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 8678a..^A13766 : ∀ 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 . (∀ 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 ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x36 x37 x38 x39 ∈ int) ⟶ ∀ x37 : ι → ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x37 x38 x39 x40 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ ∀ x40 : ι → ι → ι . (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x40 x41 x42 ∈ int) ⟶ ∀ x41 : ι → ι . (∀ x42 . x42 ∈ int ⟶ x41 x42 ∈ int) ⟶ ∀ x42 : ι → ι . (∀ x43 . x43 ∈ int ⟶ x42 x43 ∈ int) ⟶ (∀ x43 . x43 ∈ int ⟶ x0 x43 = mul_SNo 2 (add_SNo 2 x43)) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x3 x43 x44 = If_i (SNoLe x43 0) x44 (x0 (x3 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x43 . x43 ∈ int ⟶ x5 x43 = mul_SNo x4 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x6 x43 = add_SNo 1 (add_SNo (add_SNo x43 x43) x43)) ⟶ x7 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x8 x43 x44 = If_i (SNoLe x43 0) x44 (x5 (x8 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ x9 x43 = x8 (x6 x43) x7) ⟶ (∀ x43 . x43 ∈ int ⟶ x10 x43 = x9 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x11 x43 = mul_SNo (mul_SNo x43 x43) x43) ⟶ x12 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ x13 x43 = add_SNo x43 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ x14 x43 = x43) ⟶ x15 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x16 x43 x44 = If_i (SNoLe x43 0) x44 (x13 (x16 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ x17 x43 = x16 (x14 x43) x15) ⟶ (∀ x43 . x43 ∈ int ⟶ x18 x43 = x17 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x19 x43 x44 = If_i (SNoLe x43 0) x44 (x11 (x19 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ x20 x43 = x19 x12 (x18 x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x21 x43 x44 = mul_SNo x43 x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x22 x43 x44 = x44) ⟶ (∀ x43 . x43 ∈ int ⟶ x23 x43 = add_SNo 1 x43) ⟶ x24 = 1 ⟶ x25 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x26 x43 x44 x45 = If_i (SNoLe x43 0) x44 (x21 (x26 (add_SNo x43 (minus_SNo 1)) x44 x45) (x27 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x27 x43 x44 x45 = If_i (SNoLe x43 0) x45 (x22 (x26 (add_SNo x43 (minus_SNo 1)) x44 x45) (x27 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ x28 x43 = x26 (x23 x43) x24 x25) ⟶ (∀ x43 . x43 ∈ int ⟶ x29 x43 = mul_SNo x43 x43) ⟶ x30 = 1 ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x31 x43 x44 = mul_SNo x43 x44) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x32 x43 x44 = x44) ⟶ (∀ x43 . x43 ∈ int ⟶ x33 x43 = x43) ⟶ x34 = 1 ⟶ x35 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x36 x43 x44 x45 = If_i (SNoLe x43 0) x44 (x31 (x36 (add_SNo x43 (minus_SNo 1)) x44 x45) (x37 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ ∀ x45 . x45 ∈ int ⟶ x37 x43 x44 x45 = If_i (SNoLe x43 0) x45 (x32 (x36 (add_SNo x43 (minus_SNo 1)) x44 x45) (x37 (add_SNo x43 (minus_SNo 1)) x44 x45))) ⟶ (∀ x43 . x43 ∈ int ⟶ x38 x43 = x36 (x33 x43) x34 x35) ⟶ (∀ x43 . x43 ∈ int ⟶ x39 x43 = x38 x43) ⟶ (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x40 x43 x44 = If_i (SNoLe x43 0) x44 (x29 (x40 (add_SNo x43 (minus_SNo 1)) x44))) ⟶ (∀ x43 . x43 ∈ int ⟶ x41 x43 = x40 x30 (x39 x43)) ⟶ (∀ x43 . x43 ∈ int ⟶ x42 x43 = mul_SNo (mul_SNo (mul_SNo 2 (x20 x43)) (x28 x43)) (x41 x43)) ⟶ ∀ x43 . x43 ∈ int ⟶ SNoLe 0 x43 ⟶ x10 x43 = x42 x43
Conjecture d622e..^A13761 : ∀ 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 . (∀ 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 → 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 → 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 ⟶ x0 x33 = mul_SNo x33 x33) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x3 x33 x34 = If_i (SNoLe x33 0) x34 (x0 (x3 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = add_SNo (mul_SNo x4 x33) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = add_SNo 2 (add_SNo (add_SNo x33 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 = x9 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = mul_SNo x33 x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x33) ⟶ x16 = 1 ⟶ x17 = add_SNo 1 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x18 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x13 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x14 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = x18 (x15 x33) x16 x17) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x20 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x11 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x22 x12 (x21 x33)) ⟶ (∀ 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 = add_SNo 2 x33) ⟶ x27 = 1 ⟶ x28 = add_SNo 1 (mul_SNo 2 (mul_SNo 2 (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 = mul_SNo (x23 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x10 x33 = x32 x33
