Proofgold Asset

Param int^int : ι
Param mul_SNo^mul_SNo : ι → ι → ι
Param ordsucc^ordsucc : ι → ι
Param add_SNo^add_SNo : ι → ι → ι
Param If_i^If_i : ο → ι → ι → ι
Param SNoLe^SNoLe : ι → ι → ο
Param minus_SNo^minus_SNo : ι → ι
Conjecture 33b55..^A257449 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . 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 . x22 ∈ int ⟶ ∀ x23 : ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x23 x24 x25 ∈ 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 → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 : ι → ι → 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 . x32 ∈ int ⟶ x0 x32 = mul_SNo x32 x32) ⟶ x1 = 2 ⟶ (∀ x32 . x32 ∈ int ⟶ x2 x32 = add_SNo 1 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x3 x32 x33 = If_i (SNoLe x32 0) x33 (x0 (x3 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x4 x32 = x3 x1 (x2 x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x5 x32 = mul_SNo x32 x32) ⟶ x6 = 2 ⟶ (∀ x32 . x32 ∈ int ⟶ x7 x32 = x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x8 x32 x33 = If_i (SNoLe x32 0) x33 (x5 (x8 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x9 x32 = x8 x6 (x7 x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x10 x32 = add_SNo (x4 x32) (minus_SNo (x9 x32))) ⟶ x11 = 1 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x12 x32 x33 = x33) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x13 x32 x33 = If_i (SNoLe x32 0) x33 (x10 (x13 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x14 x32 x33 = x13 x11 (x12 x32 x33)) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x15 x32 x33 = add_SNo (add_SNo (x14 x32 x33) x32) x32) ⟶ (∀ x32 . x32 ∈ int ⟶ x16 x32 = x32) ⟶ x17 = 1 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x18 x32 x33 = If_i (SNoLe x32 0) x33 (x15 (x18 (add_SNo x32 (minus_SNo 1)) x33) x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x19 x32 = x18 (x16 x32) x17) ⟶ (∀ x32 . x32 ∈ int ⟶ x20 x32 = x19 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ x21 x32 = mul_SNo (add_SNo 1 (add_SNo x32 x32)) (add_SNo 1 (mul_SNo 2 (add_SNo (mul_SNo x32 x32) x32)))) ⟶ x22 = 1 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x23 x32 x33 = x33) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x24 x32 x33 = If_i (SNoLe x32 0) x33 (x21 (x24 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x25 x32 x33 = x24 x22 (x23 x32 x33)) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x26 x32 x33 = add_SNo (add_SNo (x25 x32 x33) x32) x32) ⟶ (∀ x32 . x32 ∈ int ⟶ x27 x32 = x32) ⟶ x28 = 1 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x29 x32 x33 = If_i (SNoLe x32 0) x33 (x26 (x29 (add_SNo x32 (minus_SNo 1)) x33) x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x30 x32 = x29 (x27 x32) x28) ⟶ (∀ x32 . x32 ∈ int ⟶ x31 x32 = x30 x32) ⟶ ∀ x32 . x32 ∈ int ⟶ SNoLe 0 x32 ⟶ x20 x32 = x31 x32
Conjecture 64d9a..^A257285 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x23 x24 x25 x26 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x0 x26 x27 = mul_SNo 2 (add_SNo (add_SNo x26 x26) x27)) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x1 x26 x27 = add_SNo (mul_SNo 2 (add_SNo x27 x27)) x27) ⟶ (∀ x26 . x26 ∈ int ⟶ x2 x26 = x26) ⟶ x3 = 1 ⟶ x4 = 2 ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x5 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x0 (x5 (add_SNo x26 (minus_SNo 1)) x27 x28) (x6 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x6 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x1 (x5 (add_SNo x26 (minus_SNo 1)) x27 x28) (x6 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x7 x26 = x5 (x2 x26) x3 x4) ⟶ (∀ x26 . x26 ∈ int ⟶ x8 x26 = x7 x26) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x9 x26 x27 = mul_SNo x26 x27) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x10 x26 x27 = x27) ⟶ (∀ x26 . x26 ∈ int ⟶ x11 x26 = x26) ⟶ x12 = 2 ⟶ x13 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x14 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x9 (x14 (add_SNo x26 (minus_SNo 1)) x27 x28) (x15 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x15 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x10 (x14 (add_SNo x26 (minus_SNo 1)) x27 x28) (x15 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x16 x26 = x14 (x11 x26) x12 x13) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x17 x26 x27 = mul_SNo x26 x27) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x18 x26 x27 = x27) ⟶ (∀ x26 . x26 ∈ int ⟶ x19 x26 = x26) ⟶ x20 = add_SNo 1 2 ⟶ x21 = add_SNo 2 2 ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x22 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x17 (x22 (add_SNo x26 (minus_SNo 1)) x27 x28) (x23 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x23 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x18 (x22 (add_SNo x26 (minus_SNo 1)) x27 x28) (x23 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x24 x26 = x22 (x19 x26) x20 x21) ⟶ (∀ x26 . x26 ∈ int ⟶ x25 x26 = add_SNo (mul_SNo 2 (x16 x26)) (minus_SNo (x24 x26))) ⟶ ∀ x26 . x26 ∈ int ⟶ SNoLe 0 x26 ⟶ x8 x26 = x25 x26
