Proofgold Signed Transaction

Param int^int : ι
Param add_SNo^add_SNo : ι → ι → ι
Param ordsucc^ordsucc : ι → ι
Param If_i^If_i : ο → ι → ι → ι
Param SNoLe^SNoLe : ι → ι → ο
Param minus_SNo^minus_SNo : ι → ι
Param mul_SNo^mul_SNo : ι → ι → ι
Conjecture 30ac3..^A155657 : ∀ 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 → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 : ι → ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x10 x11 x12 x13 ∈ int) ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι → 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 : 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 ⟶ x0 x31 = add_SNo (add_SNo x31 x31) x31) ⟶ x1 = 2 ⟶ (∀ x31 . x31 ∈ int ⟶ x2 x31 = x31) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x3 x31 x32 = If_i (SNoLe x31 0) x32 (x0 (x3 (add_SNo x31 (minus_SNo 1)) x32))) ⟶ (∀ x31 . x31 ∈ int ⟶ x4 x31 = x3 x1 (x2 x31)) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x5 x31 x32 = add_SNo (x4 x31) (minus_SNo x32)) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x6 x31 x32 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x32 x32)) (minus_SNo x31))) ⟶ (∀ x31 . x31 ∈ int ⟶ x7 x31 = x31) ⟶ x8 = 2 ⟶ x9 = 1 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x10 x31 x32 x33 = If_i (SNoLe x31 0) x32 (x5 (x10 (add_SNo x31 (minus_SNo 1)) x32 x33) (x11 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x11 x31 x32 x33 = If_i (SNoLe x31 0) x33 (x6 (x10 (add_SNo x31 (minus_SNo 1)) x32 x33) (x11 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ x12 x31 = x10 (x7 x31) x8 x9) ⟶ (∀ x31 . x31 ∈ int ⟶ x13 x31 = add_SNo (x12 x31) (minus_SNo 1)) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x14 x31 x32 = mul_SNo x31 x32) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x15 x31 x32 = x32) ⟶ (∀ x31 . x31 ∈ int ⟶ x16 x31 = x31) ⟶ x17 = 1 ⟶ x18 = add_SNo 1 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ 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) (x20 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ x21 x31 = x19 (x16 x31) x17 x18) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x22 x31 x32 = mul_SNo x31 x32) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x23 x31 x32 = x32) ⟶ (∀ x31 . x31 ∈ int ⟶ x24 x31 = x31) ⟶ x25 = 1 ⟶ x26 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ 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) (x28 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ x29 x31 = x27 (x24 x31) x25 x26) ⟶ (∀ x31 . x31 ∈ int ⟶ x30 x31 = add_SNo (add_SNo (x21 x31) (minus_SNo 1)) (x29 x31)) ⟶ ∀ x31 . x31 ∈ int ⟶ SNoLe 0 x31 ⟶ x13 x31 = x30 x31
Conjecture d5a46..^A155644 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ 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 . x34 ∈ int ⟶ x0 x33 x34 = mul_SNo (add_SNo 2 x34) x33) ⟶ x1 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ x2 x33 = x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x3 x33 x34 = If_i (SNoLe x33 0) x34 (x0 (x3 (add_SNo x33 (minus_SNo 1)) x34) x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x4 x33 = x3 x1 (x2 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = add_SNo (x4 x33) (minus_SNo x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = x33) ⟶ x7 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x8 x33 x34 = If_i (SNoLe x33 0) x34 (x5 (x8 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x9 x33 = x8 (x6 x33) x7) ⟶ (∀ x33 . x33 ∈ int ⟶ x10 x33 = add_SNo (mul_SNo 2 (add_SNo x33 x33)) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = If_i (SNoLe x33 0) x34 (x10 (x13 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x14 x33 = x13 (x11 x33) x12) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = add_SNo 1 (add_SNo (x9 x33) (minus_SNo (x14 x33)))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x16 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x17 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x18 x33 = x33) ⟶ x19 = 1 ⟶ x20 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x21 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x16 (x21 (add_SNo x33 (minus_SNo 1)) x34 x35) (x22 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x22 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x17 (x21 (add_SNo x33 (minus_SNo 1)) x34 x35) (x22 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x21 (x18 x33) x19 x20) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x24 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x25 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x26 x33 = x33) ⟶ x27 = 1 ⟶ x28 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x29 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x24 (x29 (add_SNo x33 (minus_SNo 1)) x34 x35) (x30 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x30 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x25 (x29 (add_SNo x33 (minus_SNo 1)) x34 x35) (x30 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x31 x33 = x29 (x26 x33) x27 x28) ⟶ (∀ x33 . x33 ∈ int ⟶ x32 x33 = add_SNo 1 (add_SNo (x23 x33) (minus_SNo (x31 x33)))) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x15 x33 = x32 x33
Conjecture 9fc99..^A155634 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x23 x24 x25 x26 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x0 x26 x27 = add_SNo (add_SNo (mul_SNo 2 (add_SNo x26 x26)) x26) x27) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x1 x26 x27 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x27 x27) x27)) x27) ⟶ (∀ x26 . x26 ∈ int ⟶ x2 x26 = x26) ⟶ x3 = 2 ⟶ 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 = add_SNo (x7 x26) (minus_SNo 1)) ⟶ (∀ 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 = 1 ⟶ 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 = 1 ⟶ x21 = add_SNo 1 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x22 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x17 (x22 (add_SNo x26 (minus_SNo 1)) x27 x28) (x23 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x23 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x18 (x22 (add_SNo x26 (minus_SNo 1)) x27 x28) (x23 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x24 x26 = x22 (x19 x26) x20 x21) ⟶ (∀ x26 . x26 ∈ int ⟶ x25 x26 = add_SNo (add_SNo (x16 x26) (minus_SNo 1)) (x24 x26)) ⟶ ∀ x26 . x26 ∈ int ⟶ SNoLe 0 x26 ⟶ x8 x26 = x25 x26
