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Proofgold Asset

asset id
7efee1d2e429591c8483447761abe8420e02cb735ca894a2fd6f419faa3fd691
asset hash
9d23fcf73b481adb2d5311388f929f480f7fe8573ed4686519bd116981655f3e
bday / block
25658
tx
048a7..
preasset
doc published by PrGxv..
Param intint : ι
Param add_SNoadd_SNo : ι → ι → ι
Param ordsuccordsucc : ι → ι
Param If_iIf_i : ο → ι → ι → ι
Param SNoLeSNoLe : ι → ι → ο
Param minus_SNominus_SNo : ι → ι
Param mul_SNomul_SNo : ι → ι → ι
Conjecture 25c23..A19613 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ int) ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x28 x29 x30 ∈ int) ⟶ ∀ x29 : ι → ι → ι . (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x29 x30 x31 ∈ int) ⟶ ∀ x30 : ι → ι . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ int) ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 : ι → ι . (∀ x35 . x35 ∈ int ⟶ x34 x35 ∈ int) ⟶ (∀ x35 . x35 ∈ int ⟶ x0 x35 = add_SNo (add_SNo x35 x35) x35) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x1 x35 x36 = add_SNo x36 x36) ⟶ x2 = 1 ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x3 x35 x36 = If_i (SNoLe x35 0) x36 (x0 (x3 (add_SNo x35 (minus_SNo 1)) x36))) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x4 x35 x36 = x3 (x1 x35 x36) x2) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x5 x35 x36 = add_SNo (x4 x35 x36) (mul_SNo 2 (add_SNo x35 x35))) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x6 x35 x36 = x36) ⟶ x7 = 1 ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x8 x35 x36 = If_i (SNoLe x35 0) x36 (x5 (x8 (add_SNo x35 (minus_SNo 1)) x36) x35)) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x9 x35 x36 = x8 (x6 x35 x36) x7) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x10 x35 x36 = add_SNo (add_SNo (x9 x35 x36) (mul_SNo 2 (add_SNo (add_SNo x35 x35) x35))) x35) ⟶ (∀ x35 . x35 ∈ int ⟶ x11 x35 = x35) ⟶ x12 = 1 ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x13 x35 x36 = If_i (SNoLe x35 0) x36 (x10 (x13 (add_SNo x35 (minus_SNo 1)) x36) x35)) ⟶ (∀ x35 . x35 ∈ int ⟶ x14 x35 = x13 (x11 x35) x12) ⟶ (∀ x35 . x35 ∈ int ⟶ x15 x35 = x14 x35) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x16 x35 x36 = add_SNo (mul_SNo 2 (add_SNo x35 x35)) (mul_SNo x36 x36)) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x17 x35 x36 = add_SNo (add_SNo x36 x36) x36) ⟶ (∀ x35 . x35 ∈ int ⟶ x18 x35 = x35) ⟶ x19 = 1 ⟶ x20 = add_SNo 1 2 ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x21 x35 x36 x37 = If_i (SNoLe x35 0) x36 (x16 (x21 (add_SNo x35 (minus_SNo 1)) x36 x37) (x22 (add_SNo x35 (minus_SNo 1)) x36 x37))) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 . x37 ∈ int ⟶ x22 x35 x36 x37 = If_i (SNoLe x35 0) x37 (x17 (x21 (add_SNo x35 (minus_SNo 1)) x36 x37) (x22 (add_SNo x35 (minus_SNo 1)) x36 x37))) ⟶ (∀ x35 . x35 ∈ int ⟶ x23 x35 = x21 (x18 x35) x19 x20) ⟶ (∀ x35 . x35 ∈ int ⟶ x24 x35 = x23 x35) ⟶ x25 = 1 ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x26 x35 x36 = x36) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x27 x35 x36 = If_i (SNoLe x35 0) x36 (x24 (x27 (add_SNo x35 (minus_SNo 1)) x36))) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x28 x35 x36 = x27 x25 (x26 x35 x36)) ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x29 x35 x36 = add_SNo (add_SNo (x28 x35 x36) (mul_SNo 2 (add_SNo (add_SNo x35 x35) x35))) x35) ⟶ (∀ x35 . x35 ∈ int ⟶ x30 x35 = x35) ⟶ x31 = 1 ⟶ (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x32 x35 x36 = If_i (SNoLe x35 0) x36 (x29 (x32 (add_SNo x35 (minus_SNo 1)) x36) x35)) ⟶ (∀ x35 . x35 ∈ int ⟶ x33 x35 = x32 (x30 x35) x31) ⟶ (∀ x35 . x35 ∈ int ⟶ x34 x35 = x33 x35) ⟶ ∀ x35 . x35 ∈ int ⟶ SNoLe 0 x35 ⟶ x15 x35 = x34 x35