Conjecture 1d1ec..^A2571 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 : ι → ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x32 x33 x34 x35 ∈ int) ⟶ ∀ x33 : ι → ι → ι → ι . (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x33 x34 x35 x36 ∈ int) ⟶ ∀ x34 : ι → ι . (∀ x35 . x35 ∈ int ⟶ x34 x35 ∈ int) ⟶ ∀ x35 : ι → ι . (∀ 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 → 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 → ι . (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x40 x41 x42 ∈ int) ⟶ ∀ x41 : ι → ι . (∀ x42 . x42 ∈ int ⟶ x41 x42 ∈ int) ⟶ ∀ x42 . x42 ∈ int ⟶ ∀ x43 : ι → ι → ι . (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x43 x44 x45 ∈ int) ⟶ ∀ x44 : ι → ι . (∀ x45 . x45 ∈ int ⟶ x44 x45 ∈ int) ⟶ ∀ x45 : ι → ι . (∀ x46 . x46 ∈ int ⟶ x45 x46 ∈ int) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x0 x46 x47 = add_SNo x46 x47) ⟶ (∀ x46 . x46 ∈ int ⟶ x1 x46 = x46) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x2 x46 x47 = add_SNo x47 x47) ⟶ x3 = 1 ⟶ x4 = 1 ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ ∀ x48 . x48 ∈ int ⟶ x5 x46 x47 x48 = If_i (SNoLe x46 0) x47 (x0 (x5 (add_SNo x46 (minus_SNo 1)) x47 x48) (x6 (add_SNo x46 (minus_SNo 1)) x47 x48))) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ ∀ x48 . x48 ∈ int ⟶ x6 x46 x47 x48 = If_i (SNoLe x46 0) x48 (x1 (x5 (add_SNo x46 (minus_SNo 1)) x47 x48))) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x7 x46 x47 = x5 (x2 x46 x47) x3 x4) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x8 x46 x47 = add_SNo (x7 x46 x47) (minus_SNo x46)) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x9 x46 x47 = add_SNo 1 x47) ⟶ x10 = 1 ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x11 x46 x47 = If_i (SNoLe x46 0) x47 (x8 (x11 (add_SNo x46 (minus_SNo 1)) x47) x46)) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x12 x46 x47 = x11 (x9 x46 x47) x10) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x13 x46 x47 = add_SNo (x12 x46 x47) (minus_SNo x46)) ⟶ (∀ x46 . x46 ∈ int ⟶ x14 x46 = x46) ⟶ x15 = 1 ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x16 x46 x47 = If_i (SNoLe x46 0) x47 (x13 (x16 (add_SNo x46 (minus_SNo 1)) x47) x46)) ⟶ (∀ x46 . x46 ∈ int ⟶ x17 x46 = x16 (x14 x46) x15) ⟶ (∀ x46 . x46 ∈ int ⟶ x18 x46 = x17 x46) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x19 x46 x47 = add_SNo x46 x47) ⟶ (∀ x46 . x46 ∈ int ⟶ x20 x46 = x46) ⟶ (∀ x46 . x46 ∈ int ⟶ x21 x46 = add_SNo x46 (minus_SNo 1)) ⟶ x22 = 2 ⟶ x23 = 1 ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ ∀ x48 . x48 ∈ int ⟶ x24 x46 x47 x48 = If_i (SNoLe x46 0) x47 (x19 (x24 (add_SNo x46 (minus_SNo 1)) x47 x48) (x25 (add_SNo x46 (minus_SNo 1)) x47 x48))) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ ∀ x48 . x48 ∈ int ⟶ x25 x46 x47 x48 = If_i (SNoLe x46 0) x48 (x20 (x24 (add_SNo x46 (minus_SNo 1)) x47 x48))) ⟶ (∀ x46 . x46 ∈ int ⟶ x26 x46 = x24 (x21 x46) x22 x23) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x27 x46 x47 = add_SNo x46 x47) ⟶ (∀ x46 . x46 ∈ int ⟶ x28 x46 = x46) ⟶ (∀ x46 . x46 ∈ int ⟶ x29 x46 = x46) ⟶ x30 = 2 ⟶ x31 = 1 ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ ∀ x48 . x48 ∈ int ⟶ x32 x46 x47 x48 = If_i (SNoLe x46 0) x47 (x27 (x32 (add_SNo x46 (minus_SNo 1)) x47 x48) (x33 (add_SNo x46 (minus_SNo 1)) x47 x48))) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ ∀ x48 . x48 ∈ int ⟶ x33 x46 x47 x48 = If_i (SNoLe x46 0) x48 (x28 (x32 (add_SNo x46 (minus_SNo 1)) x47 x48))) ⟶ (∀ x46 . x46 ∈ int ⟶ x34 x46 = x32 (x29 x46) x30 x31) ⟶ (∀ x46 . x46 ∈ int ⟶ x35 x46 = mul_SNo (x26 x46) (x34 x46)) ⟶ x36 = 1 ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x37 x46 x47 = x47) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x38 x46 x47 = If_i (SNoLe x46 0) x47 (x35 (x38 (add_SNo x46 (minus_SNo 1)) x47))) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x39 x46 x47 = x38 x36 (x37 x46 x47)) ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x40 x46 x47 = add_SNo (x39 x46 x47) (minus_SNo x46)) ⟶ (∀ x46 . x46 ∈ int ⟶ x41 x46 = x46) ⟶ x42 = 1 ⟶ (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x43 x46 x47 = If_i (SNoLe x46 0) x47 (x40 (x43 (add_SNo x46 (minus_SNo 1)) x47) x46)) ⟶ (∀ x46 . x46 ∈ int ⟶ x44 x46 = x43 (x41 x46) x42) ⟶ (∀ x46 . x46 ∈ int ⟶ x45 x46 = x44 x46) ⟶ ∀ x46 . x46 ∈ int ⟶ SNoLe 0 x46 ⟶ x18 x46 = x45 x46
Conjecture 525d6..^A256832 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι → 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 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x25 x26 x27 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x0 x28 x29 = add_SNo (add_SNo x28 x28) x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x1 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x2 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x3 x28 = x28) ⟶ x4 = 0 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x5 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x0 (x5 (add_SNo x28 (minus_SNo 1)) x29 x30) (x6 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x6 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x1 (x5 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x7 x28 x29 = x5 (x2 x28 x29) (x3 x28) x4) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x8 x28 x29 = x7 x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x28) ⟶ x10 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = If_i (SNoLe x28 0) x29 (x8 (x11 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x11 (x9 x28) x10) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x14 x28 x29 = add_SNo (add_SNo x28 x28) x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x16 x28 x29 = x29) ⟶ x17 = 2 ⟶ x18 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x19 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x14 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30) (x20 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x20 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x15 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x21 x28 x29 = x19 (x16 x28 x29) x17 x18) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x22 x28 x29 = mul_SNo (x21 x28 x29) x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x23 x28 = add_SNo x28 (minus_SNo 1)) ⟶ (∀ x28 . x28 ∈ int ⟶ x24 x28 = If_i (SNoLe x28 0) 1 2) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x25 x28 x29 = If_i (SNoLe x28 0) x29 (x22 (x25 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x25 (x23 x28) (x24 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = x26 x28) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture b30e8..