Conjecture c77a5..^A155631 : ∀ 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 → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ (∀ x30 . x30 ∈ int ⟶ x0 x30 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x30 x30)) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x1 x30 = x30) ⟶ x2 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x3 x30 x31 = If_i (SNoLe x30 0) x31 (x0 (x3 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x4 x30 = x3 (x1 x30) x2) ⟶ (∀ x30 . x30 ∈ int ⟶ x5 x30 = add_SNo x30 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x6 x30 = add_SNo x30 x30) ⟶ x7 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x8 x30 x31 = If_i (SNoLe x30 0) x31 (x5 (x8 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x9 x30 = x8 (x6 x30) x7) ⟶ (∀ x30 . x30 ∈ int ⟶ x10 x30 = add_SNo 1 (add_SNo (x4 x30) (minus_SNo (x9 x30)))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x11 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x12 x30 x31 = x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x13 x30 = x30) ⟶ x14 = 1 ⟶ x15 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x16 x30 x31 x32 = If_i (SNoLe x30 0) x31 (x11 (x16 (add_SNo x30 (minus_SNo 1)) x31 x32) (x17 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x17 x30 x31 x32 = If_i (SNoLe x30 0) x32 (x12 (x16 (add_SNo x30 (minus_SNo 1)) x31 x32) (x17 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ x18 x30 = x16 (x13 x30) x14 x15) ⟶ (∀ x30 . x30 ∈ int ⟶ x19 x30 = mul_SNo x30 x30) ⟶ x20 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ x21 x30 = add_SNo x30 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x22 x30 = x30) ⟶ x23 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x24 x30 x31 = If_i (SNoLe x30 0) x31 (x21 (x24 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x25 x30 = x24 (x22 x30) x23) ⟶ (∀ x30 . x30 ∈ int ⟶ x26 x30 = x25 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x27 x30 x31 = If_i (SNoLe x30 0) x31 (x19 (x27 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x28 x30 = x27 x20 (x26 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x29 x30 = add_SNo 1 (add_SNo (x18 x30) (minus_SNo (x28 x30)))) ⟶ ∀ x30 . x30 ∈ int ⟶ SNoLe 0 x30 ⟶ x10 x30 = x29 x30
Conjecture bb94e..^A155621 : ∀ 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 → 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 → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ (∀ x30 . x30 ∈ int ⟶ x0 x30 = add_SNo x30 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x1 x30 = add_SNo x30 x30) ⟶ x2 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x3 x30 x31 = If_i (SNoLe x30 0) x31 (x0 (x3 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x4 x30 = x3 (x1 x30) x2) ⟶ (∀ x30 . x30 ∈ int ⟶ x5 x30 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x30 x30)) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x6 x30 = x30) ⟶ x7 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x8 x30 x31 = If_i (SNoLe x30 0) x31 (x5 (x8 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x9 x30 = x8 (x6 x30) x7) ⟶ (∀ x30 . x30 ∈ int ⟶ x10 x30 = add_SNo (add_SNo (x4 x30) (minus_SNo 1)) (x9 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x11 x30 = mul_SNo x30 x30) ⟶ x12 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ x13 x30 = add_SNo x30 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x14 x30 = x30) ⟶ x15 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x16 x30 x31 = If_i (SNoLe x30 0) x31 (x13 (x16 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x17 x30 = x16 (x14 x30) x15) ⟶ (∀ x30 . x30 ∈ int ⟶ x18 x30 = x17 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x19 x30 x31 = If_i (SNoLe x30 0) x31 (x11 (x19 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x20 x30 = x19 x12 (x18 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x21 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x22 x30 x31 = x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x23 x30 = x30) ⟶ x24 = 1 ⟶ x25 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x26 x30 x31 x32 = If_i (SNoLe x30 0) x31 (x21 (x26 (add_SNo x30 (minus_SNo 1)) x31 x32) (x27 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x27 x30 x31 x32 = If_i (SNoLe x30 0) x32 (x22 (x26 (add_SNo x30 (minus_SNo 1)) x31 x32) (x27 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ x28 x30 = x26 (x23 x30) x24 x25) ⟶ (∀ x30 . x30 ∈ int ⟶ x29 x30 = add_SNo (add_SNo (x20 x30) (minus_SNo 1)) (x28 x30)) ⟶ ∀ x30 . x30 ∈ int ⟶ SNoLe 0 x30 ⟶ x10 x30 = x29 x30
Conjecture 07741..^A155594 : ∀ 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 : 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 . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x18 x19 x20 x21 ∈ int) ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ x0 x25 = add_SNo 1 (add_SNo x25 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x1 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x2 x25 = add_SNo (mul_SNo 2 (add_SNo x25 x25)) x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x3 x25 = x25) ⟶ x4 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x5 x25 x26 = If_i (SNoLe x25 0) x26 (x2 (x5 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x6 x25 = x5 (x3 x25) x4) ⟶ (∀ x25 . x25 ∈ int ⟶ x7 x25 = x6 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x8 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x8 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x9 x25 = x8 (x1 x25) (x7 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x10 x25 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x11 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x12 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x13 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x14 x25 x26 = x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x15 x25 = x25) ⟶ x16 = 1 ⟶ x17 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x18 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x13 (x18 (add_SNo x25 (minus_SNo 1)) x26 x27) (x19 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x19 x25 x26 x27 = If_i (SNoLe x25 0) x27 (x14 (x18 (add_SNo x25 (minus_SNo 1)) x26 x27) (x19 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x20 x25 = x18 (x15 x25) x16 x17) ⟶ (∀ x25 . x25 ∈ int ⟶ x21 x25 = add_SNo 1 (x20 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x22 x25 x26 = If_i (SNoLe x25 0) x26 (x11 (x22 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x23 x25 = x22 (x12 x25) (x21 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = add_SNo (x23 x25) (minus_SNo 1)) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture 9f1d0..