Conjecture 6e6db..^A13760 : ∀ 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 . (∀ 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 → 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 → 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 ⟶ x0 x33 = mul_SNo x33 x33) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x3 x33 x34 = If_i (SNoLe x33 0) x34 (x0 (x3 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = add_SNo (mul_SNo x4 x33) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = add_SNo 1 (add_SNo (add_SNo x33 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 = x9 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = mul_SNo x33 x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x33) ⟶ x16 = 1 ⟶ x17 = add_SNo 1 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x18 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x13 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x14 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = x18 (x15 x33) x16 x17) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x20 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x11 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x22 x12 (x21 x33)) ⟶ (∀ 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 = add_SNo 1 x33) ⟶ x27 = 1 ⟶ x28 = add_SNo 1 (mul_SNo 2 (mul_SNo 2 (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 = mul_SNo (x23 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x10 x33 = x32 x33
Conjecture 76284..^A13757 : ∀ 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 . (∀ 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 → 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 → 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 ⟶ x0 x33 = mul_SNo x33 x33) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x3 x33 x34 = If_i (SNoLe x33 0) x34 (x0 (x3 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = add_SNo (mul_SNo x4 x33) (minus_SNo x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = add_SNo 2 (add_SNo (add_SNo x33 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 = x9 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = mul_SNo x33 x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x33) ⟶ x16 = 1 ⟶ x17 = add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2))) (minus_SNo 1) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x18 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x13 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x14 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = x18 (x15 x33) x16 x17) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x20 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x11 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x22 x12 (x21 x33)) ⟶ (∀ 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 = add_SNo 2 x33) ⟶ x27 = 1 ⟶ x28 = add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2))) (minus_SNo 1) ⟶ (∀ 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 = mul_SNo (x23 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x10 x33 = x32 x33
Conjecture f81c8..^A13756 : ∀ 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 . (∀ 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 → 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 → 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 ⟶ x0 x33 = mul_SNo x33 x33) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x3 x33 x34 = If_i (SNoLe x33 0) x34 (x0 (x3 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = add_SNo (mul_SNo x4 x33) (minus_SNo x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = add_SNo 1 (add_SNo (add_SNo x33 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 = x9 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = mul_SNo x33 x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x33) ⟶ x16 = 1 ⟶ x17 = add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2))) (minus_SNo 1) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x18 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x13 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x14 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = x18 (x15 x33) x16 x17) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x20 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x11 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x22 x12 (x21 x33)) ⟶ (∀ 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 = add_SNo 1 x33) ⟶ x27 = 1 ⟶ x28 = add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2))) (minus_SNo 1) ⟶ (∀ 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 = mul_SNo (x23 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x10 x33 = x32 x33
Conjecture 8f5e7..^A13755 : ∀ 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 . (∀ 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 → 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 → 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 ⟶ x0 x33 = mul_SNo x33 x33) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x3 x33 x34 = If_i (SNoLe x33 0) x34 (x0 (x3 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = mul_SNo (add_SNo x4 (minus_SNo 2)) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = add_SNo 2 (add_SNo (add_SNo x33 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 = x9 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = mul_SNo x33 x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x33) ⟶ x16 = 1 ⟶ x17 = add_SNo 2 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x18 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x13 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x14 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = x18 (x15 x33) x16 x17) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x20 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x11 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x22 x12 (x21 x33)) ⟶ (∀ 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 = add_SNo 2 x33) ⟶ x27 = 1 ⟶ x28 = add_SNo 2 (mul_SNo 2 (add_SNo 2 (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 = mul_SNo (x23 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x10 x33 = x32 x33