Conjecture 63390..A195615 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x19 x20 x21 x22 ∈ int) ⟶ ∀ x20 : ι → ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x20 x21 x22 x23 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 : ι → ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ x27 x28 x29 x30 ∈ int) ⟶ ∀ x28 : ι → ι → ι → ι . (∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x28 x29 x30 x31 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 : ι → ι . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ int) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x0 x31 x32 = add_SNo (add_SNo (add_SNo x31 (minus_SNo x32)) x31) x31) ⟶ (∀ x31 . x31 ∈ int ⟶ x1 x31 = x31) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x2 x31 x32 = x32) ⟶ x3 = 1 ⟶ x4 = 0 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x5 x31 x32 x33 = If_i (SNoLe x31 0) x32 (x0 (x5 (add_SNo x31 (minus_SNo 1)) x32 x33) (x6 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x6 x31 x32 x33 = If_i (SNoLe x31 0) x33 (x1 (x5 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x7 x31 x32 = x5 (x2 x31 x32) x3 x4) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x8 x31 x32 = add_SNo (x7 x31 x32) (minus_SNo x31)) ⟶ (∀ x31 . x31 ∈ int ⟶ x9 x31 = mul_SNo (add_SNo 1 2) (add_SNo 1 x31)) ⟶ x10 = 1 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x11 x31 x32 = If_i (SNoLe x31 0) x32 (x8 (x11 (add_SNo x31 (minus_SNo 1)) x32) x31)) ⟶ (∀ x31 . x31 ∈ int ⟶ x12 x31 = x11 (x9 x31) x10) ⟶ (∀ x31 . x31 ∈ int ⟶ x13 x31 = x12 x31) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x14 x31 x32 = add_SNo x31 x32) ⟶ (∀ x31 . x31 ∈ int ⟶ x15 x31 = x31) ⟶ (∀ x31 . x31 ∈ int ⟶ x16 x31 = add_SNo 2 (add_SNo (add_SNo x31 x31) x31)) ⟶ x17 = 2 ⟶ x18 = 1 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x19 x31 x32 x33 = If_i (SNoLe x31 0) x32 (x14 (x19 (add_SNo x31 (minus_SNo 1)) x32 x33) (x20 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x20 x31 x32 x33 = If_i (SNoLe x31 0) x33 (x15 (x19 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ x21 x31 = x19 (x16 x31) x17 x18) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x22 x31 x32 = add_SNo (mul_SNo 2 (add_SNo x31 x31)) x32) ⟶ (∀ x31 . x31 ∈ int ⟶ x23 x31 = x31) ⟶ (∀ x31 . x31 ∈ int ⟶ x24 x31 = x31) ⟶ x25 = add_SNo 1 2 ⟶ x26 = 1 ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x27 x31 x32 x33 = If_i (SNoLe x31 0) x32 (x22 (x27 (add_SNo x31 (minus_SNo 1)) x32 x33) (x28 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x28 x31 x32 x33 = If_i (SNoLe x31 0) x33 (x23 (x27 (add_SNo x31 (minus_SNo 1)) x32 x33))) ⟶ (∀ x31 . x31 ∈ int ⟶ x29 x31 = x27 (x24 x31) x25 x26) ⟶ (∀ x31 . x31 ∈ int ⟶ x30 x31 = mul_SNo (x21 x31) (x29 x31)) ⟶ ∀ x31 . x31 ∈ int ⟶ SNoLe 0 x31 ⟶ x13 x31 = x30 x31
Conjecture 1d837..A195590 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : 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) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x1 x15 x16 = mul_SNo 2 (add_SNo 2 x16)) ⟶ (∀ x15 . x15 ∈ int ⟶ x2 x15 = add_SNo 2 x15) ⟶ x3 = 0 ⟶ x4 = 1 ⟶ (∀ 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 (x5 (add_SNo x15 (minus_SNo 1)) x16 x17) (x6 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x7 x15 = x5 (x2 x15) x3 x4) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = x7 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x9 x15 = add_SNo x15 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x10 x15 = x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x11 x15 = add_SNo 2 (add_SNo (mul_SNo 2 (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 = mul_SNo 2 (add_SNo 2 (x13 x15))) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x8 x15 = x14 x15