^A155477 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ 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 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 : ι → ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x34 x35 x36 x37 ∈ int) ⟶ ∀ x35 : ι → ι → ι → ι . (∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x35 x36 x37 x38 ∈ int) ⟶ ∀ x36 : ι → ι . (∀ x37 . x37 ∈ int ⟶ x36 x37 ∈ int) ⟶ ∀ x37 : ι → ι . (∀ x38 . x38 ∈ int ⟶ x37 x38 ∈ int) ⟶ (∀ x38 . x38 ∈ int ⟶ x0 x38 = add_SNo (mul_SNo x38 x38) x38) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x3 x38 x39 = If_i (SNoLe x38 0) x39 (x0 (x3 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x38 . x38 ∈ int ⟶ x5 x38 = add_SNo (mul_SNo x4 x38) x38) ⟶ (∀ x38 . x38 ∈ int ⟶ x6 x38 = add_SNo 1 (add_SNo x38 x38)) ⟶ x7 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x8 x38 x39 = If_i (SNoLe x38 0) x39 (x5 (x8 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ (∀ x38 . x38 ∈ int ⟶ x9 x38 = x8 (x6 x38) x7) ⟶ (∀ x38 . x38 ∈ int ⟶ x10 x38 = x9 x38) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x11 x38 x39 = mul_SNo x38 x39) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x12 x38 x39 = x39) ⟶ (∀ x38 . x38 ∈ int ⟶ x13 x38 = add_SNo 1 x38) ⟶ x14 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ x15 x38 = add_SNo (mul_SNo x38 x38) x38) ⟶ x16 = 2 ⟶ x17 = 2 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x18 x38 x39 = If_i (SNoLe x38 0) x39 (x15 (x18 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ x19 = x18 x16 x17 ⟶ x20 = add_SNo 1 x19 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x21 x38 x39 x40 = If_i (SNoLe x38 0) x39 (x11 (x21 (add_SNo x38 (minus_SNo 1)) x39 x40) (x22 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x22 x38 x39 x40 = If_i (SNoLe x38 0) x40 (x12 (x21 (add_SNo x38 (minus_SNo 1)) x39 x40) (x22 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ x23 x38 = x21 (x13 x38) x14 x20) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x24 x38 x39 = mul_SNo x38 x39) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x25 x38 x39 = x39) ⟶ (∀ x38 . x38 ∈ int ⟶ x26 x38 = x38) ⟶ x27 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ x28 x38 = add_SNo (mul_SNo x38 x38) x38) ⟶ x29 = 2 ⟶ x30 = 2 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x31 x38 x39 = If_i (SNoLe x38 0) x39 (x28 (x31 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ x32 = x31 x29 x30 ⟶ x33 = add_SNo 1 x32 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x34 x38 x39 x40 = If_i (SNoLe x38 0) x39 (x24 (x34 (add_SNo x38 (minus_SNo 1)) x39 x40) (x35 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x35 x38 x39 x40 = If_i (SNoLe x38 0) x40 (x25 (x34 (add_SNo x38 (minus_SNo 1)) x39 x40) (x35 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ x36 x38 = x34 (x26 x38) x27 x33) ⟶ (∀ x38 . x38 ∈ int ⟶ x37 x38 = mul_SNo (x23 x38) (x36 x38)) ⟶ ∀ x38 . x38 ∈ int ⟶ SNoLe 0 x38 ⟶ x10 x38 = x37 x38
Conjecture f8f04..^A1553 : ∀ 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 → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . 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 . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 . x25 ∈ 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 : 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 . (∀ 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 : 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 . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ ∀ x40 . x40 ∈ int ⟶ ∀ x41 : ι → ι → ι → ι . (∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x41 x42 x43 x44 ∈ int) ⟶ ∀ x42 : ι → ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x42 x43 x44 x45 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ ∀ x44 : ι → ι → ι . (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x44 x45 x46 ∈ int) ⟶ ∀ x45 : ι → ι → ι . (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x45 x46 x47 ∈ int) ⟶ ∀ x46 : ι → ι . (∀ x47 . x47 ∈ int ⟶ x46 x47 ∈ int) ⟶ ∀ x47 . x47 ∈ int ⟶ ∀ x48 . x48 ∈ int ⟶ ∀ x49 : ι → ι → ι → ι . (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x49 x50 x51 x52 ∈ int) ⟶ ∀ x50 : ι → ι → ι → ι . (∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ ∀ x53 . x53 ∈ int ⟶ x50 x51 x52 x53 ∈ int) ⟶ ∀ x51 : ι → ι . (∀ x52 . x52 ∈ int ⟶ x51 x52 ∈ int) ⟶ ∀ x52 : ι → ι . (∀ x53 . x53 ∈ int ⟶ x52 x53 ∈ int) ⟶ (∀ x53 . x53 ∈ int ⟶ x0 x53 = add_SNo (add_SNo x53 x53) x53) ⟶ (∀ x53 . x53 ∈ int ⟶ x1 x53 = x53) ⟶ x2 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x3 x53 x54 = If_i (SNoLe x53 0) x54 (x0 (x3 (add_SNo x53 (minus_SNo 1)) x54))) ⟶ (∀ x53 . x53 ∈ int ⟶ x4 x53 = x3 (x1 x53) x2) ⟶ (∀ x53 . x53 ∈ int ⟶ x5 x53 = add_SNo x53 x53) ⟶ (∀ x53 . x53 ∈ int ⟶ x6 x53 = x53) ⟶ x7 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x8 x53 x54 = If_i (SNoLe x53 0) x54 (x5 (x8 (add_SNo x53 (minus_SNo 1)) x54))) ⟶ (∀ x53 . x53 ∈ int ⟶ x9 x53 = x8 (x6 x53) x7) ⟶ (∀ x53 . x53 ∈ int ⟶ x10 x53 = add_SNo x53 x53) ⟶ (∀ x53 . x53 ∈ int ⟶ x11 x53 = x53) ⟶ x12 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x13 x53 x54 = If_i (SNoLe x53 0) x54 (x10 (x13 (add_SNo x53 (minus_SNo 1)) x54))) ⟶ (∀ x53 . x53 ∈ int ⟶ x14 x53 = x13 (x11 x53) x12) ⟶ (∀ x53 . x53 ∈ int ⟶ x15 x53 = add_SNo (mul_SNo 2 (add_SNo x53 x53)) x53) ⟶ (∀ x53 . x53 ∈ int ⟶ x16 x53 = x53) ⟶ x17 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x18 x53 x54 = If_i (SNoLe