^A256512 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x0 x23 x24 = mul_SNo 2 (mul_SNo x23 x24)) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x1 x23 x24 = x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x2 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x3 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x4 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x5 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x0 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x6 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x1 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x5 (x2 x23) (x3 x23) (x4 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x8 x23 = add_SNo x23 (x7 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x9 x23 = add_SNo x23 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x10 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x11 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x12 x23 x24 = If_i (SNoLe x23 0) x24 (x9 (x12 (add_SNo x23 (minus_SNo 1)) x24))) ⟶ (∀ x23 . x23 ∈ int ⟶ x13 x23 = x12 (x10 x23) (x11 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x14 x23 x24 = mul_SNo x23 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x15 x23 x24 = x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x16 x23 = add_SNo x23 (minus_SNo 2)) ⟶ (∀ x23 . x23 ∈ int ⟶ x17 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x18 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x19 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x14 (x19 (add_SNo x23 (minus_SNo 1)) x24 x25) (x20 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x20 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x15 (x19 (add_SNo x23 (minus_SNo 1)) x24 x25) (x20 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x21 x23 = x19 (x16 x23) (x17 x23) (x18 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = add_SNo (mul_SNo (mul_SNo (x13 x23) x23) (x21 x23)) x23) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x8 x23 = x22 x23
Conjecture ff447..^A255435 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ x0 x17 = mul_SNo x17 x17) ⟶ x1 = 2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x2 x17 x18 = x18) ⟶ (∀ 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 ⟶ ∀ x18 . x18 ∈ int ⟶ x4 x17 x18 = x3 x1 (x2 x17 x18)) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x5 x17 x18 = add_SNo (mul_SNo (mul_SNo (x4 x17 x18) x17) x18) x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = x17) ⟶ x7 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x8 x17 x18 = If_i (SNoLe x17 0) x18 (x5 (x8 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x9 x17 = x8 (x6 x17) x7) ⟶ (∀ x17 . x17 ∈ int ⟶ x10 x17 = x9 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = mul_SNo (add_SNo 1 (mul_SNo (mul_SNo (mul_SNo (mul_SNo x18 x18) x18) x18) x18)) x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x17) ⟶ x13 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x11 (x14 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 (x12 x17) x13) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = x15 x17) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x10 x17 = x16 x17
Conjecture eeb19..^A255433 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x0 x17 x18 = add_SNo (mul_SNo (mul_SNo (mul_SNo x17 x18) x18) x18) x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x1 x17 = x17) ⟶ x2 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x4 x17 = x3 (x1 x17) x2) ⟶ (∀ x17 . x17 ∈ int ⟶ x5 x17 = x4 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x6 x17 x18 = mul_SNo (add_SNo 1 (add_SNo (mul_SNo x18 x18) x18)) x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x7 x17 = add_SNo x17 (minus_SNo 1)) ⟶ x8 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x9 x17 x18 = If_i (SNoLe x17 0) x18 (x6 (x9 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x10 x17 = x9 (x7 x17) x8) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = mul_SNo x17 x18) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x13 x17 = add_SNo 1 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x11 (x14 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 (x12 x17) (x13 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = mul_SNo (x10 x17) (x15 x17)) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture ddb23..^A254 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x0 x22 x23 = mul_SNo x22 x23) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x1 x22 x23 = add_SNo x23 (minus_SNo 1)) ⟶ x2 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x3 x22 x23 = If_i (SNoLe x22 0) x23 (x0 (x3 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x4 x22 x23 = x3 (x1 x22 x23) x2) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x5 x22 x23 = add_SNo (mul_SNo x22 x23) (x4 x22 x23)) ⟶ (∀ x22 . x22 ∈ int ⟶ x6 x22 = x22) ⟶ x7 = 0 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x8 x22 x23 = If_i (SNoLe x22 0) x23 (x5 (x8 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x9 x22 = x8 (x6 x22) x7) ⟶ (∀ x22 . x22 ∈ int ⟶ x10 x22 = x9 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x11 x22 x23 = mul_SNo x22 x23) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x12 x22 x23 = add_SNo