Proofgold Signed Transaction

Param int^int : ι
Param add_SNo^add_SNo : ι → ι → ι
Param mul_SNo^mul_SNo : ι → ι → ι
Param ordsucc^ordsucc : ι → ι
Param minus_SNo^minus_SNo : ι → ι
Param If_i^If_i : ο → ι → ι → ι
Param SNoLe^SNoLe : ι → ι → ο
Conjecture 91e03..^A99953 : ∀ 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 = add_SNo (mul_SNo 2 (mul_SNo x20 x21)) (minus_SNo x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x1 x20 x21 = x21) ⟶ x2 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21) x20)) ⟶ (∀ x20 . 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 = 0 ⟶ (∀ 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 x20 x21)) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = add_SNo x21 (minus_SNo 2)) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 0 ⟶ (∀ x20 . x20 ∈ int ⟶ x15 x20 = add_SNo 1 (add_SNo 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 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture a6876..^A9992 : ∀ 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 . (∀ 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 . x31 ∈ int ⟶ x0 x30 x31 = mul_SNo x30 x31) ⟶ x1 = add_SNo 2 2 ⟶ (∀ x30 . x30 ∈ int ⟶ x2 x30 = x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x3 x30 x31 = If_i (SNoLe x30 0) x31 (x0 (x3 (add_SNo x30 (minus_SNo 1)) x31) x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x4 x30 = x3 x1 (x2 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x5 x30 = mul_SNo 2 (x4 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ x6 x30 = x30) ⟶ x7 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x8 x30 x31 = If_i (SNoLe x30 0) x31 (x5 (x8 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x9 x30 = x8 (x6 x30) x7) ⟶ (∀ x30 . x30 ∈ int ⟶ x10 x30 = x9 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x11 x30 = mul_SNo x30 x30) ⟶ x12 = 2 ⟶ (∀ x30 . x30 ∈ int ⟶ x13 x30 = add_SNo x30 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x14 x30 = x30) ⟶ x15 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x16 x30 x31 = If_i (SNoLe x30 0) x31 (x13 (x16 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x17 x30 = x16 (x14 x30) x15) ⟶ (∀ x30 . x30 ∈ int ⟶ x18 x30 = x17 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x19 x30 x31 = If_i (SNoLe x30 0) x31 (x11 (x19 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x20 x30 = x19 x12 (x18 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x21 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x22 x30 x31 = x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x23 x30 = x30) ⟶ x24 = 1 ⟶ x25 = add_SNo 1 2 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x26 x30 x31 x32 = If_i (SNoLe x30 0) x31 (x21 (x26 (add_SNo x30 (minus_SNo 1)) x31 x32) (x27 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x27 x30 x31 x32 = If_i (SNoLe x30 0) x32 (x22 (x26 (add_SNo x30 (minus_SNo 1)) x31 x32) (x27 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ x28 x30 = x26 (x23 x30) x24 x25) ⟶ (∀ x30 . x30 ∈ int ⟶ x29 x30 = mul_SNo (x20 x30) (x28 x30)) ⟶ ∀ x30 . x30 ∈ int ⟶ SNoLe 0 x30 ⟶ x10 x30 = x29 x30
Conjecture 8a4bc..^A99924 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι → 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 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x0 x18 x19 = add_SNo 1 (add_SNo 2 x19)) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x1 x18 x19 = add_SNo x18 x19) ⟶ (∀ x18 . x18 ∈ int ⟶ x2 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x3 x18 = add_SNo (add_SNo (add_SNo x18 x18) 2) 2) ⟶ (∀ x18 . x18 ∈ int ⟶ x4 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x5 x18 x19 x20 = If_i (SNoLe x18 0) x19 (x0 (x5 (add_SNo x18 (minus_SNo 1)) x19 x20) (x6 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x6 x18 x19 x20 = If_i (SNoLe x18 0) x20 (x1 (x5 (add_SNo x18 (minus_SNo 1)) x19 x20) (x6 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ x7 x18 = x5 (x2 x18) (x3 x18) (x4 x18)) ⟶ (∀ x18 . x18 ∈ int ⟶ x8 x18 = x7 x18) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x9 x18 x19 = add_SNo 1 x19) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x10 x18 x19 = add_SNo x18 x19) ⟶ (∀ x18 . x18 ∈ int ⟶ x11 x18 = x18) ⟶ (∀ x18 . x18 ∈ int ⟶ x12 x18 = add_SNo 2 (add_SNo (add_SNo 2 x18) x18)) ⟶ (∀ x18 . x18 ∈ int ⟶ x13 x18 = add_SNo 2 x18) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x14 x18 x19 x20 = If_i (SNoLe x18 0) x19 (x9 (x14 (add_SNo x18 (minus_SNo 1)) x19 x20) (x15 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x15 x18 x19 x20 = If_i (SNoLe x18 0) x20 (x10 (x14 (add_SNo x18 (minus_SNo 1)) x19 x20) (x15 (add_SNo x18 (minus_SNo 1)) x19 x20))) ⟶ (∀ x18 . x18 ∈ int ⟶ x16 x18 = x14 (x11 x18) (x12 x18) (x13 x18)) ⟶ (∀ x18 . x18 ∈ int ⟶ x17 x18 = x16 x18) ⟶ ∀ x18 . x18 ∈ int ⟶ SNoLe 0 x18 ⟶ x8 x18 = x17 x18
