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 c0a4c..^A53464 : ∀ 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 (mul_SNo 2 (add_SNo x15 x15)) x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = add_SNo x15 (minus_SNo 1)) ⟶ (∀ 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 = add_SNo x15 (minus_SNo 1)) ⟶ (∀ x15 . x15 ∈ int ⟶ x9 x15 = x15) ⟶ x10 = add_SNo 1 (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 a3d52..^A53422 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x12 x13 x14 x15 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ (∀ x15 . x15 ∈ int ⟶ x0 x15 = add_SNo 1 (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x15 x15)) x15))) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = x15) ⟶ x2 = 0 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = mul_SNo (x4 x15) x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x6 x15 x16 = add_SNo 1 (mul_SNo x15 x16)) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x7 x15 x16 = x16) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = add_SNo x15 (minus_SNo 1)) ⟶ x9 = 1 ⟶ x10 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x11 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x6 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x12 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x7 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x11 (x8 x15) x9 x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = mul_SNo x15 (x13 x15)) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture f60f5..^A533 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x12 x13 x14 x15 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ (∀ x15 . x15 ∈ int ⟶ x0 x15 = mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x15 x15)) x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = x15) ⟶ x2 = 1 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = add_SNo 1 (If_i (SNoLe x15 0) 0 (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) ⟶ x9 = 1 ⟶ x10 = add_SNo 2 (mul_SNo 2 (add_SNo 2 2)) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x11 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x6 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x12 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x7 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x11 (x8 x15) x9 x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = add_SNo 1 (If_i (SNoLe x15 0) 0 (x13 x15))) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture b96c4..^A53220 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x0 x15 x16 = add_SNo (add_SNo x15 x15) x16) ⟶ x1 = 0 ⟶ (∀ x15 . x15 ∈ int ⟶ x2 x15 = x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x3 x15 = add_SNo 1 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x5 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x0 (x5 (add_SNo x15 (minus_SNo 1)) x16 x17) (x6 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x6 x15 x16 x17 = If_i (SNoLe x15 0) x17 x1) ⟶ (∀ x15 . x15 ∈ int ⟶ x7 x15 = x5 (x2 x15) (x3 x15) (x4 x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = x7 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x9 x15 = add_SNo x15 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x10 x15 = add_SNo x15 (minus_SNo 1)) ⟶ (∀ x15 . x15 ∈ int ⟶ x11 x15 = add_SNo 2 (add_SNo (add_SNo x15 x15) x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x12 x15 x16 = If_i (SNoLe x15 0) x16 (x9 (x12 (add_SNo x15 (minus_SNo 1)) x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x12 (x10 x15) (x11 x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = If_i (SNoLe x15 0) 1 (x13 x15)) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x8 x15 = x14 x15
Conjecture b6ae7..^A52951 : ∀ 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 . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x0 x15 x16 = add_SNo (add_SNo x15 x15) x16) ⟶ x1 = 1 ⟶ (∀ x15 . x15 ∈ int ⟶ x2 x15 = x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x3 x15 = x15) ⟶ x4 = 2 ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x5 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x0 (x5 (add_SNo x15 (minus_SNo 1)) x16 x17) (x6 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x6 x15 x16 x17 = If_i (SNoLe x15 0) x17 x1) ⟶ (∀ x15 . x15 ∈ int ⟶ x7 x15 = x5 (x2 x15) (x3 x15) x4) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = add_SNo 1 (x7 x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x9 x15 = add_SNo x15 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x10 x15 = add_SNo x15 (minus_SNo 1)) ⟶ (∀ x15 . x15 ∈ int ⟶ x11 x15 = add_SNo 1 (add_SNo 2 (add_SNo x15 x15))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x12 x15 x16 = If_i (SNoLe x15 0) x16 (x9 (x12 (add_SNo x15 (minus_SNo 1)) x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x12 (x10 x15) (x11 x15)) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = If_i (SNoLe x15 0) 1 (x13 x15)) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x8 x15 = x14 x15