x23 (minus_SNo 1)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x13 x22 x23 = x23) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x14 x22 x23 = If_i (SNoLe x22 0) x23 (x11 (x14 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x15 x22 x23 = x14 (x12 x22 x23) (x13 x22 x23)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x16 x22 x23 = add_SNo (x15 x22 x23) (mul_SNo (add_SNo 1 x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x17 x22 = add_SNo x22 (minus_SNo 1)) ⟶ (∀ x22 . x22 ∈ int ⟶ x18 x22 = If_i (SNoLe x22 0) 0 1) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x19 x22 x23 = If_i (SNoLe x22 0) x23 (x16 (x19 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x20 x22 = x19 (x17 x22) (x18 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x21 x22 = x20 x22) ⟶ ∀ x22 . x22 ∈ int ⟶ SNoLe 0 x22 ⟶ x10 x22 = x21 x22
Conjecture 1cfac..^A254641 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → 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 : 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 → 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 : 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 → 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 . x22 ∈ int ⟶ ∀ x23 : ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x23 x24 x25 ∈ 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 → 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 : ι → ι → ι . (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x29 x30 x31 ∈ int) ⟶ ∀ x30 : ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x30 x31 x32 ∈ int) ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 : 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 . (∀ 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 . (∀ x41 . x41 ∈ int ⟶ x40 x41 ∈ int) ⟶ ∀ x41 : ι → ι . (∀ x42 . x42 ∈ int ⟶ x41 x42 ∈ int) ⟶ (∀ x42 . x42 ∈ int ⟶ x0 x42 = mul_SNo x42 x42) ⟶ x1 = 2 ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x2 x42 x43 = x43) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x3 x42 x43 = If_i (SNoLe x42 0) x43 (x0 (x3 (add_SNo x42 (minus_SNo 1)) x43))) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x4 x42 x43 = x3 x1 (x2 x42 x43)) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x5 x42 x43 = add_SNo (mul_SNo (mul_SNo (mul_SNo (x4 x42 x43) x43) x43) x43) x42) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x6 x42 x43 = x43) ⟶ (∀ x42 . x42 ∈ int ⟶ x7 x42 = x42) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x8 x42 x43 = If_i (SNoLe x42 0) x43 (x5 (x8 (add_SNo x42 (minus_SNo 1)) x43) x42)) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x9 x42 x43 = x8 (x6 x42 x43) (x7 x42)) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x10 x42 x43 = x9 x42 x43) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x11 x42 x43 = add_SNo 1 x43) ⟶ (∀ x42 . x42 ∈ int ⟶ x12 x42 = x42) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x13 x42 x43 = If_i (SNoLe x42 0) x43 (x10 (x13 (add_SNo x42 (minus_SNo 1)) x43) x42)) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x14 x42 x43 = x13 (x11 x42 x43) (x12 x42)) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x15 x42 x43 = x14 x42 x43) ⟶ (∀ x42 . x42 ∈ int ⟶ x16 x42 = x42) ⟶ x17 = 1 ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x18 x42 x43 = If_i (SNoLe x42 0) x43 (x15 (x18 (add_SNo x42 (minus_SNo 1)) x43) x42)) ⟶ (∀ x42 . x42 ∈ int ⟶ x19 x42 = x18 (x16 x42) x17) ⟶ (∀ x42 . x42 ∈ int ⟶ x20 x42 = x19 x42) ⟶ (∀ x42 . x42 ∈ int ⟶ x21 x42 = mul_SNo (mul_SNo x42 x42) x42) ⟶ x22 = 1 ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x23 x42 x43 = mul_SNo x43 x43) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x24 x42 x43 = If_i (SNoLe x42 0) x43 (x21 (x24 (add_SNo x42 (minus_SNo 1)) x43))) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x25 x42 x43 = x24 x22 (x23 x42 x43)) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x26 x42 x43 = add_SNo (mul_SNo (x25 x42 x43) x43) x42) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x27 x42 x43 = x43) ⟶ (∀ x42 . x42 ∈ int ⟶ x28 x42 = x42) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x29 x42 x43 = If_i (SNoLe x42 0) x43 (x26 (x29 (add_SNo x42 (minus_SNo 1)) x43) x42)) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x30 x42 x43 = x29 (x27 x42 x43) (x28 x42)) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x31 x42 x43 = x30 x42 x43) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x32 x42 x43 = x43) ⟶ (∀ x42 . x42 ∈ int ⟶ x33 x42 = x42) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x34 x42 x43 = If_i (SNoLe x42 0) x43 (x31 (x34 (add_SNo x42 (minus_SNo 1)) x43) x42)) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x35 x42 x43 = x34 (x32 x42 x43) (x33 x42)) ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x36 x42 x43 = x35 x42 x43) ⟶ (∀ x42 . x42 ∈ int ⟶ x37 x42 = add_SNo 1 x42) ⟶ x38 = 0 ⟶ (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x39 x42 x43 = If_i (SNoLe x42 0) x43 (x36 (x39 (add_SNo x42 (minus_SNo 1)) x43) x42)) ⟶ (∀ x42 . x42 ∈ int ⟶ x40 x42 = x39 (x37 x42) x38) ⟶ (∀ x42 . x42 ∈ int ⟶ x41 x42 = x40 x42) ⟶ ∀ x42 . x42 ∈ int ⟶ SNoLe 0 x42 ⟶ x20 x42 = x41 x42