Conjecture febc4..^A9991 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x0 x20 x21 = mul_SNo x20 x21) ⟶ x1 = add_SNo 2 2 ⟶ (∀ x20 . x20 ∈ int ⟶ x2 x20 = x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x4 x20 = x3 x1 (x2 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = add_SNo (mul_SNo 2 (x4 x20)) (minus_SNo x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = If_i (SNoLe x20 0) x21 (x5 (x8 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x9 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = mul_SNo x20 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 1 ⟶ x15 = add_SNo (mul_SNo 2 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2))))) (minus_SNo 1) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x16 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x11 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x17 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x12 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x16 (x13 x20) x14 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture 43213..^A9990 : ∀ 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 : 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 → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x0 x25 x26 = mul_SNo x25 x26) ⟶ x1 = add_SNo 2 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 = mul_SNo 2 (add_SNo (x4 x25) (minus_SNo 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 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x11 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x12 x25 = x25) ⟶ x13 = 1 ⟶ (∀ 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 x25) x13) ⟶ (∀ 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 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2)))) (minus_SNo 1) ⟶ (∀ 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 = mul_SNo (x15 x25) (x23 x25)) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture ed422..^A9989 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ x0 x28 = mul_SNo (add_SNo 2 (add_SNo 2 x28)) x28) ⟶ x1 = 2 ⟶ 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))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x28 . x28 ∈ int ⟶ x5 x28 = mul_SNo x4 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = x28) ⟶ x7 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x8 x28 x29 = If_i (SNoLe x28 0) x29 (x5 (x8 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x8 (x6 x28) x7) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = x9 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x12 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x28) ⟶ x14 = 1 ⟶ x15 = add_SNo 1 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x16 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x11 (x16 (add_SNo x28 (minus_SNo 1)) x29 x30) (x17 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x17 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x12 (x16 (add_SNo x28 (minus_SNo 1)) x29 x30) (x17 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x18 x28 = x16 (x13 x28) x14 x15) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x19 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x20 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x28) ⟶ x22 = 1 ⟶ x23 = add_SNo (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2))) (minus_SNo 1) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x24 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x19 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30) (x25 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x25 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x20 (x24 (add_SNo x28 (minus_SNo 1)) x29 x30) (x25 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x24 (x21 x28) x22 x23) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = mul_SNo (x18 x28) (x26 x28)) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x10 x28 = x27 x28
Conjecture 66e16..^A9988 : ∀ 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 ⟶ x0 x30 = add_SNo (mul_SNo x30 x30) x30) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x3 x30 x31 = If_i (SNoLe x30 0) x31 (x0 (x3 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x30 . x30 ∈ int ⟶ x5 x30 = mul_SNo (add_SNo 2 x4) x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x6 x30 = x30) ⟶ x7 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x8 x30 x31 = If_i (SNoLe x30 0) x31 (x5 (x8 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x9 x30 = x8 (x6 x30) x7) ⟶ (∀ x30 . x30 ∈ int ⟶ x10 x30 = x9 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x11 x30 = mul_SNo x30 x30) ⟶ x12 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ x13 x30 = add_SNo x30 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ x14 x30 = x30) ⟶ x15 = 1 ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x16 x30 x31 = If_i (SNoLe x30 0) x31 (x13 (x16 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x17 x30 = x16 (x14 x30) x15) ⟶ (∀ x30 . x30 ∈ int ⟶ x18 x30 = x17 x30) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x19 x30 x31 = If_i (SNoLe x30 0) x31 (x11 (x19 (add_SNo x30 (minus_SNo 1)) x31))) ⟶ (∀ x30 . x30 ∈ int ⟶ x20 x30 = x19 x12 (x18 x30)) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x21 x30 x31 = mul_SNo x30 x31) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x22 x30 x31 = x31) ⟶ (∀ x30 . x30 ∈ int ⟶ x23 x30 = x30) ⟶ x24 = 1 ⟶ x25 = add_SNo 1 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x26 x30 x31 x32 = If_i (SNoLe x30 0) x31 (x21 (x26 (add_SNo x30 (minus_SNo 1)) x31 x32) (x27 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x27 x30 x31 x32 = If_i (SNoLe x30 0) x32 (x22 (x26 (add_SNo x30 (minus_SNo 1)) x31 x32) (x27 (add_SNo x30 (minus_SNo 1)) x31 x32))) ⟶ (∀ x30 . x30 ∈ int ⟶ x28 x30 = x26 (x23 x30) x24 x25) ⟶ (∀ x30 . x30 ∈ int ⟶ x29 x30 = mul_SNo (x20 x30) (x28 x30)) ⟶ ∀ x30 . x30 ∈ int ⟶ SNoLe 0 x30 ⟶ x10 x30 = x29 x30
Conjecture a7651..^A9987 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ x0 x25 = add_SNo (mul_SNo x25 x25) x25) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x3 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x3 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x25 . x25 ∈ int ⟶ x5 x25 = add_SNo (mul_SNo x4 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 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x11 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x12 x25 x26 = x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x13 x25 = x25) ⟶ x14 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ x15 x25 = add_SNo (mul_SNo x25 x25) x25) ⟶ x16 = 1 ⟶ x17 = add_SNo 2 (add_SNo 2 2) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x18 x25 x26 = If_i (SNoLe x25 0) x26 (x15 (x18 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ x19 = x18 x16 x17 ⟶ x20 = add_SNo 1 x19 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x21 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x11 (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 (x12 (x21 (add_SNo x25 (minus_SNo 1)) x26 x27) (x22 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x23 x25 = x21 (x13 x25) x14 x20) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = x23 x25) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture 6e940..^A9986 : ∀ 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 : 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 → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ x0 x25 = add_SNo (mul_SNo x25 x25) x25) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x3 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x3 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x25 . x25 ∈ int ⟶ x5 x25 = mul_SNo x4 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 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x11 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x12 x25 = x25) ⟶ x13 = 1 ⟶ (∀ 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 x25) x13) ⟶ (∀ 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 1 (mul_SNo 2 (add_SNo 2 (mul_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 = mul_SNo (x15 x25) (x23 x25)) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture 65ccd..^A9985 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ x0 x20 = add_SNo (mul_SNo x20 x20) x20) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = add_SNo (mul_SNo x4 x20) (minus_SNo x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = If_i (SNoLe x20 0) x21 (x5 (x8 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x9 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = mul_SNo x20 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 1 ⟶ x15 = add_SNo 1 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 (mul_SNo 2 (add_SNo 2 2))))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x16 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x11 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x17 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x12 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x16 (x13 x20) x14 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture e6d61..^A9984 : ∀ 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 : 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 → 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 2 (add_SNo 2 x25)) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x3 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x3 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x25 . x25 ∈ int ⟶ x5 x25 = mul_SNo 2 (mul_SNo x4 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 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x11 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x12 x25 = x25) ⟶ x13 = 1 ⟶ (∀ 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 x25) x13) ⟶ (∀ 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 = mul_SNo 2 (add_SNo 2 (mul_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 = mul_SNo (x15 x25) (x23 x25)) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture bb459..