Conjecture 88f65..^A52850 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : 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 . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x0 x22 x23 = mul_SNo x22 x23) ⟶ (∀ x22 . x22 ∈ int ⟶ x1 x22 = add_SNo x22 (minus_SNo 1)) ⟶ (∀ x22 . x22 ∈ int ⟶ x2 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x3 x22 = x22) ⟶ x4 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x5 x22 x23 = If_i (SNoLe x22 0) x23 (x2 (x5 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x6 x22 = x5 (x3 x22) x4) ⟶ (∀ x22 . x22 ∈ int ⟶ x7 x22 = add_SNo (add_SNo (x6 x22) (minus_SNo 1)) x22) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x8 x22 x23 = If_i (SNoLe x22 0) x23 (x0 (x8 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x9 x22 = x8 (x1 x22) (x7 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x10 x22 = x9 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x11 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x12 x22 = x22) ⟶ x13 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x14 x22 x23 = If_i (SNoLe x22 0) x23 (x11 (x14 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x15 x22 = x14 (x12 x22) x13) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x16 x22 x23 = mul_SNo x22 x23) ⟶ (∀ x22 . x22 ∈ int ⟶ x17 x22 = add_SNo x22 (minus_SNo 1)) ⟶ x18 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x19 x22 x23 = If_i (SNoLe x22 0) x23 (x16 (x19 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x20 x22 = x19 (x17 x22) x18) ⟶ (∀ x22 . x22 ∈ int ⟶ x21 x22 = mul_SNo (add_SNo (add_SNo (x15 x22) (minus_SNo 1)) x22) (x20 x22)) ⟶ ∀ x22 . x22 ∈ int ⟶ SNoLe 0 x22 ⟶ x10 x22 = x21 x22
Conjecture bc5e6..^A52832 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x7 x8 x9 x10 ∈ int) ⟶ ∀ x8 : ι → ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x8 x9 x10 x11 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : 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 . x24 ∈ 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 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x1 x28 = add_SNo x28 (minus_SNo 1)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x2 x28 x29 = add_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x3 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x4 x28 = add_SNo x28 (minus_SNo 1)) ⟶ x5 = 1 ⟶ x6 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x7 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x2 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30) (x8 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x8 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x3 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x7 (x4 x28) x5 x6) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = add_SNo (x9 x28) (minus_SNo 1)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x11 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x11 (x1 x28) (x10 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x14 x28 x29 = add_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x16 x28 = add_SNo x28 (minus_SNo 1)) ⟶ x17 = 1 ⟶ x18 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x19 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x14 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30) (x20 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x20 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x15 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x19 (x16 x28) x17 x18) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x22 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x23 x28 = add_SNo x28 (minus_SNo 1)) ⟶ x24 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x25 x28 x29 = If_i (SNoLe x28 0) x29 (x22 (x25 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x25 (x23 x28) x24) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = mul_SNo (add_SNo (x21 x28) (minus_SNo 1)) (x26 x28)) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture bfa1d..^A52677 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x7 x8 x9 x10 ∈ int) ⟶ ∀ x8 : ι → ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x8 x9 x10 x11 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : 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 . x24 ∈ 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 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x1 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x2 x28 x29 = add_SNo (mul_SNo 2 (add_SNo x28 x28)) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x3 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x4 x28 = x28) ⟶ x5 = 1 ⟶ x6 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x7 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x2 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30) (x8 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x8 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x3 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x7 (x4 x28) x5 x6) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = x9 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x11 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x11 (x1 x28) (x10 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x14 x28 x29 = add_SNo (mul_SNo 2 (add_SNo x28 x28)) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x16 x28 = add_SNo x28 (minus_SNo 1)) ⟶ x17 = add_SNo 1 2 ⟶ x18 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x19 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x14 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30) (x20 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x20 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x15 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x19 (x16 x28) x17 x18) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x22 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x23 x28 = x28) ⟶ x24 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x25 x28 x29 = If_i (SNoLe x28 0) x29 (x22 (x25 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x25 (x23 x28) x24) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = mul_SNo (If_i (SNoLe x28 0) 1 (x21 x28)) (x26 x28)) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture dd497..