Conjecture 0ca78..^A254620 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ x0 x28 = add_SNo (add_SNo x28 x28) x28) ⟶ x1 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ x2 x28 = add_SNo x28 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x3 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x3 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x4 x28 = x3 x1 (x2 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x5 x28 x29 = mul_SNo (add_SNo 1 (add_SNo x29 x29)) (x4 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = x28) ⟶ x7 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x8 x28 x29 = If_i (SNoLe x28 0) x29 (x5 (x8 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x8 (x6 x28) x7) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = x9 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x12 x28 x29 = add_SNo 2 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x28) ⟶ x14 = 1 ⟶ x15 = add_SNo 1 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x16 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x11 (x16 (add_SNo x28 (minus_SNo 1)) x29 x30) (x17 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x17 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x12 (x16 (add_SNo x28 (minus_SNo 1)) x29 x30) (x17 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x18 x28 = x16 (x13 x28) x14 x15) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x19 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x20 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x28) ⟶ x22 = 1 ⟶ x23 = add_SNo 2 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x24 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x19 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30) (x25 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x25 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x20 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30) (x25 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x24 (x21 x28) x22 x23) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = mul_SNo (x18 x28) (x26 x28)) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x10 x28 = x27 x28
Conjecture 1ad82..^A253826 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι → ι → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x28 x29 x30 x31 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 : ι → ι . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ int) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x0 x31 x32 = add_SNo (add_SNo x32 (minus_SNo x31)) (minus_SNo x31)) ⟶ (∀ x31 . x31 ∈ int ⟶ x1 x31 = x31) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x2 x31 x32 = mul_SNo 2 (add_SNo x32 x32)) ⟶ x3 = 1 ⟶ x4 = 1 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x5 x31 x32 x33 = If_i (SNoLe x31 0) x32 (x0 (x5 (add_SNo x31 (minus_SNo 1)) x32 x33) (x6 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x6 x31 x32 x33 = If_i (SNoLe x31 0) x33 (x1 (x5 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x7 x31 x32 = x5 (x2 x31 x32) x3 x4) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x8 x31 x32 = add_SNo (x7 x31 x32) x31) ⟶ (∀ x31 . x31 ∈ int ⟶ x9 x31 = x31) ⟶ x10 = 1 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x11 x31 x32 = If_i (SNoLe x31 0) x32 (x8 (x11 (add_SNo x31 (minus_SNo 1)) x32) x31)) ⟶ (∀ x31 . x31 ∈ int ⟶ x12 x31 = x11 (x9 x31) x10) ⟶ (∀ x31 . x31 ∈ int ⟶ x13 x31 = x12 x31) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x14 x31 x32 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x31 x31) x31)) (minus_SNo x32)) ⟶ (∀ x31 . x31 ∈ int ⟶ x15 x31 = x31) ⟶ (∀ x31 . x31 ∈ int ⟶ x16 x31 = add_SNo x31 (minus_SNo 1)) ⟶ (∀ x31 . x31 ∈ int ⟶ x17 x31 = add_SNo (If_i (SNoLe x31 0) 0 2) 1) ⟶ x18 = 1 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x19 x31 x32 x33 = If_i (SNoLe x31 0) x32 (x14 (x19 (add_SNo x31 (minus_SNo 1)) x32 x33) (x20 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x20 x31 x32 x33 = If_i (SNoLe x31 0) x33 (x15 (x19 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ x21 x31 = x19 (x16 x31) (x17 x31) x18) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x22 x31 x32 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x31 x31) x31)) (minus_SNo x32)) ⟶ (∀ x31 . x31 ∈ int ⟶ x23 x31 = x31) ⟶ (∀ x31 . x31 ∈ int ⟶ x24 x31 = x31) ⟶ x25 = 1 ⟶ x26 = 0 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x27 x31 x32 x33 = If_i (SNoLe x31 0) x32 (x22 (x27 (add_SNo x31 (minus_SNo 1)) x32 x33) (x28 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x28 x31 x32 x33 = If_i (SNoLe x31 0) x33 (x23 (x27 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ x29 x31 = x27 (x24 x31) x25 x26) ⟶ (∀ x31 . x31 ∈ int ⟶ x30 x31 = mul_SNo (x21 x31) (x29 x31)) ⟶ ∀ x31 . x31 ∈ int ⟶ SNoLe 0 x31 ⟶ x13 x31 = x30 x31
Conjecture 80356..^A253208 : ∀ 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 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x4 x17 = x3 (x1 x17) x2) ⟶ (∀ x17 . x17 ∈ int ⟶ x5 x17 = add_SNo 1 (add_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 = add_SNo 1 (add_SNo 2 (x15 x17))) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture ed84c..^A250652 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : 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 ⟶ x0 x12 = add_SNo 1 (add_SNo x12 x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x1 x12 = x12) ⟶ (∀ x12 . x12 ∈ int ⟶ x2 x12 = add_SNo 2 (add_SNo 2 x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x3 x12 x13 = If_i (SNoLe x12 0) x13 (x0 (x3 (add_SNo x12 (minus_SNo 1)) x13))) ⟶ (∀ x12 . x12 ∈ int ⟶ x4 x12 = x3 (x1 x12) (x2 x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x5 x12 = add_SNo (mul_SNo (x4 x12) (add_SNo 2 x12)) 1) ⟶ (∀ x12 . x12 ∈ int ⟶ x6 x12 = add_SNo x12 x12) ⟶ (∀ x12 . x12 ∈ int ⟶ x7 x12 = x12) ⟶ (∀ x12 . x12 ∈ int ⟶ x8 x12 = add_SNo 1 (add_SNo 2 (add_SNo 2 x12))) ⟶ (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x9 x12 x13 = If_i (SNoLe x12 0) x13 (x6 (x9 (add_SNo x12 (minus_SNo 1)) x13))) ⟶ (∀ x12 . x12 ∈ int ⟶ x10 x12 = x9 (x7 x12) (x8 x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x11 x12 = add_SNo (mul_SNo (add_SNo (x10 x12) (minus_SNo 1)) (add_SNo 2 x12)) 1) ⟶ ∀ x12 . x12 ∈ int ⟶ SNoLe 0 x12 ⟶ x5 x12 = x11 x12
