Proofgold Address

Param int^int : ι
Param mul_SNo^mul_SNo : ι → ι → ι
Param add_SNo^add_SNo : ι → ι → ι
Param ordsucc^ordsucc : ι → ι
Param If_i^If_i : ο → ι → ι → ι
Param SNoLe^SNoLe : ι → ι → ο
Param minus_SNo^minus_SNo : ι → ι
Conjecture 37375..^A16101 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ 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 → 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 → 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 . x21 ∈ int ⟶ x0 x20 x21 = mul_SNo (add_SNo 2 x21) x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x1 x20 = add_SNo 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 . x20 ∈ int ⟶ x4 x20 = x3 (x1 x20) x2) ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = add_SNo (add_SNo (x4 x20) (minus_SNo 1)) (minus_SNo x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x6 x20 x21 = mul_SNo x20 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x7 x20 x21 = add_SNo 1 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x8 x20 = x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = add_SNo 1 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = add_SNo 2 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x11 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x6 (x11 (add_SNo x20 (minus_SNo 1)) x21 x22) (x12 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x12 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x7 (x11 (add_SNo x20 (minus_SNo 1)) x21 x22) (x12 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x11 (x8 x20) (x9 x20) (x10 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x14 x20 x21 = mul_SNo x20 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x15 x20 = x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x16 x20 = add_SNo 1 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x17 x20 x21 = If_i (SNoLe x20 0) x21 (x14 (x17 (add_SNo x20 (minus_SNo 1)) x21) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x17 (x15 x20) (x16 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = add_SNo (mul_SNo (x13 x20) (x18 x20)) (minus_SNo (add_SNo 1 x20))) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x5 x20 = x19 x20
Conjecture e0d6b..^A160958 : ∀ 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 = add_SNo x23 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x1 x23 = mul_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 (mul_SNo 2 (mul_SNo 2 x5)) x23) x24) ⟶ (∀ 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 2 (add_SNo (mul_SNo 2 (mul_SNo 2 (mul_SNo 2 (mul_SNo 2 (add_SNo x24 x24))))) x23)) (minus_SNo x24)) ⟶ (∀ x23 . x23 ∈ int ⟶ x15 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x16 x23 = add_SNo x23 (minus_SNo 1)) ⟶ (∀ x23 . x23 ∈ int ⟶ x17 x23 = If_i (SNoLe x23 0) 1 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 63141..^A16092 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 : ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x23 x24 x25 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι → 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 → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x28 x29 x30 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 : ι → ι . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ int) ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x36 x37 x38 x39 ∈ int) ⟶ ∀ x37 : ι → ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x37 x38 x39 x40 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ ∀ x40 . x40 ∈ int ⟶ ∀ x41 : ι → ι . (∀ x42 . x42 ∈ int ⟶ x41 x42 ∈ int) ⟶ ∀ x42 : ι → ι . (∀ x43 . x43 ∈ int ⟶ x42 x43 ∈ int) ⟶ ∀ x43 . x43 ∈ int ⟶ ∀ x44 : ι → ι → ι . (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x44 x45 x46 ∈ int) ⟶ ∀ x45 : ι → ι . (∀ x46 . x46 ∈ int ⟶ x45 x46 ∈ 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 . (∀ x49 . x49 ∈ int ⟶ x48 x49 ∈ int) ⟶ ∀ x49 : ι → ι . (∀ x50 . x50 ∈ int ⟶ x49 x50 ∈ int) ⟶ ∀ x50 . x50 ∈ int ⟶ ∀ x51 : ι → ι → ι . (∀ x52 . x52 ∈ int ⟶ ∀ x53 . x53 ∈ int ⟶ x51 x52 x53 ∈ int) ⟶ ∀ x52 : ι → ι → ι . (∀ x53 . x53 ∈ int ⟶ ∀ x54 . x54 ∈ int ⟶ x52 x53 x54 ∈ int) ⟶ ∀ x53 : ι → ι → ι . (∀ x54 . x54 ∈ int ⟶ ∀ x55 . x55 ∈ int ⟶ x53 x54 x55 ∈ int) ⟶ ∀ x54 : ι → ι → ι . (∀ x55 . x55 ∈ int ⟶ ∀ x56 . x56 ∈ int ⟶ x54 x55 x56 ∈ 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 . (∀ x59 . x59 ∈ int ⟶ x58 x59 ∈ int) ⟶ ∀ x59 : ι → ι . (∀ x60 . x60 ∈ int ⟶ x59 x60 ∈ int) ⟶ ∀ x60 . x60 ∈ int ⟶ ∀ x61 : ι → ι → ι . (∀ x62 . x62 ∈ int ⟶ ∀ x63 . x63 ∈ int ⟶ x61 x62 x63 ∈ int) ⟶ ∀ x62 : ι → ι → ι . (∀ x63 . x63 ∈ int ⟶ ∀ x64 . x64 ∈ int ⟶ x62 x63 x64 ∈ int) ⟶ ∀ x63 : ι → ι → ι . (∀ x64 . x64 ∈ int ⟶ ∀ x65 . x65 ∈ int ⟶ x63 x64 x65 ∈ int) ⟶ ∀ x64 : ι → ι → ι . (∀ x65 . x65 ∈ int ⟶ ∀ x66 . x66 ∈ int ⟶ x64 x65 x66 ∈ int) ⟶ ∀ x65 : ι → ι . (∀ x66 . x66 ∈ int ⟶ x65 x66 ∈ int) ⟶ ∀ x66 . x66 ∈ int ⟶ ∀ x67 : ι → ι → ι . (∀ x68 . x68 ∈ int ⟶ ∀ x69 . x69 ∈ int ⟶ x67 x68 x69 ∈ int) ⟶ ∀ x68 : ι → ι . (∀ x69 . x69 ∈ int ⟶ x68 x69 ∈ int) ⟶ ∀ x69 : ι → ι . (∀ x70 . x70 ∈ int ⟶ x69 x70 ∈ int) ⟶ (∀ x70 . x70 ∈ int ⟶ x0 x70 = add_SNo (add_SNo x70 x70) x70) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x1 x70 x71 = add_SNo x71 x71) ⟶ x2 = 1 ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x3 x70 x71 = If_i (SNoLe x70 0) x71 (x0 (x3 (add_SNo x70 (minus_SNo 1)) x71))) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x4 x70 x71 = x3 (x1 x70 x71) x2) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x5 x70 x71 = add_SNo (x4 x70 x71) (mul_SNo 2 (mul_SNo 2 (add_SNo x70 x70)))) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x6 x70 x71 = x71) ⟶ x7 = 1 ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x8 x70 x71 = If_i (SNoLe x70 0) x71 (x5 (x8 (add_SNo x70 (minus_SNo 1)) x71) x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x9 x70 x71 = x8 (x6 x70 x71) x7) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x10 x70 x71 = mul_SNo (add_SNo 2 x71) x70) ⟶ x11 = 2 ⟶ (∀ x70 . x70 ∈ int ⟶ x12 x70 = x70) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x13 x70 x71 = If_i (SNoLe x70 0) x71 (x10 (x13 (add_SNo x70 (minus_SNo 1)) x71) x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ x14 x70 = x13 x11 (x12 x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x15 x70 x71 = add_SNo (x9 x70 x71) (x14 x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x16 x70 x71 = x71) ⟶ x17 = 1 ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x18 x70 x71 = If_i (SNoLe x70 0) x71 (x15 (x18 (add_SNo x70 (minus_SNo 1)) x71) x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x19 x70 x71 = x18 (x16 x70 x71) x17) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x20 x70 x71 = mul_SNo (add_SNo 2 x71) x70) ⟶ x21 = 2 ⟶ (∀ x70 . x70 ∈ int ⟶ x22 x70 = x70) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x23 x70 x71 = If_i (SNoLe x70 0) x71 (x20 (x23 (add_SNo x70 (minus_SNo 1)) x71) x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ x24 x70 = x23 x21 (x22 x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x25 x70 x71 = add_SNo (add_SNo (x19 x70 x71) (minus_SNo x70)) (x24 x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ x26 x70 = x70) ⟶ x27 = 1 ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x28 x70 x71 = If_i (SNoLe x70 0) x71 (x25 (x28 (add_SNo x70 (minus_SNo 1)) x71) x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ x29 x70 = x28 (x26 x70) x27) ⟶ (∀ x70 . x70 ∈ int ⟶ x30 x70 = x29 x70) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x31 x70 x71 = add_SNo (add_SNo (add_SNo x70 x70) x70) x71) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x32 x70 x71 = add_SNo x71 x71) ⟶ (∀ x70 . x70 ∈ int ⟶ x33 x70 = x70) ⟶ x34 = 1 ⟶ x35 = 2 ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ ∀ x72 . x72 ∈ int ⟶ x36 x70 x71 x72 = If_i (SNoLe x70 0) x71 (x31 (x36 (add_SNo x70 (minus_SNo 1)) x71 x72) (x37 (add_SNo x70 (minus_SNo 1)) x71 x72))) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ ∀ x72 . x72 ∈ int ⟶ x37 x70 x71 x72 = If_i (SNoLe x70 0) x72 (x32 (x36 (add_SNo x70 (minus_SNo 1)) x71 x72) (x37 (add_SNo x70 (minus_SNo 1)) x71 x72))) ⟶ (∀ x70 . x70 ∈ int ⟶ x38 x70 = x36 (x33 x70) x34 x35) ⟶ (∀ x70 . x70 ∈ int ⟶ x39 x70 = mul_SNo x70 x70) ⟶ x40 = 1 ⟶ (∀ x70 . x70 ∈ int ⟶ x41 x70 = add_SNo x70 x70) ⟶ (∀ x70 . x70 ∈ int ⟶ x42 x70 = x70) ⟶ x43 = 1 ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x44 x70 x71 = If_i (SNoLe x70 0) x71 (x41 (x44 (add_SNo x70 (minus_SNo 1)) x71))) ⟶ (∀ x70 . x70 ∈ int ⟶ x45 x70 = x44 (x42 x70) x43) ⟶ (∀ x70 . x70 ∈ int ⟶ x46 x70 = x45 x70) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x47 x70 x71 = If_i (SNoLe x70 0) x71 (x39 (x47 (add_SNo x70 (minus_SNo 1)) x71))) ⟶ (∀ x70 . x70 ∈ int ⟶ x48 x70 = x47 x40 (x46 x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ x49 x70 = mul_SNo (x38 x70) (x48 x70)) ⟶ x50 = 1 ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x51 x70 x71 = x71) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x52 x70 x71 = If_i (SNoLe x70 0) x71 (x49 (x52 (add_SNo x70 (minus_SNo 1)) x71))) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x53 x70 x71 = x52 x50 (x51 x70 x71)) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x54 x70 x71 = add_SNo (add_SNo (x53 x70 x71) x70) (mul_SNo (mul_SNo (mul_SNo x70 2) 2) 2)) ⟶ (∀ x70 . x70 ∈ int ⟶ x55 x70 = x70) ⟶ x56 = 1 ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x57 x70 x71 = If_i (SNoLe x70 0) x71 (x54 (x57 (add_SNo x70 (minus_SNo 1)) x71) x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ x58 x70 = x57 (x55 x70) x56) ⟶ (∀ x70 . x70 ∈ int ⟶ x59 x70 = x58 x70) ⟶ x60 = 1 ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x61 x70 x71 = x71) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x62 x70 x71 = If_i (SNoLe x70 0) x71 (x59 (x62 (add_SNo x70 (minus_SNo 1)) x71))) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x63 x70 x71 = x62 x60 (x61 x70 x71)) ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x64 x70 x71 = add_SNo (add_SNo (x63 x70 x71) x70) (mul_SNo (add_SNo (mul_SNo (mul_SNo x70 2) 2) x70) 2)) ⟶ (∀ x70 . x70 ∈ int ⟶ x65 x70 = x70) ⟶ x66 = 1 ⟶ (∀ x70 . x70 ∈ int ⟶ ∀ x71 . x71 ∈ int ⟶ x67 x70 x71 = If_i (SNoLe x70 0) x71 (x64 (x67 (add_SNo x70 (minus_SNo 1)) x71) x70)) ⟶ (∀ x70 . x70 ∈ int ⟶ x68 x70 = x67 (x65 x70) x66) ⟶ (∀ x70 . x70 ∈ int ⟶ x69 x70 = x68 x70) ⟶ ∀ x70 . x70 ∈ int ⟶ SNoLe 0 x70 ⟶ x30 x70 = x69 x70
Conjecture 45fca..^A160912 : ∀ 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 . x3 ∈ int ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x0 x10 x11 = add_SNo (add_SNo x10 x11) x11) ⟶ x1 = 2 ⟶ (∀ x10 . x10 ∈ int ⟶ x2 x10 = add_SNo x10 x10) ⟶ x3 = 1 ⟶ (∀ x10 . x10 ∈ int ⟶ x4 x10 = x10) ⟶ (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x5 x10 x11 x12 = If_i (SNoLe x10 0) x11 (x0 (x5 (add_SNo x10 (minus_SNo 1)) x11 x12) (x6 (add_SNo x10 (minus_SNo 1)) x11 x12))) ⟶ (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x6 x10 x11 x12 = If_i (SNoLe x10 0) x12 x1) ⟶ (∀ x10 . x10 ∈ int ⟶ x7 x10 = x5 (x2 x10) x3 (x4 x10)) ⟶ (∀ x10 . x10 ∈ int ⟶ x8 x10 = x7 x10) ⟶ (∀ x10 . x10 ∈ int ⟶ x9 x10 = add_SNo 1 (mul_SNo 2 (add_SNo (add_SNo (mul_SNo 2 (add_SNo x10 x10)) (minus_SNo (If_i (SNoLe x10 0) 0 2))) x10))) ⟶ ∀ x10 . x10 ∈ int ⟶ SNoLe 0 x10 ⟶ x8 x10 = x9 x10
Conjecture 3f71c..^A16065 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ 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 1 x21) (mul_SNo x20 x21)) ⟶ (∀ 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 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x4 x20 x21 = x3 (x1 x20 x21) x2) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x5 x20 x21 = add_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 = add_SNo 1 (mul_SNo (add_SNo (mul_SNo x21 x21) x21) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = add_SNo x21 (minus_SNo 1)) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = add_SNo x20 (minus_SNo 1)) ⟶ x14 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ x15 x20 = x20) ⟶ (∀ 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 . x20 ∈ int ⟶ x19 x20 = add_SNo (mul_SNo (x18 x20) (If_i (SNoLe x20 0) 0 2)) 1) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture 051f5..^A159941 : ∀ 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 . x8 ∈ int ⟶ x0 x7 x8 = add_SNo (mul_SNo x8 x8) x7) ⟶ (∀ x7 . x7 ∈ int ⟶ x1 x7 = x7) ⟶ (∀ x7 . x7 ∈ int ⟶ x2 x7 = x7) ⟶ (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x3 x7 x8 = If_i (SNoLe x7 0) x8 (x0 (x3 (add_SNo x7 (minus_SNo 1)) x8) x7)) ⟶ (∀ x7 . x7 ∈ int ⟶ x4 x7 = x3 (x1 x7) (x2 x7)) ⟶ (∀ x7 . x7 ∈ int ⟶ x5 x7 = mul_SNo 2 (mul_SNo 2 (add_SNo 2 (mul_SNo (add_SNo 1 2) (x4 x7))))) ⟶ (∀ x7 . x7 ∈ int ⟶ x6 x7 = add_SNo 2 (mul_SNo 2 (mul_SNo (add_SNo 1 (add_SNo x7 x7)) (add_SNo 1 (add_SNo 2 (add_SNo (mul_SNo x7 x7) x7)))))) ⟶ ∀ x7 . x7 ∈ int ⟶ SNoLe 0 x7 ⟶ x5 x7 = x6 x7
Conjecture 3c883..^A159721 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ x0 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x1 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x2 x17 = add_SNo 2 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x4 x17 = x3 (x1 x17) (x2 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x5 x17 = mul_SNo (add_SNo 1 2) (x4 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = mul_SNo x17 x17) ⟶ x7 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ x8 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x9 x17 = x17) ⟶ x10 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = If_i (SNoLe x17 0) x18 (x8 (x11 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x11 (x9 x17) x10) ⟶ (∀ x17 . x17 ∈ int ⟶ x13 x17 = x12 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x6 (x14 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 x7 (x13 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = mul_SNo (add_SNo 1 2) (mul_SNo (add_SNo 2 x17) (x15 x17))) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture 732e2..^A1596 : ∀ 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 → 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 . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x10 x11 x12 x13 ∈ int) ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ 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 = 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 ⟶ ∀ x29 . x29 ∈ int ⟶ x5 x28 x29 = mul_SNo (mul_SNo x28 x28) x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = x28) ⟶ x7 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ x8 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x10 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x5 (x10 (add_SNo x28 (minus_SNo 1)) x29 x30) (x11 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x11 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x6 (x10 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x10 x7 (x8 x28) (x9 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = add_SNo (x4 x28) (x12 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x14 x28 = mul_SNo (mul_SNo x28 x28) x28) ⟶ x15 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ x16 x28 = mul_SNo x28 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x17 x28 x29 = If_i (SNoLe x28 0) x29 (x14 (x17 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x18 x28 = x17 x15 (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 = 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 = add_SNo (mul_SNo (x18 x28) x28) (x26 x28)) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture 43359..^A159669 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ 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 → 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 . 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 = add_SNo (mul_SNo x23 x23) x24) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x3 x23 x24 = If_i (SNoLe x23 0) x24 (x0 (x3 (add_SNo x23 (minus_SNo 1)) x24) x23)) ⟶ x4 = x3 x1 x2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x5 x23 x24 = add_SNo (add_SNo (mul_SNo x4 x23) x23) x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x6 x23 = add_SNo 0 (minus_SNo 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 (x5 (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))) ⟶ (∀ 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 (mul_SNo 2 (add_SNo 2 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2))))) x23) (minus_SNo x24)) ⟶ (∀ x23 . x23 ∈ int ⟶ x15 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x16 x23 = add_SNo x23 (minus_SNo 1)) ⟶ (∀ x23 . x23 ∈ int ⟶ x17 x23 = add_SNo (If_i (SNoLe x23 0) 0 (mul_SNo 2 (add_SNo 2 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2)))))) 1) ⟶ 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 316a0..^A1594 : ∀ 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 . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ x0 x25 = mul_SNo x25 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 ∈ int ⟶ x4 x25 = x3 x1 (x2 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x5 x25 = mul_SNo 2 (add_SNo (add_SNo x25 x25) x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x6 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 = add_SNo (mul_SNo (mul_SNo (x4 x25) x25) x25) (x9 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x11 x25 = mul_SNo (mul_SNo x25 x25) x25) ⟶ x12 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ x13 x25 = mul_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x14 x25 x26 = If_i (SNoLe x25 0) x26 (x11 (x14 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x15 x25 = x14 x12 (x13 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x16 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x17 x25 x26 = x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x18 x25 = x25) ⟶ x19 = 1 ⟶ x20 = add_SNo 2 (add_SNo 2 2) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x21 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x16 (x21 (add_SNo x25 (minus_SNo 1)) x26 x27) (x22 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x22 x25 x26 x27 = If_i (SNoLe x25 0) x27 (x17 (x21 (add_SNo x25 (minus_SNo 1)) x26 x27) (x22 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x23 x25 = x21 (x18 x25) x19 x20) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = add_SNo (x15 x25) (x23 x25)) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture fa476..^A1589 : ∀ 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 . x6 ∈ int ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ (∀ x22 . x22 ∈ int ⟶ x0 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x1 x22 = add_SNo x22 x22) ⟶ x2 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x3 x22 x23 = If_i (SNoLe x22 0) x23 (x0 (x3 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x4 x22 = x3 (x1 x22) x2) ⟶ (∀ x22 . x22 ∈ int ⟶ x5 x22 = mul_SNo x22 x22) ⟶ x6 = 2 ⟶ (∀ x22 . x22 ∈ int ⟶ x7 x22 = x22) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x8 x22 x23 = If_i (SNoLe x22 0) x23 (x5 (x8 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x9 x22 = x8 x6 (x7 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x10 