^A52661 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x7 x8 x9 x10 ∈ int) ⟶ ∀ x8 : ι → ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x8 x9 x10 x11 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 : ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x25 x26 x27 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x0 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x1 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x2 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x3 x28 x29 = add_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x4 x28 = x28) ⟶ x5 = 1 ⟶ x6 = 0 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x7 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x2 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30) (x8 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x8 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x3 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30) (x8 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x7 (x4 x28) x5 x6) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = add_SNo 1 (x9 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x11 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x11 (x1 x28) (x10 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x14 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x15 x28 x29 = add_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x16 x28 = x28) ⟶ x17 = 1 ⟶ x18 = 0 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x19 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x14 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30) (x20 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x20 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x15 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30) (x20 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x19 (x16 x28) x17 x18) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x22 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x23 x28 = x28) ⟶ x24 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x25 x28 x29 = If_i (SNoLe x28 0) x29 (x22 (x25 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x25 (x23 x28) x24) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = mul_SNo (add_SNo 1 (x21 x28)) (x26 x28)) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture 8de98..^A52635 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x7 x8 x9 x10 ∈ int) ⟶ ∀ x8 : ι → ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x8 x9 x10 x11 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : 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 . x24 ∈ 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 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x1 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x2 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x3 x28 x29 = add_SNo (add_SNo (add_SNo x28 x29) x29) x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x4 x28 = x28) ⟶ x5 = 1 ⟶ x6 = 0 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x7 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x2 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30) (x8 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x8 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x3 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30) (x8 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x7 (x4 x28) x5 x6) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = x9 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x11 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x11 (x1 x28) (x10 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x14 x28 x29 = add_SNo (add_SNo (add_SNo x28 x28) x28) x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x16 x28 = add_SNo x28 (minus_SNo 1)) ⟶ x17 = 0 ⟶ x18 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x19 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x14 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30) (x20 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x20 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x15 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x19 (x16 x28) x17 x18) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x22 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x23 x28 = x28) ⟶ x24 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x25 x28 x29 = If_i (SNoLe x28 0) x29 (x22 (x25 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x25 (x23 x28) x24) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = mul_SNo (If_i (SNoLe x28 0) 1 (x21 x28)) (x26 x28)) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture ee7c0..