Conjecture 5c1ae..^A250212 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → 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 : 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 → 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 . (∀ 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 → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι → 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 → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 : ι → ι → 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 . x32 ∈ int ⟶ x0 x32 = mul_SNo x32 x32) ⟶ x1 = 2 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x2 x32 x33 = x33) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x3 x32 x33 = If_i (SNoLe x32 0) x33 (x0 (x3 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x4 x32 x33 = x3 x1 (x2 x32 x33)) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x5 x32 x33 = add_SNo (mul_SNo (mul_SNo (mul_SNo (x4 x32 x33) x33) x33) x33) x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x6 x32 x33 = add_SNo 1 x33) ⟶ (∀ x32 . x32 ∈ int ⟶ x7 x32 = x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x8 x32 x33 = If_i (SNoLe x32 0) x33 (x5 (x8 (add_SNo x32 (minus_SNo 1)) x33) x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x9 x32 x33 = x8 (x6 x32 x33) (x7 x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x10 x32 x33 = x9 x32 x33) ⟶ (∀ x32 . x32 ∈ int ⟶ x11 x32 = x32) ⟶ x12 = 1 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x13 x32 x33 = If_i (SNoLe x32 0) x33 (x10 (x13 (add_SNo x32 (minus_SNo 1)) x33) x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x14 x32 = x13 (x11 x32) x12) ⟶ (∀ x32 . x32 ∈ int ⟶ x15 x32 = x14 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ x16 x32 = mul_SNo (mul_SNo x32 x32) x32) ⟶ x17 = 1 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x18 x32 x33 = mul_SNo x33 x33) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x19 x32 x33 = If_i (SNoLe x32 0) x33 (x16 (x19 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x20 x32 x33 = x19 x17 (x18 x32 x33)) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x21 x32 x33 = add_SNo (mul_SNo (x20 x32 x33) x33) x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x22 x32 x33 = x33) ⟶ (∀ x32 . x32 ∈ int ⟶ x23 x32 = x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x24 x32 x33 = If_i (SNoLe x32 0) x33 (x21 (x24 (add_SNo x32 (minus_SNo 1)) x33) x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x25 x32 x33 = x24 (x22 x32 x33) (x23 x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x26 x32 x33 = x25 x32 x33) ⟶ (∀ x32 . x32 ∈ int ⟶ x27 x32 = add_SNo 1 x32) ⟶ x28 = 0 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x29 x32 x33 = If_i (SNoLe x32 0) x33 (x26 (x29 (add_SNo x32 (minus_SNo 1)) x33) x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x30 x32 = x29 (x27 x32) x28) ⟶ (∀ x32 . x32 ∈ int ⟶ x31 x32 = x30 x32) ⟶ ∀ x32 . x32 ∈ int ⟶ SNoLe 0 x32 ⟶ x15 x32 = x31 x32
Conjecture 63963..^A250162 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ 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 ⟶ ∀ x23 . x23 ∈ int ⟶ x0 x22 x23 = mul_SNo 2 (add_SNo x22 (minus_SNo x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x1 x22 = x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x2 x22 = add_SNo 2 (add_SNo x22 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x3 x22 = x22) ⟶ x4 = 2 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x5 x22 x23 = If_i (SNoLe x22 0) x23 (x2 (x5 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x6 x22 = x5 (x3 x22) x4) ⟶ (∀ x22 . x22 ∈ int ⟶ x7 x22 = x6 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x8 x22 x23 = If_i (SNoLe x22 0) x23 (x0 (x8 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x9 x22 = x8 (x1 x22) (x7 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x10 x22 = mul_SNo 2 (x9 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x11 x22 = add_SNo (mul_SNo x22 x22) x22) ⟶ x12 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ x13 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x14 x22 = x22) ⟶ x15 = 2 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x16 x22 x23 = If_i (SNoLe x22 0) x23 (x13 (x16 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x17 x22 = x16 (x14 x22) x15) ⟶ (∀ x22 . x22 ∈ int ⟶ x18 x22 = add_SNo 1 (minus_SNo (x17 x22))) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x19 x22 x23 = If_i (SNoLe x22 0) x23 (x11 (x19 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x20 x22 = x19 x12 (x18 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x21 x22 = mul_SNo (add_SNo (add_SNo (add_SNo (x20 x22) 2) x22) x22) 2) ⟶ ∀ x22 . x22 ∈ int ⟶ SNoLe 0 x22 ⟶ x10 x22 = x21 x22