x53 0) x54 (x15 (x18 (add_SNo x53 (minus_SNo 1)) x54))) ⟶ (∀ x53 . x53 ∈ int ⟶ x19 x53 = x18 (x16 x53) x17) ⟶ (∀ x53 . x53 ∈ int ⟶ x20 x53 = add_SNo (mul_SNo (add_SNo (x4 x53) (x9 x53)) (add_SNo 1 (x14 x53))) (add_SNo 1 (x19 x53))) ⟶ (∀ x53 . x53 ∈ int ⟶ x21 x53 = add_SNo (mul_SNo x53 x53) x53) ⟶ x22 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ x23 x53 = add_SNo x53 x53) ⟶ (∀ x53 . x53 ∈ int ⟶ x24 x53 = x53) ⟶ x25 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x26 x53 x54 = If_i (SNoLe x53 0) x54 (x23 (x26 (add_SNo x53 (minus_SNo 1)) x54))) ⟶ (∀ x53 . x53 ∈ int ⟶ x27 x53 = x26 (x24 x53) x25) ⟶ (∀ x53 . x53 ∈ int ⟶ x28 x53 = x27 x53) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x29 x53 x54 = If_i (SNoLe x53 0) x54 (x21 (x29 (add_SNo x53 (minus_SNo 1)) x54))) ⟶ (∀ x53 . x53 ∈ int ⟶ x30 x53 = x29 x22 (x28 x53)) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x31 x53 x54 = mul_SNo x53 x54) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x32 x53 x54 = x54) ⟶ (∀ x53 . x53 ∈ int ⟶ x33 x53 = x53) ⟶ (∀ x53 . x53 ∈ int ⟶ x34 x53 = add_SNo x53 x53) ⟶ (∀ x53 . x53 ∈ int ⟶ x35 x53 = x53) ⟶ x36 = 1 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x37 x53 x54 = If_i (SNoLe x53 0) x54 (x34 (x37 (add_SNo x53 (minus_SNo 1)) x54))) ⟶ (∀ x53 . x53 ∈ int ⟶ x38 x53 = x37 (x35 x53) x36) ⟶ (∀ x53 . x53 ∈ int ⟶ x39 x53 = add_SNo 1 (x38 x53)) ⟶ x40 = add_SNo 1 2 ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x41 x53 x54 x55 = If_i (SNoLe x53 0) x54 (x31 (x41 (add_SNo x53 (minus_SNo 1)) x54 x55) (x42 (add_SNo x53 (minus_SNo 1)) x54 x55))) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x42 x53 x54 x55 = If_i (SNoLe x53 0) x55 (x32 (x41 (add_SNo x53 (minus_SNo 1)) x54 x55) (x42 (add_SNo x53 (minus_SNo 1)) x54 x55))) ⟶ (∀ x53 . x53 ∈ int ⟶ x43 x53 = x41 (x33 x53) (x39 x53) x40) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x44 x53 x54 = mul_SNo x53 x54) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x45 x53 x54 = x54) ⟶ (∀ x53 . x53 ∈ int ⟶ x46 x53 = x53) ⟶ x47 = 1 ⟶ x48 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x49 x53 x54 x55 = If_i (SNoLe x53 0) x54 (x44 (x49 (add_SNo x53 (minus_SNo 1)) x54 x55) (x50 (add_SNo x53 (minus_SNo 1)) x54 x55))) ⟶ (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x50 x53 x54 x55 = If_i (SNoLe x53 0) x55 (x45 (x49 (add_SNo x53 (minus_SNo 1)) x54 x55) (x50 (add_SNo x53 (minus_SNo 1)) x54 x55))) ⟶ (∀ x53 . x53 ∈ int ⟶ x51 x53 = x49 (x46 x53) x47 x48) ⟶ (∀ x53 . x53 ∈ int ⟶ x52 x53 = add_SNo (add_SNo (add_SNo 1 (x30 x53)) (x43 x53)) (x51 x53)) ⟶ ∀ x53 . x53 ∈ int ⟶ SNoLe 0 x53 ⟶ x20 x53 = x52 x53
Conjecture 835fe..^A1545 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : 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 ⟶ x0 x12 x13 = add_SNo 2 (add_SNo x12 x13)) ⟶ (∀ x12 . x12 ∈ int ⟶ x1 x12 = add_SNo (mul_SNo 2 (add_SNo x12 x12)) x12) ⟶ x2 = 2 ⟶ (∀ 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 . x12 ∈ int ⟶ x4 x12 = x3 (x1 x12) x2) ⟶ (∀ x12 . x12 ∈ int ⟶ x5 x12 = mul_SNo 2 (x4 x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x6 x12 = add_SNo (mul_SNo x12 x12) x12) ⟶ x7 = 1 ⟶ (∀ x12 . x12 ∈ int ⟶ x8 x12 = add_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x12 x12)) 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 (x8 x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x11 x12 = add_SNo (x10 x12) (minus_SNo 2)) ⟶ ∀ x12 . x12 ∈ int ⟶ SNoLe 0 x12 ⟶ x5 x12 = x11 x12
Conjecture 901e9..^A15457 : ∀ 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 . x3 ∈ int ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 . x5 ∈ 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 . x9 ∈ int ⟶ ∀ x10 : ι → ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x10 x11 x12 x13 ∈ int) ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x0 x23 x24 = x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x1 x23 = add_SNo 1 (add_SNo x23 x23)) ⟶ x2 = 2 ⟶ x3 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x4 x23 x24 = If_i (SNoLe x23 0) x24 (x1 (x4 (add_SNo x23 (minus_SNo 1)) x24))) ⟶ x5 = x4 x2 x3 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x6 x23 x24 = add_SNo (mul_SNo x5 x24) x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x23) ⟶ x8 = 1 ⟶ x9 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x10 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x0 (x10 (add_SNo x23 (minus_SNo 1)) x24 x25) (x11 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x11 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x6 (x10 (add_SNo x23 (minus_SNo 1)) x24 x25) (x11 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x12 x23 = x10 (x7 x23) x8 x9) ⟶ (∀ x23 . x23 ∈ int ⟶ x13 x23 = x12 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x14 x23 x24 = add_SNo (mul_SNo (add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) x23) x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x15 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x16 x23 = add_SNo x23 (minus_SNo 2)) ⟶ (∀ x23 . x23 ∈ int ⟶ x17 x23 = If_i (SNoLe (add_SNo x23 (minus_SNo 1)) 0) 1 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2)))) ⟶ x18 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x19 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x14 (x19 (add_SNo x23 (minus_SNo 1)) x24 x25) (x20 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x20 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x15 (x19 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x21 x23 = x19 (x16 x23) (x17 x23) x18) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = x21 x23) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x13 x23 = x22 x23
Conjecture e962a..^A154575 : ∀ 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 → 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 → 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 ⟶ x0 x12 x13 = add_SNo 2 (add_SNo x12 x13)) ⟶ (∀ x12 . x12 ∈ int ⟶ x1 x12 = mul_SNo 2 (add_SNo 2 x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x2 x12 = 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 . x12 ∈ int ⟶ x4 x12 = x3 (x1 x12) (x2 x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x5 x12 = add_SNo (add_SNo (x4 x12) x12) x12) ⟶ (∀ x12 . x12 ∈ int ⟶ x6 x12 = mul_SNo x12 x12) ⟶ x7 = 1 ⟶ (∀ x12 . x12 ∈ int ⟶ x8 x12 = add_SNo 1 (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 (x8 x12)) ⟶ (∀ x12 . x12 ∈ int ⟶ x11 x12 = mul_SNo 2 (add_SNo (add_SNo (x10 x12) x12) x12)) ⟶ ∀ x12 . x12 ∈ int ⟶ SNoLe 0 x12 ⟶ x5 x12 = x11 x12