^A52606 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 . x6 ∈ int ⟶ ∀ x7 : ι → ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x7 x8 x9 x10 ∈ int) ⟶ ∀ x8 : ι → ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x8 x9 x10 x11 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : 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 . x24 ∈ 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 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x1 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x2 x28 x29 = add_SNo (mul_SNo 2 (add_SNo x28 x28)) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x3 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x4 x28 = add_SNo x28 (minus_SNo 1)) ⟶ (∀ x28 . x28 ∈ int ⟶ x5 x28 = If_i (SNoLe x28 0) 1 2) ⟶ x6 = 0 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x7 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x2 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30) (x8 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x8 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x3 (x7 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x7 (x4 x28) (x5 x28) x6) ⟶ (∀ x28 . x28 ∈ int ⟶ x10 x28 = x9 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = If_i (SNoLe x28 0) x29 (x0 (x11 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x11 (x1 x28) (x10 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x14 x28 x29 = add_SNo (mul_SNo 2 (add_SNo x28 x28)) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x16 x28 = add_SNo x28 (minus_SNo 1)) ⟶ x17 = 2 ⟶ x18 = 0 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x19 x28 x29 x30 = If_i (SNoLe x28 0) x29 (x14 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30) (x20 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x20 x28 x29 x30 = If_i (SNoLe x28 0) x30 (x15 (x19 (add_SNo x28 (minus_SNo 1)) x29 x30))) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = x19 (x16 x28) x17 x18) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x22 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x23 x28 = x28) ⟶ x24 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x25 x28 x29 = If_i (SNoLe x28 0) x29 (x22 (x25 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x25 (x23 x28) x24) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = mul_SNo (If_i (SNoLe x28 0) 1 (x21 x28)) (x26 x28)) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture e2ad3..^A52584 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : 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 . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x0 x22 x23 = mul_SNo x22 x23) ⟶ (∀ x22 . x22 ∈ int ⟶ x1 x22 = x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x2 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x3 x22 = add_SNo x22 (minus_SNo 1)) ⟶ x4 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x5 x22 x23 = If_i (SNoLe x22 0) x23 (x2 (x5 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x6 x22 = x5 (x3 x22) x4) ⟶ (∀ x22 . x22 ∈ int ⟶ x7 x22 = add_SNo 1 (x6 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x8 x22 x23 = If_i (SNoLe x22 0) x23 (x0 (x8 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x9 x22 = x8 (x1 x22) (x7 x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x10 x22 = x9 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x11 x22 = add_SNo x22 x22) ⟶ (∀ x22 . x22 ∈ int ⟶ x12 x22 = add_SNo x22 (minus_SNo 1)) ⟶ x13 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x14 x22 x23 = If_i (SNoLe x22 0) x23 (x11 (x14 (add_SNo x22 (minus_SNo 1)) x23))) ⟶ (∀ x22 . x22 ∈ int ⟶ x15 x22 = x14 (x12 x22) x13) ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x16 x22 x23 = mul_SNo x22 x23) ⟶ (∀ x22 . x22 ∈ int ⟶ x17 x22 = x22) ⟶ x18 = 1 ⟶ (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x19 x22 x23 = If_i (SNoLe x22 0) x23 (x16 (x19 (add_SNo x22 (minus_SNo 1)) x23) x22)) ⟶ (∀ x22 . x22 ∈ int ⟶ x20 x22 = x19 (x17 x22) x18) ⟶ (∀ x22 . x22 ∈ int ⟶ x21 x22 = mul_SNo (add_SNo 1 (x15 x22)) (x20 x22)) ⟶ ∀ x22 . x22 ∈ int ⟶ SNoLe 0 x22 ⟶ x10 x22 = x21 x22
Conjecture 30d4f..^A52482 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ 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 = x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x2 x17 x18 = add_SNo x17 x18) ⟶ (∀ x17 . x17 ∈ int ⟶ x3 x17 = add_SNo 2 x17) ⟶ x4 = 0 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x5 x17 x18 = If_i (SNoLe x17 0) x18 (x2 (x5 (add_SNo x17 (minus_SNo 1)) x18) x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = x5 (x3 x17) x4) ⟶ (∀ x17 . x17 ∈ int ⟶ x7 x17 = x6 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x8 x17 x18 = If_i (SNoLe x17 0) x18 (x0 (x8 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x9 x17 = x8 (x1 x17) (x7 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x10 x17 = x9 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x11 x17 = add_SNo x17 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = add_SNo x17 (minus_SNo 1)) ⟶ (∀ x17 . x17 ∈ int ⟶ x13 x17 = add_SNo 2 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x11 (x14 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 (x12 x17) (x13 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = mul_SNo (add_SNo 1 (add_SNo 2 x17)) (If_i (SNoLe x17 0) 1 (x15 x17))) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x10 x17 = x16 x17