Conjecture f3d66..^A13754 : ∀ 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 . (∀ 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 → 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 → 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 ⟶ x0 x33 = mul_SNo x33 x33) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x3 x33 x34 = If_i (SNoLe x33 0) x34 (x0 (x3 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = mul_SNo (add_SNo x4 (minus_SNo 2)) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = add_SNo 1 (add_SNo (add_SNo x33 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 = x9 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = mul_SNo x33 x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x33) ⟶ x16 = 1 ⟶ x17 = add_SNo 2 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x18 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x13 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x14 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = x18 (x15 x33) x16 x17) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x20 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x11 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x22 x12 (x21 x33)) ⟶ (∀ 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 = add_SNo 1 x33) ⟶ x27 = 1 ⟶ x28 = add_SNo 2 (mul_SNo 2 (add_SNo 2 (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 = mul_SNo (x23 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x10 x33 = x32 x33
Conjecture 965f9..^A13753 : ∀ 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 → 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 → 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) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = add_SNo 2 (add_SNo (add_SNo x33 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 = x9 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = mul_SNo x33 x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x33) ⟶ x16 = 1 ⟶ x17 = add_SNo 1 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x18 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x13 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x14 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = x18 (x15 x33) x16 x17) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x20 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x11 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x22 x12 (x21 x33)) ⟶ (∀ 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 = add_SNo 2 x33) ⟶ x27 = 1 ⟶ x28 = add_SNo 1 (mul_SNo 2 (add_SNo 2 (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 = mul_SNo (x23 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x10 x33 = x32 x33
Conjecture 01e12..^A13752 : ∀ 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 → 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 → 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) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = add_SNo 1 (add_SNo (add_SNo x33 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 = x9 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = mul_SNo x33 x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x33) ⟶ x16 = 1 ⟶ x17 = add_SNo 1 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x18 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x13 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x14 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = x18 (x15 x33) x16 x17) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x20 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x11 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x22 x12 (x21 x33)) ⟶ (∀ 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 = add_SNo 1 x33) ⟶ x27 = 1 ⟶ x28 = add_SNo 1 (mul_SNo 2 (add_SNo 2 (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 = mul_SNo (x23 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x10 x33 = x32 x33
Conjecture 12182..^A13751 : ∀ 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 → 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 → 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 = x4 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = add_SNo 2 (add_SNo (add_SNo x33 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 = x9 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = mul_SNo x33 x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x33) ⟶ x16 = 2 ⟶ x17 = mul_SNo 2 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x18 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x13 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x14 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = x18 (x15 x33) x16 x17) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x20 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x11 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x22 x12 (x21 x33)) ⟶ (∀ 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 = add_SNo 1 x33) ⟶ x27 = add_SNo 1 2 ⟶ x28 = mul_SNo 2 (add_SNo 2 (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 = mul_SNo (x23 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x10 x33 = x32 x33
