37 x45 x46 = If_i (SNoLe x45 0) x46 (x34 (x37 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x38 x45 x46 = x37 x35 (x36 x45 x46)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x39 x45 x46 = add_SNo (add_SNo (x38 x45 x46) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x45 x45)) x45))) x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x40 x45 = x45) ⟶ x41 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x42 x45 x46 = If_i (SNoLe x45 0) x46 (x39 (x42 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x43 x45 = x42 (x40 x45) x41) ⟶ (∀ x45 . x45 ∈ int ⟶ x44 x45 = x43 x45) ⟶ ∀ x45 . x45 ∈ int ⟶ SNoLe 0 x45 ⟶ x25 x45 = x44 x45
Conjecture c4cd1..^A20568 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 . 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 . (∀ 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 . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ 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 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x36 x37 x38 x39 ∈ int) ⟶ ∀ x37 : ι → ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x37 x38 x39 x40 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ ∀ x40 . x40 ∈ int ⟶ ∀ x41 : ι → ι → ι . (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x41 x42 x43 ∈ int) ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι → ι . (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x43 x44 x45 ∈ int) ⟶ ∀ x44 : ι → ι → ι . (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x44 x45 x46 ∈ int) ⟶ ∀ x45 : ι → ι . (∀ x46 . x46 ∈ int ⟶ x45 x46 ∈ int) ⟶ ∀ x46 . x46 ∈ 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 : ι → ι . (∀ x50 . x50 ∈ int ⟶ x49 x50 ∈ int) ⟶ (∀ x50 . x50 ∈ int ⟶ x0 x50 = add_SNo (mul_SNo 2 (add_SNo x50 x50)) x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x1 x50 = x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x2 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x3 x50 = x50) ⟶ x4 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x5 x50 x51 = If_i (SNoLe x50 0) x51 (x2 (x5 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x6 x50 = x5 (x3 x50) x4) ⟶ (∀ x50 . x50 ∈ int ⟶ x7 x50 = add_SNo (x6 x50) (minus_SNo 1)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x8 x50 x51 = If_i (SNoLe x50 0) x51 (x0 (x8 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x9 x50 = x8 (x1 x50) (x7 x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x10 x50 = x9 x50) ⟶ x11 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x12 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x13 x50 x51 = If_i (SNoLe x50 0) x51 (x10 (x13 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x14 x50 x51 = x13 x11 (x12 x50 x51)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x15 x50 x51 = mul_SNo (add_SNo 2 x51) x50) ⟶ x16 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ x17 x50 = x50) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x18 x50 x51 = If_i (SNoLe x50 0) x51 (x15 (x18 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x19 x50 = x18 x16 (x17 x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x20 x50 x51 = add_SNo (x14 x50 x51) (x19 x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x21 x50 = x50) ⟶ x22 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x23 x50 x51 = If_i (SNoLe x50 0) x51 (x20 (x23 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x24 x50 = x23 (x21 x50) x22) ⟶ (∀ x50 . x50 ∈ int ⟶ x25 x50 = x24 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x26 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x27 x50 = x50) ⟶ x28 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x29 x50 x51 = If_i (SNoLe x50 0) x51 (x26 (x29 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x30 x50 = x29 (x27 x50) x28) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x31 x50 x51 = mul_SNo x50 x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x32 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ x33 x50 = x50) ⟶ x34 = 1 ⟶ x35 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x36 x50 x51 x52 = If_i (SNoLe x50 0) x51 (x31 (x36 (add_SNo x50 (minus_SNo 1)) x51 x52) (x37 (add_SNo x50 (minus_SNo 1)) x51 x52))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x37 x50 x51 x52 = If_i (SNoLe x50 0) x52 (x32 (x36 (add_SNo x50 (minus_SNo 1)) x51 x52) (x37 (add_SNo x50 (minus_SNo 1)) x51 x52))) ⟶ (∀ x50 . x50 ∈ int ⟶ x38 x50 = x36 (x33 x50) x34 x35) ⟶ (∀ x50 . x50 ∈ int ⟶ x39 x50 = mul_SNo (add_SNo (x30 x50) (minus_SNo 1)) (x38 x50)) ⟶ x40 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x41 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x42 x50 x51 = If_i (SNoLe x50 0) x51 (x39 (x42 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x43 x50 x51 = x42 x40 (x41 x50 x51)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x44 x50 x51 = add_SNo (x43 x50 x51) (mul_SNo 2 (mul_SNo 2 (add_SNo (add_SNo x50 x50) x50)))) ⟶ (∀ x50 . x50 ∈ int ⟶ x45 x50 = x50) ⟶ x46 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x47 x50 x51 = If_i (SNoLe x50 0) x51 (x44 (x47 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x48 x50 = x47 (x45 x50) x46) ⟶ (∀ x50 . x50 ∈ int ⟶ x49 x50 = x48 x50) ⟶ ∀ x50 . x50 ∈ int ⟶ SNoLe 0 x50 ⟶ x25 x50 = x49 x50