Conjecture fa3b4..^A50915 : ∀ 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 = 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 = add_SNo 1 (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 = add_SNo x17 (minus_SNo 1)) ⟶ x10 = 2 ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x11 x17 x18 = If_i (SNoLe x17 0) x18 (x8 (x11 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x12 x17 = x11 (x9 x17) x10) ⟶ (∀ x17 . x17 ∈ int ⟶ x13 x17 = x12 x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x14 x17 x18 = If_i (SNoLe x17 0) x18 (x6 (x14 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x15 x17 = x14 x7 (x13 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = add_SNo 1 (mul_SNo (x15 x17) x17)) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x5 x17 = x16 x17
Conjecture 31702..^A5062 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x23 x24 x25 x26 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x0 x26 x27 = add_SNo (add_SNo (mul_SNo 2 (add_SNo x26 x26)) x26) x27) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x1 x26 x27 = mul_SNo 2 (add_SNo (add_SNo x27 x27) x27)) ⟶ (∀ x26 . x26 ∈ int ⟶ x2 x26 = x26) ⟶ x3 = 0 ⟶ x4 = 1 ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x5 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x0 (x5 (add_SNo x26 (minus_SNo 1)) x27 x28) (x6 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x6 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x1 (x5 (add_SNo x26 (minus_SNo 1)) x27 x28) (x6 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x7 x26 = x5 (x2 x26) x3 x4) ⟶ (∀ x26 . x26 ∈ int ⟶ x8 x26 = x7 x26) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x9 x26 x27 = mul_SNo x26 x27) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x10 x26 x27 = x27) ⟶ (∀ x26 . x26 ∈ int ⟶ x11 x26 = x26) ⟶ x12 = 1 ⟶ x13 = add_SNo 2 (add_SNo 2 2) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x14 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x9 (x14 (add_SNo x26 (minus_SNo 1)) x27 x28) (x15 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x15 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x10 (x14 (add_SNo x26 (minus_SNo 1)) x27 x28) (x15 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x16 x26 = x14 (x11 x26) x12 x13) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x17 x26 x27 = mul_SNo x26 x27) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x18 x26 x27 = x27) ⟶ (∀ x26 . x26 ∈ int ⟶ x19 x26 = x26) ⟶ x20 = 1 ⟶ x21 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x22 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x17 (x22 (add_SNo x26 (minus_SNo 1)) x27 x28) (x23 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x23 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x18 (x22 (add_SNo x26 (minus_SNo 1)) x27 x28) (x23 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x24 x26 = x22 (x19 x26) x20 x21) ⟶ (∀ x26 . x26 ∈ int ⟶ x25 x26 = add_SNo (x16 x26) (minus_SNo (x24 x26))) ⟶ ∀ x26 . x26 ∈ int ⟶ SNoLe 0 x26 ⟶ x8 x26 = x25 x26
Conjecture 19951..^A50621 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x18 x19 x20 x21 ∈ int) ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ (∀ x25 . x25 ∈ int ⟶ x0 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x1 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x2 x25 = add_SNo (mul_SNo 2 (add_SNo x25 x25)) x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x3 x25 = x25) ⟶ x4 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x5 x25 x26 = If_i (SNoLe x25 0) x26 (x2 (x5 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x6 x25 = x5 (x3 x25) x4) ⟶ (∀ x25 . x25 ∈ int ⟶ x7 x25 = add_SNo 1 (x6 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x8 x25 x26 = If_i (SNoLe x25 0) x26 (x0 (x8 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x9 x25 = x8 (x1 x25) (x7 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x10 x25 = x9 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x11 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x12 x25 = x25) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x13 x25 x26 = mul_SNo x25 x26) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x14 x25 x26 = x26) ⟶ (∀ x25 . x25 ∈ int ⟶ x15 x25 = x25) ⟶ x16 = 1 ⟶ x17 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x18 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x13 (x18 (add_SNo x25 (minus_SNo 1)) x26 x27) (x19 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x19 x25 x26 x27 = If_i (SNoLe x25 0) x27 (x14 (x18 (add_SNo x25 (minus_SNo 1)) x26 x27) (x19 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x20 x25 = x18 (x15 x25) x16 x17) ⟶ (∀ x25 . x25 ∈ int ⟶ x21 x25 = add_SNo 1 (x20 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x22 x25 x26 = If_i (SNoLe x25 0) x26 (x11 (x22 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x23 x25 = x22 (x12 x25) (x21 x25)) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = x23 x25) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture b53ef..^A5060 : ∀ 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 (add_SNo (mul_SNo 2 (add_SNo x28 x28)) (mul_SNo x29 x29)) x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x1 x28 x29 = add_SNo x29 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x2 x28 = x28) ⟶ x3 = 0 ⟶ 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 = 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 1 (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 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 (x16 x28) (minus_SNo (x26 x28))) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x8 x28 = x27 x28