x22 = add_SNo (x4 x22) (x9 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x11 x22 = mul_SNo x22 x22) ⟶ x12 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ x13 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x14 x22 = x22) ⟶ x15 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x16 x22 x23 = If_i (SNoLe x22 0) x23 (x13 (x16 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x17 x22 = x16 (x14 x22) x15) ⟶ (∀ x22 . x22 ∈ int ⟶ x18 x22 = x17 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x19 x22 x23 = If_i (SNoLe x22 0) x23 (x11 (x19 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x20 x22 = x19 x12 (x18 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x21 x22 = add_SNo (mul_SNo (mul_SNo (mul_SNo x22 x22) x22) x22) (x20 x22)) ⟶ ∀ x22 . x22 ∈ int ⟶ SNoLe 0 x22 ⟶ x10 x22 = x21 x22
Conjecture a187d..^A158749 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x12 x13 x14 x15 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ (∀ x15 . x15 ∈ int ⟶ x0 x15 = add_SNo (add_SNo x15 x15) x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = add_SNo x15 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x2 x15 = x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) (x2 x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = x4 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x6 x15 x16 = mul_SNo x15 x16) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x7 x15 x16 = x16) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x9 x15 = x15) ⟶ x10 = add_SNo 1 (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 x15) x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = x13 x15) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture a85cc..^A158609 : ∀ 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 . (∀ 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 . (∀ 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 : 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 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 : ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x23 x24 x25 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι → 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 = add_SNo x33 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x1 x33 = add_SNo (add_SNo x33 x33) x33) ⟶ x2 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ x3 x33 = x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x4 x33 x34 = If_i (SNoLe x33 0) x34 (x1 (x4 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x5 x33 = x4 x2 (x3 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x6 x33 = x5 x33) ⟶ x7 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ x8 x33 = x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x9 x33 x34 = If_i (SNoLe x33 0) x34 (x6 (x9 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x10 x33 = x9 x7 (x8 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x11 x33 = x10 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x12 x33 = x33) ⟶ x13 = 1 ⟶ x14 = mul_SNo 2 (add_SNo 2 2) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x15 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x0 (x15 (add_SNo x33 (minus_SNo 1)) x34 x35) (x16 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x16 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x11 (x15 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ x17 x33 = x15 (x12 x33) x13 x14) ⟶ (∀ x33 . x33 ∈ int ⟶ x18 x33 = x17 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x19 x33 x34 = add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo x34 x34))) x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x20 x33 = add_SNo (add_SNo x33 x33) x33) ⟶ x21 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ x22 x33 = x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x23 x33 x34 = If_i (SNoLe x33 0) x34 (x20 (x23 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x24 x33 = x23 x21 (x22 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x25 x33 x34 = add_SNo (x24 x33) x34) ⟶ (∀ x33 . x33 ∈ int ⟶ x26 x33 = x33) ⟶ x27 = 1 ⟶ x28 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x29 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x19 (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 = x31 x33) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x18 x33 = x32 x33