Conjecture 1d45d..^A20567 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 . 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 . (∀ 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 . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ 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 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x36 x37 x38 x39 ∈ int) ⟶ ∀ x37 : ι → ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x37 x38 x39 x40 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ ∀ x40 . x40 ∈ int ⟶ ∀ x41 : ι → ι → ι . (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x41 x42 x43 ∈ int) ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι → ι . (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x43 x44 x45 ∈ int) ⟶ ∀ x44 : ι → ι → ι . (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x44 x45 x46 ∈ int) ⟶ ∀ x45 : ι → ι . (∀ x46 . x46 ∈ int ⟶ x45 x46 ∈ int) ⟶ ∀ x46 . x46 ∈ 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 : ι → ι . (∀ x50 . x50 ∈ int ⟶ x49 x50 ∈ int) ⟶ (∀ x50 . x50 ∈ int ⟶ x0 x50 = add_SNo (mul_SNo 2 (add_SNo x50 x50)) x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x1 x50 = x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x2 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x3 x50 = x50) ⟶ x4 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x5 x50 x51 = If_i (SNoLe x50 0) x51 (x2 (x5 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x6 x50 = x5 (x3 x50) x4) ⟶ (∀ x50 . x50 ∈ int ⟶ x7 x50 = add_SNo (x6 x50) (minus_SNo 1)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x8 x50 x51 = If_i (SNoLe x50 0) x51 (x0 (x8 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x9 x50 = x8 (x1 x50) (x7 x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x10 x50 = x9 x50) ⟶ x11 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x12 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x13 x50 x51 = If_i (SNoLe x50 0) x51 (x10 (x13 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x14 x50 x51 = x13 x11 (x12 x50 x51)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x15 x50 x51 = mul_SNo (add_SNo 2 x51) x50) ⟶ x16 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ x17 x50 = x50) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x18 x50 x51 = If_i (SNoLe x50 0) x51 (x15 (x18 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x19 x50 = x18 x16 (x17 x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x20 x50 x51 = add_SNo (x14 x50 x51) (add_SNo (x19 x50) (minus_SNo x50))) ⟶ (∀ x50 . x50 ∈ int ⟶ x21 x50 = x50) ⟶ x22 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x23 x50 x51 = If_i (SNoLe x50 0) x51 (x20 (x23 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x24 x50 = x23 (x21 x50) x22) ⟶ (∀ x50 . x50 ∈ int ⟶ x25 x50 = x24 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x26 x50 = add_SNo x50 x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x27 x50 = x50) ⟶ x28 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x29 x50 x51 = If_i (SNoLe x50 0) x51 (x26 (x29 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x30 x50 = x29 (x27 x50) x28) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x31 x50 x51 = mul_SNo x50 x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x32 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ x33 x50 = x50) ⟶ x34 = 1 ⟶ x35 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x36 x50 x51 x52 = If_i (SNoLe x50 0) x51 (x31 (x36 (add_SNo x50 (minus_SNo 1)) x51 x52) (x37 (add_SNo x50 (minus_SNo 1)) x51 x52))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x37 x50 x51 x52 = If_i (SNoLe x50 0) x52 (x32 (x36 (add_SNo x50 (minus_SNo 1)) x51 x52) (x37 (add_SNo x50 (minus_SNo 1)) x51 x52))) ⟶ (∀ x50 . x50 ∈ int ⟶ x38 x50 = x36 (x33 x50) x34 x35) ⟶ (∀ x50 . x50 ∈ int ⟶ x39 x50 = mul_SNo (add_SNo (x30 x50) (minus_SNo 1)) (x38 x50)) ⟶ x40 