Conjecture 7f6a7..^A25007 : ∀ 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 . x11 ∈ int ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι → ι . (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x33 x34 x35 ∈ int) ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 : ι → ι . (∀ x37 . x37 ∈ int ⟶ x36 x37 ∈ 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 → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x39 x40 x41 ∈ int) ⟶ ∀ x40 : ι → ι . (∀ x41 . x41 ∈ int ⟶ x40 x41 ∈ int) ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ ∀ x44 : ι → ι . (∀ x45 . x45 ∈ int ⟶ x44 x45 ∈ int) ⟶ (∀ x45 . x45 ∈ int ⟶ x0 x45 = add_SNo 1 (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x45 x45)) x45))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x1 x45 x46 = x46) ⟶ x2 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x3 x45 x46 = If_i (SNoLe x45 0) x46 (x0 (x3 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x4 x45 x46 = x3 (x1 x45 x46) x2) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x5 x45 x46 = add_SNo (x4 x45 x46) (mul_SNo 2 (mul_SNo 2 (add_SNo 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 = 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 ⟶ 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 (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x45 x45)) x45)) x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x22 x45 x46 = add_SNo 1 (mul_SNo 2 (mul_SNo 2 (add_SNo x46 x46)))) ⟶ (∀ x45 . x45 ∈ int ⟶ x23 x45 = x45) ⟶ x24 = 1 ⟶ x25 = add_SNo 1 (mul_SNo 2 (add_SNo 2 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 = x28 x45) ⟶ x30 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x31 x45 x46 = x46) ⟶ (∀ 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 ⟶ ∀ x46 . x46 ∈ int ⟶ x33 x45 x46 = x32 x30 (x31 x45 x46)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x34 x45 x46 = mul_SNo (add_SNo 2 x46) x45) ⟶ x35 = 2 ⟶ (∀ x45 . x45 ∈ int ⟶ x36 x45 = x45) ⟶ (∀ 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 . x45 ∈ int ⟶ x38 x45 = x37 x35 (x36 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x39 x45 x46 = add_SNo (x33 x45 x46) (x38 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 67729..^A24772 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 : ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x23 x24 x25 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 : ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ int) ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x28 x29 x30 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x31 x32 x33 x34 ∈ int) ⟶ ∀ x32 : ι → ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x32 x33 x34 x35 ∈ int) ⟶ ∀ x33 : ι → ι → ι . (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x33 x34 x35 ∈ int) ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι . (∀ x36 . x36 ∈ int ⟶ x35 x36 ∈ int) ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ ∀ x40 . x40 ∈ int ⟶ ∀ x41 : 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 1 (mul_SNo 2 (mul_SNo 2 (add_SNo x50 x50)))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x1 x50 x51 = x51) ⟶ x2 = 1 ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x3 x50 x51 = If_i (SNoLe x50 0) x51 (x0 (x3 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x4 x50 x51 = x3 (x1 x50 x51) x2) ⟶ (∀ x50 . x50 ∈ int ⟶ x5 x50 = add_SNo (add_SNo x50 x50) x50) ⟶ x6 = 2 ⟶ (∀ x50 . x50 ∈ int ⟶ x7 x50 = x50) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x8 x50 x51 = If_i (SNoLe x50 0) x51 (x5 (x8 (add_SNo x50 (minus_SNo 1)) x51))) ⟶ (∀ x50 . x50 ∈ int ⟶ x9 x50 = x8 x6 (x7 x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x10 x50 x51 = add_SNo (x4 x50 x51) (x9 x50)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x11 x50 x51 = x51) ⟶ x12 = 1 ⟶ (∀ 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 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x14 x50 x51 = x13 (x11 x50 x51) x12) ⟶ (∀ 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 (add_SNo (x14 x50 x51) (minus_SNo x50)) (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 ⟶ ∀ x51 . x51 ∈ int ⟶ x26 x50 x51 = add_SNo 1 (mul_SNo x50 x51)) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x27 x50 x51 = x51) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x28 x50 x51 = x51) ⟶ x29 = 1 ⟶ x30 = mul_SNo 2 (add_SNo 2 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 ⟶ ∀ x51 . x51 ∈ int ⟶ x33 x50 x51 = x31 (x28 x50 x51) x29 x30) ⟶ (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x34 x50 x51 = add_SNo (add_SNo (x33 x50 x51) (mul_SNo (mul_SNo (add_SNo x50 x50) 2) 2)) x50) ⟶ (∀ x50 . x50 ∈ int ⟶ x35 x50 = x50) ⟶ x36 = 1 ⟶ (∀ 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 . x50 ∈ int ⟶ x38 x50 = x37 (x35 x50) x36) ⟶ (∀ x50 . x50 ∈ int ⟶ x39 x50 = 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) x50) (mul_SNo (add_SNo (mul_SNo (add_SNo x50 x50) 2) x50) 2)) ⟶ (∀ 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 bf554..^A2453 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x23 x24 x25 ∈ 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 → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x28 x29 x30 ∈ 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 . 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 ⟶ x0 x35 = add_SNo (add_SNo x35 x35) x35) ⟶ x1 = 2 ⟶ (∀ x35 . x35 ∈ int ⟶ x2 x35 = x35) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x3 x35 x36 = If_i (SNoLe x35 0) x36 (x0 (x3 (add_SNo x35 (minus_SNo 1)) x36))) ⟶ (∀ x35 . x35 ∈ int ⟶ x4 x35 = x3 x1 (x2 x35)) ⟶ (∀ x35 . x35 ∈ int ⟶ x5 x35 = add_SNo 1 (x4 x35)) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x6 x35 x36 = x36) ⟶ x7 = 1 ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x8 x35 x36 = If_i (SNoLe x35 0) x36 (x5 (x8 (add_SNo x35 (minus_SNo 1)) x36))) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x9 x35 x36 = x8 (x6 x35 x36) x7) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x10 x35 x36 = mul_SNo x35 x36) ⟶ x11 = add_SNo 2 2 ⟶ (∀ x35 . x35 ∈ int ⟶ x12 x35 = x35) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x13 x35 x36 = If_i (SNoLe x35 0) x36 (x10 (x13 (add_SNo x35 (minus_SNo 1)) x36) x35)) ⟶ (∀ x35 . x35 ∈ int ⟶ x14 x35 = x13 x11 (x12 x35)) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x15 x35 x36 = add_SNo (add_SNo (x9 x35 x36) (x14 x35)) x35) ⟶ (∀ x35 . x35 ∈ int ⟶ x16 x35 = x35) ⟶ x17 = 1 ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x18 x35 x36 = If_i (SNoLe x35 0) x36 (x15 (x18 (add_SNo x35 (minus_SNo 1)) x36) x35)) ⟶ (∀ x35 . x35 ∈ int ⟶ x19 x35 = x18 (x16 x35) x17) ⟶ (∀ x35 . x35 ∈ int ⟶ x20 x35 = x19 x35) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x21 x35 x36 = add_SNo 1 (mul_SNo x35 x36)) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x22 x35 x36 = x36) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x23 x35 x36 = x36) ⟶ x24 = 1 ⟶ x25 = add_SNo 1 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2)))) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x26 x35 x36 x37 = If_i (SNoLe x35 0) x36 (x21 (x26 (add_SNo x35 (minus_SNo 1)) x36 x37) (x27 (add_SNo x35 (minus_SNo 1)) x36 x37))) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x27 x35 x36 x37 = If_i (SNoLe x35 0) x37 (x22 (x26 (add_SNo x35 (minus_SNo 1)) x36 x37) (x27 (add_SNo x35 (minus_SNo 1)) x36 x37))) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x28 x35 x36 = x26 (x23 x35 x36) x24 x25) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x29 x35 x36 = add_SNo (add_SNo (x28 x35 x36) (mul_SNo (mul_SNo (mul_SNo x35 2) 2) 2)) x35) ⟶ (∀ x35 . x35 ∈ int ⟶ x30 x35 = x35) ⟶ x31 = 1 ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x32 x35 x36 = If_i (SNoLe x35 0) x36 (x29 (x32 (add_SNo x35 (minus_SNo 1)) x36) x35)) ⟶ (∀ x35 . x35 ∈ int ⟶ x33 x35 = x32 (x30 x35) x31) ⟶ (∀ x35 . x35 ∈ int ⟶ x34 x35 = x33 x35) ⟶ ∀ x35 . x35 ∈ int ⟶ SNoLe 0 x35 ⟶ x20 x35 = x34 x35
Conjecture 910d8..^A2451 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ x0 x25 = add_SNo 1 (mul_SNo 2 (add_SNo x25 x25))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x1 x25 x26 = x26) ⟶ x2 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x3 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x3 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x4 x25 x26 = x3 (x1 x25 x26) x2) ⟶ (∀ x25 . x25 ∈ int ⟶ x5 x25 = add_SNo (add_SNo x25 x25) x25) ⟶ x6 = 2 ⟶ (∀ x25 . x25 ∈ int ⟶ x7 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x8 x25 x26 = If_i (SNoLe x25 0) x26 (x5 (x8 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x9 x25 = x8 x6 (x7 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x10 x25 x26 = add_SNo (x4 x25 x26) (x9 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x11 x25 = x25) ⟶ x12 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x13 x25 x26 = If_i (SNoLe x25 0) x26 (x10 (x13 (add_SNo x25 (minus_SNo 1)) x26) x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x14 x25 = x13 (x11 x25) x12) ⟶ (∀ x25 . x25 ∈ int ⟶ x15 x25 = x14 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x16 x25 x26 = add_SNo (mul_SNo (add_SNo 1 (mul_SNo 2 (add_SNo 2 2))) x25) x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x17 x25 x26 = add_SNo 1 (mul_SNo 2 (add_SNo x26 x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x18 x25 = x25) ⟶ x19 = 1 ⟶ x20 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x21 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x16 (x21 (add_SNo x25 (minus_SNo 1)) x26 x27) (x22 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x22 x25 x26 x27 = If_i (SNoLe x25 0) x27 (x17 (x21 (add_SNo x25 (minus_SNo 1)) x26 x27) (x22 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x23 x25 = x21 (x18 x25) x19 x20) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = x23 x25) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x15 x25 = x24 x25
Conjecture dee8e..^A245020 : ∀ 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 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : 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 : 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 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 = 0 ⟶ x4 = 1 ⟶ (∀ 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 = add_SNo (add_SNo (x7 x43 x44) (mul_SNo 2 (add_SNo x43 x43))) x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x9 x43 = x43) ⟶ x10 = 0 ⟶ (∀ 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 x43) x10) ⟶ (∀ x43 . x43 ∈ int ⟶ x13 x43 = mul_SNo (x12 x43) 2) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x14 x43 x44 = mul_SNo x43 x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x15 x43 x44 = x44) ⟶ (∀ x43 . x43 ∈ int ⟶ x16 x43 = x43) ⟶ x17 = 1 ⟶ x18 = add_SNo 2 (add_SNo 2 2) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x19 x43 x44 x45 = If_i (SNoLe x43 0) x44 (x14 (x19 (add_SNo x43 (minus_SNo 1)) x44 x45) (x20 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x20 x43 x44 x45 = If_i (SNoLe x43 0) x45 (x15 (x19 (add_SNo x43 (minus_SNo 1)) x44 x45) (x20 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ x21 x43 = x19 (x16 x43) x17 x18) ⟶ (∀ x43 . x43 ∈ int ⟶ x22 x43 = mul_SNo x43 x43) ⟶ x23 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ x24 x43 = add_SNo x43 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x25 x43 = add_SNo x43 (minus_SNo 1)) ⟶ x26 = 2 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x27 x43 x44 = If_i (SNoLe x43 0) x44 (x24 (x27 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ x28 x43 = x27 (x25 x43) x26) ⟶ (∀ x43 . x43 ∈ int ⟶ x29 x43 = x28 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x30 x43 x44 = If_i (SNoLe x43 0) x44 (x22 (x30 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ x31 x43 = x30 x23 (x29 x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x32 x43 = add_SNo (x21 x43) (minus_SNo (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 (add_SNo (add_SNo (add_SNo (x36 x43 x44) x43) x43) x43) x43) x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x38 x43 = x43) ⟶ x39 = 0 ⟶ (∀ 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 ⟶ x13 x43 = x42 x43