Conjecture 1c640..^A158455 : ∀ 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 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x0 x17 x18 = mul_SNo 2 (mul_SNo x17 x18)) ⟶ (∀ x17 . x17 ∈ int ⟶ x1 x17 = x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x2 x17 = add_SNo 1 (mul_SNo 2 (add_SNo 2 (add_SNo x17 x17)))) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x4 x17 = x3 (x1 x17) (x2 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x5 x17 = x4 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x7 x17 = x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x8 x17 = add_SNo 1 (mul_SNo 2 (add_SNo 2 (add_SNo x17 x17)))) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x9 x17 x18 = If_i (SNoLe x17 0) x18 (x6 (x9 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x10 x17 = x9 (x7 x17) (x8 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = mul_SNo x17 x18) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x17) ⟶ x13 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x11 (x14 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 (x12 x17) x13) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = mul_SNo (x10 x17) (x15 x17)) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture f635b..^A1582 : ∀ 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 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x8 x9 x10 x11 ∈ int) ⟶ ∀ x9 : ι → ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x9 x10 x11 x12 ∈ 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 → 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 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ 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 ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 : ι → ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x30 x31 x32 x33 ∈ int) ⟶ ∀ x31 : ι → ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x31 x32 x33 x34 ∈ int) ⟶ ∀ x32 : ι → ι . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x0 x34 x35 = add_SNo (add_SNo x34 x34) x35) ⟶ (∀ x34 . x34 ∈ int ⟶ x1 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ x2 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x3 x34 x35 = add_SNo x34 x35) ⟶ (∀ x34 . x34 ∈ int ⟶ x4 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ x5 x34 = x34) ⟶ x6 = 1 ⟶ x7 = 0 ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x8 x34 x35 x36 = If_i (SNoLe x34 0) x35 (x3 (x8 (add_SNo x34 (minus_SNo 1)) x35 x36) (x9 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x9 x34 x35 x36 = If_i (SNoLe x34 0) x36 (x4 (x8 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ x10 x34 = x8 (x5 x34) x6 x7) ⟶ (∀ x34 . x34 ∈ int ⟶ x11 x34 = x10 x34) ⟶ x12 = 0 ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x13 x34 x35 x36 = If_i (SNoLe x34 0) x35 (x0 (x13 (add_SNo x34 (minus_SNo 1)) x35 x36) (x14 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x14 x34 x35 x36 = If_i (SNoLe x34 0) x36 (x1 (x13 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ x15 x34 = x13 (x2 x34) (x11 x34) x12) ⟶ (∀ x34 . x34 ∈ int ⟶ x16 x34 = x15 x34) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x17 x34 x35 = add_SNo (add_SNo x34 x34) x35) ⟶ (∀ x34 . x34 ∈ int ⟶ x18 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ x19 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x20 x34 x35 = add_SNo x34 x35) ⟶ (∀ x34 . x34 ∈ int ⟶ x21 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ x22 x34 = add_SNo x34 (minus_SNo 1)) ⟶ x23 = 1 ⟶ x24 = 1 ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x25 x34 x35 x36 = If_i (SNoLe x34 0) x35 (x20 (x25 (add_SNo x34 (minus_SNo 1)) x35 x36) (x26 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x26 x34 x35 x36 = If_i (SNoLe x34 0) x36 (x21 (x25 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ x27 x34 = x25 (x22 x34) x23 x24) ⟶ (∀ x34 . x34 ∈ int ⟶ x28 x34 = x27 x34) ⟶ x29 = 0 ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x30 x34 x35 x36 = If_i (SNoLe x34 0) x35 (x17 (x30 (add_SNo x34 (minus_SNo 1)) x35 x36) (x31 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x31 x34 x35 x36 = If_i (SNoLe x34 0) x36 (x18 (x30 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ x32 x34 = x30 (x19 x34) (x28 x34) x29) ⟶ (∀ x34 . x34 ∈ int ⟶ x33 x34 = x32 x34) ⟶ ∀ x34 . x34 ∈ int ⟶ SNoLe 0 x34 ⟶ x16 x34 = x33 x34
Conjecture bd96e..^A1579 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → 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 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 : ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x30 x31 x32 ∈ int) ⟶ ∀ x31 : ι → ι . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ ∀ x32 : ι → ι . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ int) ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 : ι → ι → ι → 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 (add_SNo x38 x38) x38) ⟶ (∀ x38 . x38 ∈ int ⟶ x1 x38 = x38) ⟶ (∀ x38 . x38 ∈ int ⟶ x2 x38 = add_SNo x38 x38) ⟶ (∀ x38 . x38 ∈ int ⟶ x3 x38 = x38) ⟶ x4 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x5 x38 x39 = If_i (SNoLe x38 0) x39 (x2 (x5 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ (∀ x38 . x38 ∈ int ⟶ x6 x38 = x5 (x3 x38) x4) ⟶ (∀ x38 . x38 ∈ int ⟶ x7 x38 = add_SNo 1 (x6 x38)) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x8 x38 x39 = If_i (SNoLe x38 0) x39 (x0 (x8 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ (∀ x38 . x38 ∈ int ⟶ x9 x38 = x8 (x1 x38) (x7 x38)) ⟶ (∀ x38 . x38 ∈ int ⟶ x10 x38 = add_SNo (mul_SNo 2 (add_SNo x38 x38)) x38) ⟶ (∀ x38 . x38 ∈ int ⟶ x11 x38 = x38) ⟶ x12 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x13 x38 x39 = If_i (SNoLe x38 0) x39 (x10 (x13 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ (∀ x38 . x38 ∈ int ⟶ x14 x38 = x13 (x11 x38) x12) ⟶ (∀ x38 . x38 ∈ int ⟶ x15 x38 = add_SNo (x9 x38) (x14 x38)) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x16 x38 x39 = mul_SNo x38 x39) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x17 x38 x39 = x39) ⟶ (∀ x38 . x38 ∈ int ⟶ x18 x38 = x38) ⟶ x19 = 1 ⟶ x20 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x21 x38 x39 x40 = If_i (SNoLe x38 0) x39 (x16 (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 (x17 (x21 (add_SNo x38 (minus_SNo 1)) x39 x40) (x22 (add_SNo x38 (minus_SNo 1)) x39 x40))) ⟶ (∀ x38 . x38 ∈ int ⟶ x23 x38 = x21 (x18 x38) x19 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) ⟶ (∀ x38 . x38 ∈ int ⟶ x27 x38 = add_SNo x38 x38) ⟶ (∀ x38 . x38 ∈ int ⟶ x28 x38 = x38) ⟶ x29 = 1 ⟶ (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x30 x38 x39 = If_i (SNoLe x38 0) x39 (x27 (x30 (add_SNo x38 (minus_SNo 1)) x39))) ⟶ (∀ x38 . x38 ∈ int ⟶ x31 x38 = x30 (x28 x38) x29) ⟶ (∀ x38 . x38 ∈ int ⟶ x32 x38 = add_SNo 1 (x31 x38)) ⟶ x33 = add_SNo 1 2 ⟶ (∀ 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) (x32 x38) x33) ⟶ (∀ x38 . x38 ∈ int ⟶ x37 x38 = add_SNo (x23 x38) (x36 x38)) ⟶ ∀ x38 . x38 ∈ int ⟶ SNoLe 0 x38 ⟶ x15 x38 = x37 x38
Conjecture 2f13f..^A156084 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι → ι → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x28 x29 x30 x31 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 : ι → ι . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ int) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x0 x31 x32 = add_SNo (mul_SNo 2 (add_SNo x31 x31)) x32) ⟶ (∀ x31 . x31 ∈ int ⟶ x1 x31 = x31) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x2 x31 x32 = add_SNo x32 x32) ⟶ x3 = 0 ⟶ x4 = 1 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x5 x31 x32 x33 = If_i (SNoLe x31 0) x32 (x0 (x5 (add_SNo x31 (minus_SNo 1)) x32 x33) (x6 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x6 x31 x32 x33 = If_i (SNoLe x31 0) x33 (x1 (x5 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x7 x31 x32 = x5 (x2 x31 x32) x3 x4) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x8 x31 x32 = add_SNo (x7 x31 x32) (minus_SNo x31)) ⟶ (∀ x31 . x31 ∈ int ⟶ x9 x31 = x31) ⟶ x10 = 0 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x11 x31 x32 = If_i (SNoLe x31 0) x32 (x8 (x11 (add_SNo x31 (minus_SNo 1)) x32) x31)) ⟶ (∀ x31 . x31 ∈ int ⟶ x12 x31 = x11 (x9 x31) x10) ⟶ (∀ x31 . x31 ∈ int ⟶ x13 x31 = x12 x31) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x14 x31 x32 = add_SNo (mul_SNo 2 (add_SNo x31 x31)) x32) ⟶ (∀ x31 . x31 ∈ int ⟶ x15 x31 = x31) ⟶ (∀ x31 . x31 ∈ int ⟶ x16 x31 = x31) ⟶ x17 = 1 ⟶ x18 = 0 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x19 x31 x32 x33 = If_i (SNoLe x31 0) x32 (x14 (x19 (add_SNo x31 (minus_SNo 1)) x32 x33) (x20 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x20 x31 x32 x33 = If_i (SNoLe x31 0) x33 (x15 (x19 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ x21 x31 = x19 (x16 x31) x17 x18) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x22 x31 x32 = add_SNo (mul_SNo 2 (add_SNo x31 x31)) x32) ⟶ (∀ x31 . x31 ∈ int ⟶ x23 x31 = x31) ⟶ (∀ x31 . x31 ∈ int ⟶ x24 x31 = add_SNo x31 (minus_SNo 2)) ⟶ (∀ x31 . x31 ∈ int ⟶ x25 x31 = If_i (SNoLe (add_SNo x31 (minus_SNo 1)) 0) x31 (add_SNo 2 2)) ⟶ x26 = 1 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x27 x31 x32 x33 = If_i (SNoLe x31 0) x32 (x22 (x27 (add_SNo x31 (minus_SNo 1)) x32 x33) (x28 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x28 x31 x32 x33 = If_i (SNoLe x31 0) x33 (x23 (x27 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ x29 x31 = x27 (x24 x31) (x25 x31) x26) ⟶ (∀ x31 . x31 ∈ int ⟶ x30 x31 = mul_SNo (x21 x31) (x29 x31)) ⟶ ∀ x31 . x31 ∈ int ⟶ SNoLe 0 x31 ⟶ x13 x31 = x30 x31