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x41 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x42 x50 x51 = If_i (SNoLe x50 0) x51 (x39 (x42 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x43 x50 x51 = x42 x40 (x41 x50 x51)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x44 x50 x51 = add_SNo (add_SNo (x43 x50 x51) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x50 x50)) x50))) x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x45 x50 = x50) ⟶ x46 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x47 x50 x51 = If_i (SNoLe x50 0) x51 (x44 (x47 (add_SNo x50 (minus_SNo 1)) x51) x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ x48 x50 = x47 (x45 x50) x46) ⟶ (∀ x50 . x50 ∈ int ⟶ x49 x50 = x48 x50) ⟶ ∀ x50 . x50 ∈ int ⟶ SNoLe 0 x50 ⟶ x25 x50 = x49 x50
Conjecture 1a6bd..^A20566 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι → ι . (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x33 x34 x35 ∈ int) ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι . (∀ x36 . x36 ∈ int ⟶ x35 x36 ∈ int) ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ (∀ x40 . x40 ∈ int ⟶ x0 x40 = add_SNo (add_SNo x40 x40) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x1 x40 x41 = add_SNo x41 x41) ⟶ x2 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x3 x40 x41 = If_i (SNoLe x40 0) x41 (x0 (x3 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x4 x40 x41 = x3 (x1 x40 x41) x2) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x5 x40 x41 = mul_SNo (add_SNo 2 x41) x40) ⟶ x6 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ x7 x40 = x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x8 x40 x41 = If_i (SNoLe x40 0) x41 (x5 (x8 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x9 x40 = x8 x6 (x7 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x10 x40 x41 = add_SNo (x4 x40 x41) (x9 x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x11 x40 x41 = x41) ⟶ x12 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x13 x40 x41 = If_i (SNoLe x40 0) x41 (x10 (x13 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x14 x40 x41 = x13 (x11 x40 x41) x12) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x15 x40 x41 = add_SNo (add_SNo (x14 x40 x41) (mul_SNo 2 (add_SNo 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)) (mul_SNo x41 x41)) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x22 x40 x41 = add_SNo (add_SNo x41 x41) x41) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x40) ⟶ x24 = 1 ⟶ x25 = add_SNo 1 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 7c4af..^A20537 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . 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 = x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x2 x22 = mul_SNo 2 (add_SNo 2 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x3 x22 = add_SNo x22 x22) ⟶ x4 = 0 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x5 x22 x23 = If_i (SNoLe x22 0) x23 (x2 (x5 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x6 x22 = x5 (x3 x22) x4) ⟶ (∀ x22 . x22 ∈ int ⟶ x7 x22 = add_SNo 1 (x6 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x8 x22 x23 = If_i (SNoLe x22 0) x23 (x0 (x8 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x9 x22 = x8 (x1 x22) (x7 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x10 x22 = x9 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x11 x22 = add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo (mul_SNo (mul_SNo x22 x22) x22) (minus_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 = x20 x22) ⟶ ∀ x22 . x22 ∈ int ⟶ SNoLe 0 x22 ⟶ x10 x22 = x21 x22
Conjecture 0e624..^A20530 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . 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 = x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x2 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x3 x22 = add_SNo x22 x22) ⟶ x4 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x5 x22 x23 = If_i (SNoLe x22 0) x23 (x2 (x5 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x6 x22 = x5 (x3 x22) x4) ⟶ (∀ x22 . x22 ∈ int ⟶ x7 x22 = add_SNo 2 (x6 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x8 x22 x23 = If_i (SNoLe x22 0) x23 (x0 (x8 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x9 x22 = x8 (x1 x22) (x7 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x10 x22 = x9 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x11 x22 = mul_SNo (add_SNo 2 (mul_SNo x22 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 = x20 x22) ⟶ ∀ x22 . x22 ∈ int ⟶ SNoLe 0 x22 ⟶ x10 x22 = x21 x22