Conjecture a8aa1..A19490 : ∀ 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 . x11 ∈ int ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ 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 → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 . x22 ∈ int ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 . x25 ∈ int ⟶ ∀ x26 : ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι → ι . (∀ x30 . x30 ∈ int ⟶ ∀ x31 . x31 ∈ int ⟶ x29 x30 x31 ∈ int) ⟶ ∀ x30 : ι → ι . (∀ x31 . x31 ∈ int ⟶ x30 x31 ∈ int) ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x36 x37 x38 x39 ∈ int) ⟶ ∀ x37 : ι → ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x37 x38 x39 x40 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x39 x40 x41 ∈ int) ⟶ ∀ x40 : ι → ι → ι . (∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x40 x41 x42 ∈ int) ⟶ ∀ x41 : ι → ι . (∀ x42 . x42 ∈ int ⟶ x41 x42 ∈ int) ⟶ ∀ x42 . x42 ∈ int ⟶ ∀ x43 . x43 ∈ int ⟶ ∀ x44 : ι → ι → ι → ι . (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x44 x45 x46 x47 ∈ int) ⟶ ∀ x45 : ι → ι → ι → ι . (∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ ∀ x48 . x48 ∈ int ⟶ x45 x46 x47 x48 ∈ int) ⟶ ∀ x46 : ι → ι . (∀ x47 . x47 ∈ int ⟶ x46 x47 ∈ int) ⟶ ∀ x47 : ι → ι . (∀ x48 . x48 ∈ int ⟶ x47 x48 ∈ int) ⟶ (∀ x48 . x48 ∈ int ⟶ x0 x48 = mul_SNo 2 (add_SNo (add_SNo x48 x48) x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ x1 x48 = x48) ⟶ (∀ x48 . x48 ∈ int ⟶ x2 x48 = add_SNo x48 x48) ⟶ (∀ x48 . x48 ∈ int ⟶ x3 x48 = x48) ⟶ x4 = 2 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x5 x48 x49 = If_i (SNoLe x48 0) x49 (x2 (x5 (add_SNo x48 (minus_SNo 1)) x49))) ⟶ (∀ x48 . x48 ∈ int ⟶ x6 x48 = x5 (x3 x48) x4) ⟶ (∀ x48 . x48 ∈ int ⟶ x7 x48 = add_SNo (x6 x48) (minus_SNo 1)) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x8 x48 x49 = If_i (SNoLe x48 0) x49 (x0 (x8 (add_SNo x48 (minus_SNo 1)) x49))) ⟶ (∀ x48 . x48 ∈ int ⟶ x9 x48 = x8 (x1 x48) (x7 x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ x10 x48 = x9 x48) ⟶ x11 = 1 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x12 x48 x49 = x49) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x13 x48 x49 = If_i (SNoLe x48 0) x49 (x10 (x13 (add_SNo x48 (minus_SNo 1)) x49))) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x14 x48 x49 = x13 x11 (x12 x48 x49)) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x15 x48 x49 = add_SNo (x14 x48 x49) (mul_SNo 2 (add_SNo x48 x48))) ⟶ (∀ x48 . x48 ∈ int ⟶ x16 x48 = x48) ⟶ x17 = 1 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x18 x48 x49 = If_i (SNoLe x48 0) x49 (x15 (x18 (add_SNo x48 (minus_SNo 1)) x49) x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ x19 x48 = x18 (x16 x48) x17) ⟶ (∀ x48 . x48 ∈ int ⟶ x20 x48 = x19 x48) ⟶ (∀ x48 . x48 ∈ int ⟶ x21 x48 = add_SNo (mul_SNo x48 x48) (minus_SNo x48)) ⟶ x22 = 1 ⟶ (∀ x48 . x48 ∈ int ⟶ x23 x48 = add_SNo x48 x48) ⟶ (∀ x48 . x48 ∈ int ⟶ x24 x48 = x48) ⟶ x25 = 1 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x26 x48 x49 = If_i (SNoLe x48 0) x49 (x23 (x26 (add_SNo x48 (minus_SNo 1)) x49))) ⟶ (∀ x48 . x48 ∈ int ⟶ x27 x48 = x26 (x24 x48) x25) ⟶ (∀ x48 . x48 ∈ int ⟶ x28 x48 = x27 x48) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x29 