Conjecture 5fd3f..^A15262 : ∀ 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 . (∀ 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 → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 . x24 ∈ 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 → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x28 x29 x30 ∈ 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 . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ 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 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ ∀ x39 : ι → ι → ι → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x39 x40 x41 x42 ∈ int) ⟶ ∀ x40 : ι → ι → ι → ι . (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ x40 x41 x42 x43 ∈ int) ⟶ ∀ x41 : ι → ι → 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 → ι . (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x47 x48 x49 ∈ int) ⟶ ∀ x48 : ι → ι → ι . (∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x48 x49 x50 ∈ int) ⟶ ∀ x49 : ι → ι . (∀ x50 . x50 ∈ int ⟶ x49 x50 ∈ int) ⟶ ∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ ∀ x52 : ι → ι → ι → ι . (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x52 x53 x54 x55 ∈ int) ⟶ ∀ x53 : ι → ι → ι → ι . (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ ∀ x56 . x56 ∈ int ⟶ x53 x54 x55 x56 ∈ int) ⟶ ∀ x54 : ι → ι . (∀ x55 . x55 ∈ int ⟶ x54 x55 ∈ int) ⟶ ∀ x55 : ι → ι . (∀ x56 . x56 ∈ int ⟶ x55 x56 ∈ int) ⟶ ∀ x56 . x56 ∈ int ⟶ ∀ x57 : ι → ι → ι . (∀ x58 . x58 ∈ int ⟶ ∀ x59 . x59 ∈ int ⟶ x57 x58 x59 ∈ int) ⟶ ∀ x58 : ι → ι → ι . (∀ x59 . x59 ∈ int ⟶ ∀ x60 . x60 ∈ int ⟶ x58 x59 x60 ∈ int) ⟶ ∀ x59 : ι → ι → ι . (∀ x60 . x60 ∈ int ⟶ ∀ x61 . x61 ∈ int ⟶ x59 x60 x61 ∈ int) ⟶ ∀ x60 : ι → ι → ι . (∀ x61 . x61 ∈ int ⟶ ∀ x62 . x62 ∈ int ⟶ x60 x61 x62 ∈ int) ⟶ ∀ x61 : ι → ι . (∀ x62 . x62 ∈ int ⟶ x61 x62 ∈ int) ⟶ ∀ x62 . x62 ∈ int ⟶ ∀ x63 : ι → ι → ι . (∀ x64 . x64 ∈ int ⟶ ∀ x65 . x65 ∈ int ⟶ x63 x64 x65 ∈ int) ⟶ ∀ x64 : ι → ι . (∀ x65 . x65 ∈ int ⟶ x64 x65 ∈ int) ⟶ ∀ x65 : ι → ι . (∀ x66 . x66 ∈ int ⟶ x65 x66 ∈ int) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x0 x66 x67 = mul_SNo (add_SNo 2 x67) x66) ⟶ x1 = 2 ⟶ (∀ x66 . x66 ∈ int ⟶ x2 x66 = x66) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x3 x66 x67 = If_i (SNoLe x66 0) x67 (x0 (x3 (add_SNo x66 (minus_SNo 1)) x67) x66)) ⟶ (∀ x66 . x66 ∈ int ⟶ x4 x66 = x3 x1 (x2 x66)) ⟶ (∀ x66 . x66 ∈ int ⟶ x5 x66 = add_SNo (x4 x66) (minus_SNo x66)) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x6 x66 x67 = x67) ⟶ x7 = 1 ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x8 x66 x67 = If_i (SNoLe x66 0) x67 (x5 (x8 (add_SNo x66 (minus_SNo 1)) x67))) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x9 x66 x67 = x8 (x6 x66 x67) x7) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x10 x66 x67 = add_SNo (x9 x66 x67) (minus_SNo x66)) ⟶ (∀ x66 . x66 ∈ int ⟶ x11 x66 = x66) ⟶ x12 = 1 ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x13 x66 x67 = If_i (SNoLe x66 0) x67 (x10 (x13 (add_SNo x66 (minus_SNo 1)) x67) x66)) ⟶ (∀ x66 . x66 ∈ int ⟶ x14 x66 = x13 (x11 x66) x12) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x15 x66 x67 = mul_SNo x66 x67) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x16 x66 x67 = x67) ⟶ (∀ x66 . x66 ∈ int ⟶ x17 x66 = x66) ⟶ x18 = 1 ⟶ x19 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ ∀ x68 . x68 ∈ int ⟶ x20 x66 x67 x68 = If_i (SNoLe x66 0) x67 (x15 (x20 (add_SNo x66 (minus_SNo 1)) x67 x68) (x21 (add_SNo x66 (minus_SNo 1)) x67 x68))) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ ∀ x68 . x68 ∈ int ⟶ x21 x66 x67 x68 = If_i (SNoLe x66 0) x68 (x16 (x20 (add_SNo x66 (minus_SNo 1)) x67 x68) (x21 (add_SNo x66 (minus_SNo 1)) x67 x68))) ⟶ (∀ x66 . x66 ∈ int ⟶ x22 x66 = x20 (x17 x66) x18 x19) ⟶ (∀ x66 . x66 ∈ int ⟶ x23 x66 = mul_SNo (x14 x66) (x22 x66)) ⟶ x24 = 1 ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x25 x66 x67 = x67) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x26 x66 x67 = If_i (SNoLe x66 0) x67 (x23 (x26 (add_SNo x66 (minus_SNo 1)) x67))) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x27 x66 x67 = x26 x24 (x25 x66 x67)) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x28 x66 x67 = add_SNo (x27 x66 x67) x66) ⟶ (∀ x66 . x66 ∈ int ⟶ x29 x66 = x66) ⟶ x30 = 1 ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x31 x66 x67 = If_i (SNoLe x66 0) x67 (x28 (x31 (add_SNo x66 (minus_SNo 1)) x67) x66)) ⟶ (∀ x66 . x66 ∈ int ⟶ x32 x66 = x31 (x29 x66) x30) ⟶ (∀ x66 . x66 ∈ int ⟶ x33 x66 = x32 x66) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x34 x66 x67 = mul_SNo x66 x67) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x35 x66 x67 = x67) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x36 x66 x67 = x67) ⟶ x37 = 1 ⟶ x38 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ ∀ x68 . x68 ∈ int ⟶ x39 x66 x67 x68 = If_i (SNoLe x66 0) x67 (x34 (x39 (add_SNo x66 (minus_SNo 1)) x67 x68) (x40 (add_SNo x66 (minus_SNo 1)) x67 x68))) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ ∀ x68 . x68 ∈ int ⟶ x40 x66 x67 x68 = If_i (SNoLe x66 0) x68 (x35 (x39 (add_SNo x66 (minus_SNo 1)) x67 x68) (x40 (add_SNo x66 (minus_SNo 1)) x67 x68))) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x41 x66 x67 = x39 (x36 x66 x67) x37 x38) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x42 x66 x67 = add_SNo (x41 x66 x67) (minus_SNo x66)) ⟶ (∀ x66 . x66 ∈ int ⟶ x43 x66 = x66) ⟶ x44 = 1 ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x45 x66 x67 = If_i (SNoLe x66 0) x67 (x42 (x45 (add_SNo x66 (minus_SNo 1)) x67) x66)) ⟶ (∀ x66 . x66 ∈ int ⟶ x46 x66 = x45 (x43 x66) x44) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x47 x66 x67 = mul_SNo x66 x67) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x48 