^A9983 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x24 x25 x26 x27 ∈ int) ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ x0 x28 = add_SNo 2 (mul_SNo x28 x28)) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x3 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x3 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x28 . x28 ∈ int ⟶ x5 x28 = add_SNo (mul_SNo x4 x28) x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = x28) ⟶ x7 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x8 x28 x29 = If_i (SNoLe x28 0) x29 (x5 (x8 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x8 (x6 x28) x7) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = x9 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x12 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x28) ⟶ x14 = 1 ⟶ x15 = add_SNo 1 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x16 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x11 (x16 (add_SNo x28 (minus_SNo 1)) x29 x30) (x17 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x17 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x12 (x16 (add_SNo x28 (minus_SNo 1)) x29 x30) (x17 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x18 x28 = x16 (x13 x28) x14 x15) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x19 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x20 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x28) ⟶ x22 = 1 ⟶ x23 = add_SNo 1 (mul_SNo 2 (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 ⟶ x10 x28 = x27 x28
Conjecture dcaf0..^A9982 : ∀ 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 : 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 → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ x0 x25 = add_SNo 2 (mul_SNo x25 x25)) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x3 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x3 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x25 . x25 ∈ int ⟶ x5 x25 = mul_SNo x4 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 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x11 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x12 x25 = x25) ⟶ x13 = 1 ⟶ (∀ 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 x25) x13) ⟶ (∀ 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 1 (add_SNo 2 (mul_SNo 2 (mul_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 = mul_SNo (x15 x25) (x23 x25)) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture 49fec..^A9981 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ x0 x25 = mul_SNo 2 (add_SNo (add_SNo x25 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 = add_SNo (x4 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 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x11 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x12 x25 x26 = x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x13 x25 = x25) ⟶ x14 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ x15 x25 = mul_SNo x25 x25) ⟶ x16 = 1 ⟶ x17 = add_SNo 2 (add_SNo 2 2) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x18 x25 x26 = If_i (SNoLe x25 0) x26 (x15 (x18 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ x19 = x18 x16 x17 ⟶ x20 = add_SNo 1 x19 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x21 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x11 (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 (x12 (x21 (add_SNo x25 (minus_SNo 1)) x26 x27) (x22 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x23 x25 = x21 (x13 x25) x14 x20) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = x23 x25) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture d2273..^A9980 : ∀ 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 = mul_SNo 2 (add_SNo (add_SNo x20 x20) 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 ∈ 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 = 1 ⟶ x12 = add_SNo 2 (add_SNo 2 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 d7f09..