Conjecture 74df6..^A49678 : ∀ 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 . 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 . (∀ 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 → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι → ι → ι . (∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x23 x24 x25 x26 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x0 x26 x27 = add_SNo (add_SNo (mul_SNo 2 (add_SNo (add_SNo x26 x26) x26)) (minus_SNo x27)) x26) ⟶ (∀ x26 . x26 ∈ int ⟶ x1 x26 = x26) ⟶ (∀ x26 . x26 ∈ int ⟶ x2 x26 = add_SNo x26 x26) ⟶ x3 = 1 ⟶ x4 = 0 ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x5 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x0 (x5 (add_SNo x26 (minus_SNo 1)) x27 x28) (x6 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x6 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x1 (x5 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x7 x26 = x5 (x2 x26) x3 x4) ⟶ (∀ x26 . x26 ∈ int ⟶ x8 x26 = x7 x26) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x9 x26 x27 = add_SNo (add_SNo (mul_SNo 2 (add_SNo (add_SNo x26 x26) x26)) (minus_SNo x27)) x26) ⟶ (∀ x26 . x26 ∈ int ⟶ x10 x26 = x26) ⟶ (∀ x26 . x26 ∈ int ⟶ x11 x26 = add_SNo x26 (minus_SNo 1)) ⟶ (∀ x26 . x26 ∈ int ⟶ x12 x26 = If_i (SNoLe x26 0) 1 (add_SNo 2 (add_SNo 2 2))) ⟶ x13 = 1 ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x14 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x9 (x14 (add_SNo x26 (minus_SNo 1)) x27 x28) (x15 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x15 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x10 (x14 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x16 x26 = x14 (x11 x26) (x12 x26) x13) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x17 x26 x27 = add_SNo x26 x27) ⟶ (∀ x26 . x26 ∈ int ⟶ x18 x26 = x26) ⟶ (∀ x26 . x26 ∈ int ⟶ x19 x26 = mul_SNo 2 (add_SNo x26 x26)) ⟶ x20 = 1 ⟶ x21 = 1 ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x22 x26 x27 x28 = If_i (SNoLe x26 0) x27 (x17 (x22 (add_SNo x26 (minus_SNo 1)) x27 x28) (x23 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x23 x26 x27 x28 = If_i (SNoLe x26 0) x28 (x18 (x22 (add_SNo x26 (minus_SNo 1)) x27 x28))) ⟶ (∀ x26 . x26 ∈ int ⟶ x24 x26 = x22 (x19 x26) x20 x21) ⟶ (∀ x26 . x26 ∈ int ⟶ x25 x26 = mul_SNo (x16 x26) (x24 x26)) ⟶ ∀ x26 . x26 ∈ int ⟶ SNoLe 0 x26 ⟶ x8 x26 = x25 x26
Conjecture c2d1c..^A49670 : ∀ 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 → 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 . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 . x18 ∈ 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 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ 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 = add_SNo 1 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 ⟶ ∀ x29 . x29 ∈ int ⟶ x5 x28 x29 = add_SNo (mul_SNo x4 x28) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x6 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x7 x28 = x28) ⟶ x8 = 0 ⟶ x9 = add_SNo 1 (minus_SNo 2) ⟶ (∀ 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 x28) x8 x9) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x14 x28 = mul_SNo (mul_SNo x28 x28) x28) ⟶ x15 = 1 ⟶ x16 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x17 x28 x29 = If_i (SNoLe x28 0) x29 (x14 (x17 (add_SNo x28 (minus_SNo 1)) x29))) ⟶ x18 = x17 x15 x16 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x19 x28 x29 = add_SNo (mul_SNo (add_SNo x18 (minus_SNo 2)) x28) (minus_SNo x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x20 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x21 x28 = add_SNo x28 (minus_SNo 1)) ⟶ (∀ x28 . x28 ∈ int ⟶ x22 x28 = If_i (SNoLe x28 0) 0 1) ⟶ x23 = 0 ⟶ (∀ 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))) ⟶ (∀ x28 . x28 ∈ int ⟶ x26 x28 = x24 (x21 x28) (x22 x28) x23) ⟶ (∀ x28 . x28 ∈ int ⟶ x27 x28 = x26 x28) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture 5e293..^A49668 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 . x5 ∈ int ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ ∀ x10 : ι → ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x10 x11 x12 x13 ∈ int) ⟶ ∀ x11 : ι → ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x11 x12 x13 x14 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x0 x23 x24 = x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x1 x23 = add_SNo 1 (add_SNo x23 x23)) ⟶ x2 = add_SNo 2 2 ⟶ x3 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x4 x23 x24 = If_i (SNoLe x23 0) x24 (x1 (x4 (add_SNo x23 (minus_SNo 1)) x24))) ⟶ x5 = x4 x2 x3 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x6 x23 x24 = add_SNo (mul_SNo x5 x24) (minus_SNo x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x23) ⟶ x8 = 0 ⟶ x9 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x10 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x0 (x10 (add_SNo x23 (minus_SNo 1)) x24 x25) (x11 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x11 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x6 (x10 (add_SNo x23 (minus_SNo 1)) x24 x25) (x11 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x12 x23 = x10 (x7 x23) x8 x9) ⟶ (∀ x23 . x23 ∈ int ⟶ x13 x23 = x12 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x14 x23 x24 = add_SNo (mul_SNo (add_SNo (mul_SNo 2 (mul_SNo 2 (mul_SNo 2 (add_SNo 2 (add_SNo 2 2))))) (minus_SNo 1)) 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) 0 1) ⟶ x18 = 0 ⟶ (∀ 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