Conjecture d9b9e..^A13750 : ∀ 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 → 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 → 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 = x4 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = add_SNo 1 (add_SNo (add_SNo x33 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 = x9 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = mul_SNo x33 x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x33) ⟶ x16 = 1 ⟶ x17 = mul_SNo 2 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x18 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x13 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x14 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = x18 (x15 x33) x16 x17) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x20 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x11 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x22 x12 (x21 x33)) ⟶ (∀ 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 = add_SNo 1 x33) ⟶ x27 = 1 ⟶ x28 = mul_SNo 2 (add_SNo 2 (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 = mul_SNo (x23 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x10 x33 = x32 x33
Conjecture 7a7c2..^A13749 : ∀ 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 → 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 → 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 = add_SNo 2 (add_SNo (add_SNo x33 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 = x9 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = mul_SNo x33 x33) ⟶ x12 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x33) ⟶ x16 = 1 ⟶ x17 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x18 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x13 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x14 (x18 (add_SNo x33 (minus_SNo 1)) x34 x35) (x19 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = x18 (x15 x33) x16 x17) ⟶ (∀ x33 . x33 ∈ int ⟶ x21 x33 = x20 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = If_i (SNoLe x33 0) x34 (x11 (x22 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x22 x12 (x21 x33)) ⟶ (∀ 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 = add_SNo 2 x33) ⟶ x27 = 1 ⟶ x28 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (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 = mul_SNo (x23 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x10 x33 = x32 x33
Conjecture 8db9b..^A13748 : ∀ 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 → 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 ⟶ ∀ x26 . x26 ∈ int ⟶ x0 x25 x26 = mul_SNo (add_SNo 2 x26) x25) ⟶ x1 = 2 ⟶ (∀ x25 . x25 ∈ int ⟶ x2 x25 = x25) ⟶ (∀ 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 . x25 ∈ int ⟶ x4 x25 = x3 x1 (x2 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x5 x25 = add_SNo (x4 x25) (minus_SNo x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x6 x25 = add_SNo 1 (add_SNo (add_SNo x25 x25) x25)) ⟶ x7 = 1 ⟶ (∀ 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 x25) x7) ⟶ (∀ x25 . x25 ∈ int ⟶ x10 x25 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x11 x25 = mul_SNo (add_SNo (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x25 x25)) x25)) x25) (mul_SNo x25 x25)) ⟶ x12 = 1 ⟶ (∀ 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 (mul_SNo 2 (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 = 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 (x21 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = x23 x25) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture 057bb..^A13747 : ∀ 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 → 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 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ x0 x28 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x28 x28)) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x1 x28 = add_SNo 2 (add_SNo (add_SNo x28 x28) x28)) ⟶ x2 = 1 ⟶ (∀ 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 x28) x2) ⟶ (∀ x28 . x28 ∈ int ⟶ x5 x28 = x4 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = mul_SNo x28 x28) ⟶ x7 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x8 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x9 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = x28) ⟶ x11 = 1 ⟶ x12 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x13 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x8 (x13 (add_SNo x28 (minus_SNo 1)) x29 x30) (x14 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x14 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x9 (x13 (add_SNo x28 (minus_SNo 1)) x29 x30) (x14 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x13 (x10 x28) x11 x12) ⟶ (∀ x28 . x28 ∈ int ⟶ x16 x28 = x15 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x17 x28 x29 = If_i (SNoLe x28 0) x29 (x6 (x17 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x18 x28 = x17 x7 (x16 x28)) ⟶ (∀ 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 = add_SNo 2 x28) ⟶ x22 = 1 ⟶ x23 = add_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 ⟶ x5 x28 = x27 x28
Conjecture 2f2e8..^A13746 : ∀ 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 → 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 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ x0 x28 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x28 x28)) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x1 x28 = add_SNo 1 (add_SNo (add_SNo x28 x28) x28)) ⟶ x2 = 1 ⟶ (∀ 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 x28) x2) ⟶ (∀ x28 . x28 ∈ int ⟶ x5 x28 = x4 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = mul_SNo x28 x28) ⟶ x7 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x8 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x9 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = x28) ⟶ x11 = 1 ⟶ x12 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x13 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x8 (x13 (add_SNo x28 (minus_SNo 1)) x29 x30) (x14 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x14 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x9 (x13 (add_SNo x28 (minus_SNo 1)) x29 x30) (x14 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x13 (x10 x28) x11 x12) ⟶ (∀ x28 . x28 ∈ int ⟶ x16 x28 = x15 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x17 x28 x29 = If_i (SNoLe x28 0) x29 (x6 (x17 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x18 x28 = x17 x7 (x16 x28)) ⟶ (∀ 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 = add_SNo 1 x28) ⟶ x22 = 1 ⟶ x23 = add_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 ⟶ x5 x28 = x27 x28