^A9979 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ x0 x25 = mul_SNo 2 (add_SNo (add_SNo x25 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 = add_SNo (x4 x25) (minus_SNo 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 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x11 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x12 x25 x26 = x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x13 x25 = x25) ⟶ x14 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ x15 x25 = mul_SNo x25 x25) ⟶ x16 = 1 ⟶ x17 = add_SNo 2 (add_SNo 2 2) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x18 x25 x26 = If_i (SNoLe x25 0) x26 (x15 (x18 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ x19 = x18 x16 x17 ⟶ x20 = add_SNo x19 (minus_SNo 1) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x21 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x11 (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 (x12 (x21 (add_SNo x25 (minus_SNo 1)) x26 x27) (x22 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x23 x25 = x21 (x13 x25) x14 x20) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = x23 x25) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture 917b1..^A9978 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ x0 x20 = mul_SNo x20 x20) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = mul_SNo 2 (add_SNo (mul_SNo x4 x20) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = If_i (SNoLe x20 0) x21 (x5 (x8 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x9 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = mul_SNo x20 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 1 ⟶ x15 = add_SNo 2 (mul_SNo 2 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x16 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x11 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x17 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x12 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x16 (x13 x20) x14 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture 55bed..^A9977 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ x0 x20 = mul_SNo x20 x20) ⟶ x1 = 2 ⟶ x2 = 2 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ x4 = x3 x1 x2 ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = add_SNo (mul_SNo 2 (mul_SNo x4 x20)) x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = If_i (SNoLe x20 0) x21 (x5 (x8 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x9 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = mul_SNo x20 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = x20) ⟶ x14 = 1 ⟶ x15 = add_SNo 1 (mul_SNo 2 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x16 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x11 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x17 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x12 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x16 (x13 x20) x14 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = x18 x20) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20
Conjecture 4a984..^A9976 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ x0 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x1 x17 = add_SNo (mul_SNo 2 (add_SNo x17 x17)) x17) ⟶ x2 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x3 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x3 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x4 x17 = x3 (x1 x17) x2) ⟶ (∀ x17 . x17 ∈ int ⟶ x5 x17 = x4 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = mul_SNo (mul_SNo (mul_SNo (mul_SNo x17 x17) x17) 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 = x15 x17) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture f891a..^A9975 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 . x1 ∈ int ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x0 x20 x21 = mul_SNo (add_SNo 2 (add_SNo 2 x21)) x20) ⟶ x1 = 2 ⟶ (∀ x20 . x20 ∈ int ⟶ x2 x20 = x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x3 x20 x21 = If_i (SNoLe x20 0) x21 (x0 (x3 (add_SNo x20 (minus_SNo 1)) x21) x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x4 x20 = x3 x1 (x2 x20)) ⟶ (∀ x20 . x20 ∈ int ⟶ x5 x20 = add_SNo (x4 x20) x20) ⟶ (∀ x20 . x20 ∈ int ⟶ x6 x20 = x20) ⟶ x7 = 1 ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x8 x20 x21 = If_i (SNoLe x20 0) x21 (x5 (x8 (add_SNo x20 (minus_SNo 1)) x21))) ⟶ (∀ x20 . x20 ∈ int ⟶ x9 x20 = x8 (x6 x20) x7) ⟶ (∀ x20 . x20 ∈ int ⟶ x10 x20 = x9 x20) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x11 x20 x21 = mul_SNo x20 x21) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x12 x20 x21 = x21) ⟶ (∀ x20 . x20 ∈ int ⟶ x13 x20 = add_SNo x20 (minus_SNo 1)) ⟶ x14 = 1 ⟶ x15 = add_SNo (mul_SNo 2 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) (minus_SNo 1) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x16 x20 x21 x22 = If_i (SNoLe x20 0) x21 (x11 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x17 x20 x21 x22 = If_i (SNoLe x20 0) x22 (x12 (x16 (add_SNo x20 (minus_SNo 1)) x21 x22) (x17 (add_SNo x20 (minus_SNo 1)) x21 x22))) ⟶ (∀ x20 . x20 ∈ int ⟶ x18 x20 = x16 (x13 x20) x14 x15) ⟶ (∀ x20 . x20 ∈ int ⟶ x19 x20 = mul_SNo (x18 x20) (If_i (SNoLe x20 0) 1 (add_SNo (mul_SNo 2 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 2)))) (minus_SNo 1)))) ⟶ ∀ x20 . x20 ∈ int ⟶ SNoLe 0 x20 ⟶ x10 x20 = x19 x20