x66 x67 = x67) ⟶ (∀ x66 . x66 ∈ int ⟶ x49 x66 = x66) ⟶ x50 = 1 ⟶ x51 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ ∀ x68 . x68 ∈ int ⟶ x52 x66 x67 x68 = If_i (SNoLe x66 0) x67 (x47 (x52 (add_SNo x66 (minus_SNo 1)) x67 x68) (x53 (add_SNo x66 (minus_SNo 1)) x67 x68))) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ ∀ x68 . x68 ∈ int ⟶ x53 x66 x67 x68 = If_i (SNoLe x66 0) x68 (x48 (x52 (add_SNo x66 (minus_SNo 1)) x67 x68) (x53 (add_SNo x66 (minus_SNo 1)) x67 x68))) ⟶ (∀ x66 . x66 ∈ int ⟶ x54 x66 = x52 (x49 x66) x50 x51) ⟶ (∀ x66 . x66 ∈ int ⟶ x55 x66 = mul_SNo (x46 x66) (x54 x66)) ⟶ x56 = 1 ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x57 x66 x67 = x67) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x58 x66 x67 = If_i (SNoLe x66 0) x67 (x55 (x58 (add_SNo x66 (minus_SNo 1)) x67))) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x59 x66 x67 = x58 x56 (x57 x66 x67)) ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x60 x66 x67 = add_SNo (x59 x66 x67) x66) ⟶ (∀ x66 . x66 ∈ int ⟶ x61 x66 = x66) ⟶ x62 = 1 ⟶ (∀ x66 . x66 ∈ int ⟶ ∀ x67 . x67 ∈ int ⟶ x63 x66 x67 = If_i (SNoLe x66 0) x67 (x60 (x63 (add_SNo x66 (minus_SNo 1)) x67) x66)) ⟶ (∀ x66 . x66 ∈ int ⟶ x64 x66 = x63 (x61 x66) x62) ⟶ (∀ x66 . x66 ∈ int ⟶ x65 x66 = x64 x66) ⟶ ∀ x66 . x66 ∈ int ⟶ SNoLe 0 x66 ⟶ x33 x66 = x65 x66
Conjecture 330d1..^A15261 : ∀ 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 . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ 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 → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x23 x24 x25 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 . x25 ∈ 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 : 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 → 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 . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ ∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 : ι → ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x42 x43 x44 x45 ∈ int) ⟶ ∀ x43 : ι → ι → ι → ι . (∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x43 x44 x45 x46 ∈ 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 → ι . (∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x48 x49 x50 ∈ int) ⟶ ∀ x49 : ι → ι → ι . (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x49 x50 x51 ∈ int) ⟶ ∀ x50 : ι → ι → ι . (∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x50 x51 x52 ∈ int) ⟶ ∀ x51 : ι → ι . (∀ x52 . x52 ∈ int ⟶ x51 x52 ∈ int) ⟶ ∀ x52 . x52 ∈ int ⟶ ∀ x53 : ι → ι → ι . (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x53 x54 x55 ∈ int) ⟶ ∀ x54 : ι → ι . (∀ x55 . x55 ∈ int ⟶ x54 x55 ∈ int) ⟶ ∀ x55 : ι → ι . (∀ x56 . x56 ∈ int ⟶ x55 x56 ∈ int) ⟶ (∀ x56 . x56 ∈ int ⟶ x0 x56 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x56 x56)) x56)) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x1 x56 x57 = x57) ⟶ x2 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x3 x56 x57 = If_i (SNoLe x56 0) x57 (x0 (x3 (add_SNo x56 (minus_SNo 1)) x57))) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x4 x56 x57 = x3 (x1 x56 x57) x2) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x5 x56 x57 = add_SNo (x4 x56 x57) (minus_SNo x56)) ⟶ (∀ x56 . x56 ∈ int ⟶ x6 x56 = x56) ⟶ x7 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x8 x56 x57 = If_i (SNoLe x56 0) x57 (x5 (x8 (add_SNo x56 (minus_SNo 1)) x57) x56)) ⟶ (∀ x56 . x56 ∈ int ⟶ x9 x56 = x8 (x6 x56) x7) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x10 x56 x57 = mul_SNo x56 x57) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x11 x56 x57 = x57) ⟶ (∀ x56 . x56 ∈ int ⟶ x12 x56 = x56) ⟶ x13 = 1 ⟶ x14 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x15 x56 x57 x58 = If_i (SNoLe x56 0) x57 (x10 (x15 (add_SNo x56 (minus_SNo 1)) x57 x58) (x16 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x16 x56 x57 x58 = If_i (SNoLe x56 0) x58 (x11 (x15 (add_SNo x56 (minus_SNo 1)) x57 x58) (x16 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ x17 x56 = x15 (x12 x56) x13 x14) ⟶ (∀ x56 . x56 ∈ int ⟶ x18 x56 = mul_SNo (x9 x56) (x17 x56)) ⟶ x19 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x20 x56 x57 = x57) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x21 x56 x57 = If_i (SNoLe x56 0) x57 (x18 (x21 (add_SNo x56 (minus_SNo 1)) x57))) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x22 x56 x57 = x21 x19 (x20 x56 x57)) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x23 x56 x57 = add_SNo (x22 x56 x57) x56) ⟶ (∀ x56 . x56 ∈ int ⟶ x24 x56 = x56) ⟶ x25 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x26 x56 x57 = If_i (SNoLe x56 0) x57 (x23 (x26 (add_SNo x56 (minus_SNo 1)) x57) x56)) ⟶ (∀ x56 . x56 ∈ int ⟶ x27 x56 = x26 (x24 x56) x25) ⟶ (∀ x56 . x56 ∈ int ⟶ x28 x56 = x27 x56) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x29 x56 x57 = add_SNo x57 (minus_SNo x56)) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x30 x56 x57 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x57 x57)) x57)) ⟶ (∀ x56 . x56 ∈ int ⟶ x31 x56 = x56) ⟶ x32 = 1 ⟶ x33 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x34 x56 x57 x58 = If_i (SNoLe x56 0) x57 (x29 (x34 (add_SNo x56 (minus_SNo 1)) x57 x58) (x35 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x35 x56 x57 x58 = If_i (SNoLe x56 0) x58 (x30 (x34 (add_SNo x56 (minus_SNo 1)) x57 x58) (x35 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ x36 x56 = x34 (x31 x56) x32 x33) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x37 x56 x57 = mul_SNo x56 x57) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x38 x56 x57 = x57) ⟶ (∀ x56 . x56 ∈ int ⟶ x39 x56 = x56) ⟶ x40 = 1 ⟶ x41 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x42 x56 x57 x58 = If_i (SNoLe x56 0) x57 (x37 (x42 (add_SNo x56 (minus_SNo 1)) x57 x58) (x43 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x43 x56 x57 x58 = If_i (SNoLe x56 0) x58 (x38 (x42 (add_SNo x56 (minus_SNo 1)) x57 x58) (x43 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ x44 x56 = x42 (x39 x56) x40 x41) ⟶ (∀ x56 . x56 ∈ int ⟶ x45 x56 = mul_SNo (x36 x56) (x44 x56)) ⟶ x46 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x47 x56 x57 = x57) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x48 x56 x57 = If_i (SNoLe x56 0) x57 (x45 (x48 (add_SNo x56 (minus_SNo 1)) x57))) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x49 x56 x57 = x48 x46 (x47 x56 x57)) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x50 x56 x57 = add_SNo (x49 x56 x57) x56) ⟶ (∀ x56 . x56 ∈ int ⟶ x51 x56 = x56) ⟶ x52 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x53 x56 x57 = If_i (SNoLe x56 0) x57 (x50 (x53 (add_SNo x56 (minus_SNo 1)) x57) x56)) ⟶ (∀ x56 . x56 ∈ int ⟶ x54 x56 = x53 (x51 x56) x52) ⟶ (∀ x56 . x56 ∈ int ⟶ x55 x56 = x54 x56) ⟶ ∀ x56 . x56 ∈ int ⟶ SNoLe 0 x56 ⟶ x28 x56 = x55 x56