Conjecture df025..^A13745 : ∀ 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 → 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 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 : ι → ι → 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 ⟶ x0 x33 = add_SNo (add_SNo x33 x33) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x1 x33 = mul_SNo 2 (add_SNo 2 (add_SNo (add_SNo x33 x33) x33))) ⟶ x2 = 1 ⟶ (∀ 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 ∈ int ⟶ x4 x33 = x3 (x1 x33) x2) ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = x4 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = mul_SNo x33 x33) ⟶ x7 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x8 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x9 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x10 x33 = x33) ⟶ x11 = add_SNo 1 2 ⟶ x12 = add_SNo 1 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x13 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x8 (x13 (add_SNo x33 (minus_SNo 1)) x34 x35) (x14 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x14 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x9 (x13 (add_SNo x33 (minus_SNo 1)) x34 x35) (x14 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x15 x33 = x13 (x10 x33) x11 x12) ⟶ (∀ x33 . x33 ∈ int ⟶ x16 x33 = x15 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x17 x33 x34 = If_i (SNoLe x33 0) x34 (x6 (x17 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x18 x33 = x17 x7 (x16 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x19 x33 = mul_SNo x33 x33) ⟶ x20 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x21 x33 x34 = mul_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x33) ⟶ x24 = add_SNo 1 2 ⟶ x25 = add_SNo 1 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x26 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x21 (x26 (add_SNo x33 (minus_SNo 1)) x34 x35) (x27 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x27 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x22 (x26 (add_SNo x33 (minus_SNo 1)) x34 x35) (x27 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x28 x33 = x26 (x23 x33) x24 x25) ⟶ (∀ x33 . x33 ∈ int ⟶ x29 x33 = x28 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x30 x33 x34 = If_i (SNoLe x33 0) x34 (x19 (x30 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x31 x33 = x30 x20 (x29 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x32 x33 = mul_SNo (x18 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x5 x33 = x32 x33
Conjecture 7f021..^A13744 : ∀ 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 → 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 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ x0 x20 = add_SNo (add_SNo x20 x20) x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x1 x20 = add_SNo 2 (mul_SNo 2 (add_SNo (add_SNo x20 x20) x20))) ⟶ x2 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x4 x20 = x3 (x1 x20) x2) ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = x4 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = mul_SNo x20 x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = mul_SNo x20 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x9 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x20) ⟶ x11 = add_SNo 1 2 ⟶ x12 = mul_SNo (add_SNo 1 (mul_SNo 2 (add_SNo 2 2))) (add_SNo 1 2) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x13 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x8 (x13 (add_SNo x20 (minus_SNo 1)) x21 x22) (x14 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x14 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x9 (x13 (add_SNo x20 (minus_SNo 1)) x21 x22) (x14 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x15 x20 = x13 (x10 x20) x11 x12) ⟶ (∀ x20 . x20 ∈ int ⟶ x16 x20 = x15 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x17 x20 x21 = If_i (SNoLe x20 0) x21 (x6 (x17 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x17 x7 (x16 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x5 x20 = x19 x20
Conjecture 34c6b..^A13743 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ 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 : 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 . (∀ 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 . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ (∀ x32 . x32 ∈ int ⟶ x0 x32 = add_SNo x32 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x1 x32 x33 = add_SNo (add_SNo (add_SNo x32 x32) x32) x33) ⟶ x2 = 2 ⟶ (∀ x32 . x32 ∈ int ⟶ x3 x32 = x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x4 x32 x33 = If_i (SNoLe x32 0) x33 (x1 (x4 (add_SNo x32 (minus_SNo 1)) x33) x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x5 x32 = x4 x2 (x3 x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x6 x32 = x5 x32) ⟶ x7 = 2 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x8 x32 x33 = If_i (SNoLe x32 0) x33 (x0 (x8 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x9 x32 = x8 (x6 x32) x7) ⟶ (∀ x32 . x32 ∈ int ⟶ x10 x32 = x9 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ x11 x32 = mul_SNo x32 x32) ⟶ x12 = 2 ⟶ (∀ x32 . x32 ∈ int ⟶ x13 x32 = add_SNo x32 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ x14 x32 = x32) ⟶ x15 = 1 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x16 x32 x33 = If_i (SNoLe x32 0) x33 (x13 (x16 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x17 x32 = x16 (x14 x32) x15) ⟶ (∀ x32 . x32 ∈ int ⟶ x18 x32 = x17 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x19 x32 x33 = If_i (SNoLe x32 0) x33 (x11 (x19 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x20 x32 = x19 x12 (x18 x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x21 x32 = mul_SNo (mul_SNo x32 x32) (mul_SNo 2 (mul_SNo (mul_SNo x32 x32) x32))) ⟶ x22 = 1 ⟶ (∀ x32 . x32 ∈ int ⟶ x23 x32 = add_SNo x32 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ x24 x32 = x32) ⟶ x25 = 2 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x26 x32 x33 = If_i (SNoLe x32 0) x33 (x23 (x26 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x27 x32 = x26 (x24 x32) x25) ⟶ (∀ x32 . x32 ∈ int ⟶ x28 x32 = x27 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x29 x32 x33 = If_i (SNoLe x32 0) x33 (x21 (x29 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x30 x32 = x29 x22 (x28 x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x31 x32 = mul_SNo (x20 x32) (x30 x32)) ⟶ ∀ x32 . x32 ∈ int ⟶ SNoLe 0 x32 ⟶ x10 x32 = x31 x32
Conjecture 52246..^A13742 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ 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 : 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 . (∀ 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 . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ (∀ x32 . x32 ∈ int ⟶ x0 x32 = add_SNo x32 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ x1 x32 = add_SNo (add_SNo x32 x32) x32) ⟶ x2 = 2 ⟶ (∀ x32 . x32 ∈ int ⟶ x3 x32 = x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x4 x32 x33 = If_i (SNoLe x32 0) x33 (x1 (x4 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x5 x32 = x4 x2 (x3 x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x6 x32 = add_SNo 2 (x5 x32)) ⟶ x7 = 2 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x8 x32 x33 = If_i (SNoLe x32 0) x33 (x0 (x8 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x9 x32 = x8 (x6 x32) x7) ⟶ (∀ x32 . x32 ∈ int ⟶ x10 x32 = x9 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ x11 x32 = mul_SNo 2 (mul_SNo x32 x32)) ⟶ x12 = 2 ⟶ (∀ x32 . x32 ∈ int ⟶ x13 x32 = add_SNo x32 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ x14 x32 = x32) ⟶ x15 = 1 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x16 x32 x33 = If_i (SNoLe x32 0) x33 (x13 (x16 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x17 x32 = x16 (x14 x32) x15) ⟶ (∀ x32 . x32 ∈ int ⟶ x18 x32 = x17 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x19 x32 x33 = If_i (SNoLe x32 0) x33 (x11 (x19 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x20 x32 = x19 x12 (x18 x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x21 x32 = mul_SNo (mul_SNo (mul_SNo (mul_SNo x32 x32) x32) x32) x32) ⟶ x22 = 1 ⟶ (∀ x32 . x32 ∈ int ⟶ x23 x32 = add_SNo x32 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ x24 x32 = x32) ⟶ x25 = 1 ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x26 x32 x33 = If_i (SNoLe x32 0) x33 (x23 (x26 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x27 x32 = x26 (x24 x32) x25) ⟶ (∀ x32 . x32 ∈ int ⟶ x28 x32 = x27 x32) ⟶ (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x29 x32 x33 = If_i (SNoLe x32 0) x33 (x21 (x29 (add_SNo x32 (minus_SNo 1)) x33))) ⟶ (∀ x32 . x32 ∈ int ⟶ x30 x32 = x29 x22 (x28 x32)) ⟶ (∀ x32 . x32 ∈ int ⟶ x31 x32 = mul_SNo (x20 x32) (x30 x32)) ⟶ ∀ x32 . x32 ∈ int ⟶ SNoLe 0 x32 ⟶ x10 x32 = x31 x32
Conjecture e1d55..^A13741 : ∀ 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 → 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 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ x0 x28 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x28 x28) x28)) x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x1 x28 = add_SNo 2 (add_SNo (add_SNo x28 x28) x28)) ⟶ x2 = 1 ⟶ (∀ 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 x28) x2) ⟶ (∀ x28 . x28 ∈ int ⟶ x5 x28 = x4 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = mul_SNo x28 x28) ⟶ x7 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x8 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x9 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = x28) ⟶ x11 = 1 ⟶ x12 = add_SNo 1 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x13 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x8 (x13 (add_SNo x28 (minus_SNo 1)) x29 x30) (x14 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x14 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x9 (x13 (add_SNo x28 (minus_SNo 1)) x29 x30) (x14 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x13 (x10 x28) x11 x12) ⟶ (∀ x28 . x28 ∈ int ⟶ x16 x28 = x15 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x17 x28 x29 = If_i (SNoLe x28 0) x29 (x6 (x17 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x18 x28 = x17 x7 (x16 x28)) ⟶ (∀ 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 = add_SNo 2 x28) ⟶ x22 = 1 ⟶ x23 = add_SNo 1 (add_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 ⟶ x5 x28 = x27 x28