Conjecture 75f23..^A155670 : ∀ 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 → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ 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 ⟶ x0 x33 = add_SNo (add_SNo x33 x33) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x1 x33 = add_SNo 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 ⟶ ∀ x34 . x34 ∈ int ⟶ x5 x33 x34 = mul_SNo (add_SNo 2 x34) x33) ⟶ x6 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ x7 x33 = x33) ⟶ (∀ 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 . x33 ∈ int ⟶ x9 x33 = x8 x6 (x7 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x10 x33 = add_SNo (x9 x33) (minus_SNo 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 (add_SNo (x4 x33) (minus_SNo 1)) (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 (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 = add_SNo (add_SNo (x23 x33) (minus_SNo 1)) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x15 x33 = x32 x33
Conjecture 5da00..^A155667 : ∀ 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 . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x25 x26 x27 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x0 x28 x29 = add_SNo (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x28 x28)) x28)) x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x1 x28 x29 = mul_SNo 2 (mul_SNo 2 (add_SNo x29 x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x2 x28 = x28) ⟶ x3 = 0 ⟶ x4 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x5 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x0 (x5 (add_SNo x28 (minus_SNo 1)) x29 x30) (x6 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x6 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x1 (x5 (add_SNo x28 (minus_SNo 1)) x29 x30) (x6 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x7 x28 = x5 (x2 x28) x3 x4) ⟶ (∀ x28 . x28 ∈ int ⟶ x8 x28 = add_SNo 1 (x7 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x9 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x10 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x11 x28 = x28) ⟶ x12 = 1 ⟶ x13 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x14 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x9 (x14 (add_SNo x28 (minus_SNo 1)) x29 x30) (x15 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x15 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x10 (x14 (add_SNo x28 (minus_SNo 1)) x29 x30) (x15 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x16 x28 = x14 (x11 x28) x12 x13) ⟶ (∀ x28 . x28 ∈ int ⟶ x17 x28 = mul_SNo (mul_SNo x28 x28) x28) ⟶ x18 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ x19 x28 = add_SNo x28 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x20 x28 = x28) ⟶ x21 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x22 x28 x29 = If_i (SNoLe x28 0) x29 (x19 (x22 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x23 x28 = x22 (x20 x28) x21) ⟶ (∀ x28 . x28 ∈ int ⟶ x24 x28 = x23 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x25 x28 x29 = If_i (SNoLe x28 0) x29 (x17 (x25 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x25 x18 (x24 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = add_SNo 1 (add_SNo (x16 x28) (minus_SNo (x26 x28)))) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x8 x28 = x27 x28
Conjecture 9dd36..^A155663 : ∀ 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 . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : 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 ⟶ ∀ x29 . x29 ∈ int ⟶ x0 x28 x29 = add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo x28 x28))) (mul_SNo x29 x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x1 x28 x29 = add_SNo (add_SNo x29 x29) x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x2 x28 = x28) ⟶ x3 = 2 ⟶ x4 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x5 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x0 (x5 (add_SNo x28 (minus_SNo 1)) x29 x30) (x6 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x6 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x1 (x5 (add_SNo x28 (minus_SNo 1)) x29 x30) (x6 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x7 x28 = x5 (x2 x28) x3 x4) ⟶ (∀ x28 . x28 ∈ int ⟶ x8 x28 = add_SNo (x7 x28) (minus_SNo 1)) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = mul_SNo (mul_SNo x28 x28) x28) ⟶ x10 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ x11 x28 = add_SNo x28 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x28) ⟶ x13 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x14 x28 x29 = If_i (SNoLe x28 0) x29 (x11 (x14 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x14 (x12 x28) x13) ⟶ (∀ x28 . x28 ∈ int ⟶ x16 x28 = x15 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x17 x28 x29 = If_i (SNoLe x28 0) x29 (x9 (x17 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x18 x28 = x17 x10 (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 = x28) ⟶ x22 = 1 ⟶ x23 = add_SNo 1 (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 = add_SNo (add_SNo (x18 x28) (minus_SNo 1)) (x26 x28)) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x8 x28 = x27 x28