Conjecture acb81..^A15259 : ∀ 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 → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x13 x14 x15 x16 ∈ int) ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ 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 . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x28 x29 x30 ∈ 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 . (∀ x38 . x38 ∈ int ⟶ x37 x38 ∈ 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 : 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 : ι → ι → ι . (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x47 x48 x49 ∈ int) ⟶ ∀ x48 : ι → ι → ι . (∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x48 x49 x50 ∈ int) ⟶ ∀ x49 : ι → ι → ι . (∀ x50 . x50 ∈ int ⟶ ∀ x51 . x51 ∈ int ⟶ x49 x50 x51 ∈ int) ⟶ ∀ x50 : ι → ι → ι . (∀ x51 . x51 ∈ int ⟶ ∀ x52 . x52 ∈ int ⟶ x50 x51 x52 ∈ int) ⟶ ∀ x51 : ι → ι . (∀ x52 . x52 ∈ int ⟶ x51 x52 ∈ int) ⟶ ∀ x52 . x52 ∈ int ⟶ ∀ x53 : ι → ι → ι . (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x53 x54 x55 ∈ int) ⟶ ∀ x54 : ι → ι . (∀ x55 . x55 ∈ int ⟶ x54 x55 ∈ int) ⟶ ∀ x55 : ι → ι . (∀ x56 . x56 ∈ int ⟶ x55 x56 ∈ int) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x0 x56 x57 = add_SNo (mul_SNo (mul_SNo x57 x57) x57) (minus_SNo x56)) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x1 x56 x57 = add_SNo x57 x57) ⟶ (∀ x56 . x56 ∈ int ⟶ x2 x56 = x56) ⟶ x3 = 1 ⟶ x4 = 2 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x5 x56 x57 x58 = If_i (SNoLe x56 0) x57 (x0 (x5 (add_SNo x56 (minus_SNo 1)) x57 x58) (x6 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x6 x56 x57 x58 = If_i (SNoLe x56 0) x58 (x1 (x5 (add_SNo x56 (minus_SNo 1)) x57 x58) (x6 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ x7 x56 = x5 (x2 x56) x3 x4) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x8 x56 x57 = mul_SNo x56 x57) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x9 x56 x57 = x57) ⟶ (∀ x56 . x56 ∈ int ⟶ x10 x56 = x56) ⟶ x11 = 1 ⟶ x12 = mul_SNo 2 (add_SNo 2 2) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x13 x56 x57 x58 = If_i (SNoLe x56 0) x57 (x8 (x13 (add_SNo x56 (minus_SNo 1)) x57 x58) (x14 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x14 x56 x57 x58 = If_i (SNoLe x56 0) x58 (x9 (x13 (add_SNo x56 (minus_SNo 1)) x57 x58) (x14 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ x15 x56 = x13 (x10 x56) x11 x12) ⟶ (∀ x56 . x56 ∈ int ⟶ x16 x56 = mul_SNo (x7 x56) (x15 x56)) ⟶ x17 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x18 x56 x57 = x57) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x19 x56 x57 = If_i (SNoLe x56 0) x57 (x16 (x19 (add_SNo x56 (minus_SNo 1)) x57))) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x20 x56 x57 = x19 x17 (x18 x56 x57)) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x21 x56 x57 = add_SNo (x20 x56 x57) x56) ⟶ (∀ x56 . x56 ∈ int ⟶ x22 x56 = x56) ⟶ x23 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x24 x56 x57 = If_i (SNoLe x56 0) x57 (x21 (x24 (add_SNo x56 (minus_SNo 1)) x57) x56)) ⟶ (∀ x56 . x56 ∈ int ⟶ x25 x56 = x24 (x22 x56) x23) ⟶ (∀ x56 . x56 ∈ int ⟶ x26 x56 = x25 x56) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x27 x56 x57 = add_SNo (mul_SNo (mul_SNo x57 x57) x57) (minus_SNo x56)) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x28 x56 x57 = add_SNo x57 x57) ⟶ (∀ x56 . x56 ∈ int ⟶ x29 x56 = x56) ⟶ x30 = 1 ⟶ x31 = 2 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x32 x56 x57 x58 = If_i (SNoLe x56 0) x57 (x27 (x32 (add_SNo x56 (minus_SNo 1)) x57 x58) (x33 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ ∀ x58 . x58 ∈ int ⟶ x33 x56 x57 x58 = If_i (SNoLe x56 0) x58 (x28 (x32 (add_SNo x56 (minus_SNo 1)) x57 x58) (x33 (add_SNo x56 (minus_SNo 1)) x57 x58))) ⟶ (∀ x56 . x56 ∈ int ⟶ x34 x56 = x32 (x29 x56) x30 x31) ⟶ (∀ x56 . x56 ∈ int ⟶ x35 x56 = mul_SNo (mul_SNo x56 x56) x56) ⟶ x36 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ x37 x56 = add_SNo x56 x56) ⟶ (∀ x56 . x56 ∈ int ⟶ x38 x56 = x56) ⟶ x39 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x40 x56 x57 = If_i (SNoLe x56 0) x57 (x37 (x40 (add_SNo x56 (minus_SNo 1)) x57))) ⟶ (∀ x56 . x56 ∈ int ⟶ x41 x56 = x40 (x38 x56) x39) ⟶ (∀ x56 . x56 ∈ int ⟶ x42 x56 = x41 x56) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x43 x56 x57 = If_i (SNoLe x56 0) x57 (x35 (x43 (add_SNo x56 (minus_SNo 1)) x57))) ⟶ (∀ x56 . x56 ∈ int ⟶ x44 x56 = x43 x36 (x42 x56)) ⟶ (∀ x56 . x56 ∈ int ⟶ x45 x56 = mul_SNo (x34 x56) (x44 x56)) ⟶ x46 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x47 x56 x57 = x57) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x48 x56 x57 = If_i (SNoLe x56 0) x57 (x45 (x48 (add_SNo x56 (minus_SNo 1)) x57))) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x49 x56 x57 = x48 x46 (x47 x56 x57)) ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x50 x56 x57 = add_SNo (x49 x56 x57) x56) ⟶ (∀ x56 . x56 ∈ int ⟶ x51 x56 = x56) ⟶ x52 = 1 ⟶ (∀ x56 . x56 ∈ int ⟶ ∀ x57 . x57 ∈ int ⟶ x53 x56 x57 = If_i (SNoLe x56 0) x57 (x50 (x53 (add_SNo x56 (minus_SNo 1)) x57) x56)) ⟶ (∀ x56 . x56 ∈ int ⟶ x54 x56 = x53 (x51 x56) x52) ⟶ (∀ x56 . x56 ∈ int ⟶ x55 x56 = x54 x56) ⟶ ∀ x56 . x56 ∈ int ⟶ SNoLe 0 x56 ⟶ x26 x56 = x55 x56
Conjecture 15163..^A15013 : ∀ 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 . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ x0 x20 = add_SNo 1 (minus_SNo (add_SNo x20 x20))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x1 x20 x21 = x21) ⟶ x2 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x4 x20 x21 = x3 (x1 x20 x21) x2) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x5 x20 x21 = mul_SNo (x4 x20 x21) x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = If_i (SNoLe x20 0) x21 (x5 (x8 (add_SNo x20 (minus_SNo 1)) x21) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x9 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = mul_SNo x20 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = add_SNo 1 (minus_SNo (add_SNo x21 x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 1 ⟶ x15 = add_SNo 0 (minus_SNo 1) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x16 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x11 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x17 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x12 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x16 (x13 x20) x14 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture 1b62e..^A15000 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x0 x20 x21 = mul_SNo (add_SNo 2 x21) x20) ⟶ x1 = 2 ⟶ (∀ x20 . x20 ∈ int ⟶ x2 x20 = x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x4 x20 = x3 x1 (x2 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = add_SNo 1 (minus_SNo (add_SNo (x4 x20) x20))) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = If_i (SNoLe x20 0) x21 (x5 (x8 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x9 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = add_SNo 1 (minus_SNo (mul_SNo x20 x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 1 ⟶ x15 = add_SNo 1 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x16 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x11 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x17 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x12 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x16 (x13 x20) x14 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture 37f08..^A14994 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x0 x20 x21 = mul_SNo (add_SNo 2 x21) x20) ⟶ x1 = 2 ⟶ (∀ x20 . x20 ∈ int ⟶ x2 x20 = x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x4 x20 = x3 x1 (x2 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = add_SNo 1 (minus_SNo (x4 x20))) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = If_i (SNoLe x20 0) x21 (x5 (x8 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x9 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = add_SNo 1 (minus_SNo (mul_SNo x20 x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 1 ⟶ x15 = mul_SNo 2 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x16 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x11 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x17 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x12 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x16 (x13 x20) x14 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture ba35e..^A14993 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x0 x20 x21 = mul_SNo (add_SNo 2 x21) x20) ⟶ x1 = 2 ⟶ (∀ x20 . x20 ∈ int ⟶ x2 x20 = x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x4 x20 = x3 x1 (x2 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = add_SNo 1 (add_SNo x20 (minus_SNo (x4 x20)))) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = If_i (SNoLe x20 0) x21 (x5 (x8 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x9 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = add_SNo 1 (mul_SNo x20 x21)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 1 ⟶ x15 = add_SNo 1 (minus_SNo (mul_SNo 2 (add_SNo 2 (add_SNo 2 2)))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x16 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x11 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x17 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x12 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x16 (x13 x20) x14 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture 11705..^A14992 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x12 x13 x14 x15 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ (∀ x15 . x15 ∈ int ⟶ x0 x15 = add_SNo 1 (minus_SNo (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x15 x15)) x15)))) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = x15) ⟶ x2 = 1 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = x4 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x6 x15 x16 = add_SNo 1 (minus_SNo (mul_SNo x15 x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x7 x15 x16 = x16) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = x15) ⟶ x9 = 1 ⟶ x10 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x11 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x6 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x12 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x7 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x11 (x8 x15) x9 x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = x13 x15) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture cee99..^A14991 : ∀ 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 . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ x0 x20 = add_SNo (add_SNo x20 x20) x20) ⟶ x1 = 2 ⟶ (∀ x20 . x20 ∈ int ⟶ x2 x20 = x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x4 x20 = x3 x1 (x2 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = add_SNo 1 (minus_SNo (x4 x20))) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = If_i (SNoLe x20 0) x21 (x5 (x8 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x9 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = add_SNo 1 (minus_SNo (mul_SNo x20 x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 1 ⟶ x15 = add_SNo 1 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x16 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x11 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x17 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x12 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x16 (x13 x20) x14 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20