x48 x49 = If_i (SNoLe x48 0) x49 (x21 (x29 (add_SNo x48 (minus_SNo 1)) x49))) ⟶ (∀ x48 . x48 ∈ int ⟶ x30 x48 = x29 x22 (x28 x48)) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x31 x48 x49 = mul_SNo x48 x49) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x32 x48 x49 = x49) ⟶ (∀ x48 . x48 ∈ int ⟶ x33 x48 = x48) ⟶ x34 = add_SNo 1 2 ⟶ x35 = add_SNo 1 2 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x36 x48 x49 x50 = If_i (SNoLe x48 0) x49 (x31 (x36 (add_SNo x48 (minus_SNo 1)) x49 x50) (x37 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x37 x48 x49 x50 = If_i (SNoLe x48 0) x50 (x32 (x36 (add_SNo x48 (minus_SNo 1)) x49 x50) (x37 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ x38 x48 = x36 (x33 x48) x34 x35) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x39 x48 x49 = mul_SNo x48 x49) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ x40 x48 x49 = x49) ⟶ (∀ x48 . x48 ∈ int ⟶ x41 x48 = x48) ⟶ x42 = 1 ⟶ x43 = add_SNo 2 2 ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x44 x48 x49 x50 = If_i (SNoLe x48 0) x49 (x39 (x44 (add_SNo x48 (minus_SNo 1)) x49 x50) (x45 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ ∀ x49 . x49 ∈ int ⟶ ∀ x50 . x50 ∈ int ⟶ x45 x48 x49 x50 = If_i (SNoLe x48 0) x50 (x40 (x44 (add_SNo x48 (minus_SNo 1)) x49 x50) (x45 (add_SNo x48 (minus_SNo 1)) x49 x50))) ⟶ (∀ x48 . x48 ∈ int ⟶ x46 x48 = x44 (x41 x48) x42 x43) ⟶ (∀ x48 . x48 ∈ int ⟶ x47 x48 = add_SNo (mul_SNo (x30 x48) (x38 x48)) (x46 x48)) ⟶ ∀ x48 . x48 ∈ int ⟶ SNoLe 0 x48 ⟶ x20 x48 = x47 x48
Conjecture 6cafe..A19483 : ∀ 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 → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . 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 → 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 : ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x25 x26 x27 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 : ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x30 x31 x32 ∈ int) ⟶ ∀ x31 : ι → ι . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ ∀ x32 : ι → ι . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ int) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x0 x33 x34 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x33 x33) x33)) (mul_SNo x34 x34)) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x1 x33 x34 = add_SNo x34 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x2 x33 x34 = x34) ⟶ x3 = 1 ⟶ x4 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x5 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x0 (x5 (add_SNo x33 (minus_SNo 1)) x34 x35) (x6 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x6 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x1 (x5 (add_SNo x33 (minus_SNo 1)) x34 x35) (x6 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x7 x33 x34 = x5 (x2 x33 x34) x3 x4) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x8 x33 x34 = add_SNo (x7 x33 x34) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x33 x33)) x33))) ⟶ (∀ x33 . x33 ∈ int ⟶ x9 x33 = x33) ⟶ x10 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x11 x33 x34 = If_i (SNoLe x33 0) x34 (x8 (x11 (add_SNo x33 (minus_SNo 1)) x34) x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x12 x33 = x11 (x9 x33) x10) ⟶ (∀ x33 . x33 ∈ int ⟶ x13 x33 = x12 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x14 x33 x34 = add_SNo (add_SNo (add_SNo x33 x33) x33) x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x15 x33 x34 = add_SNo x34 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x16 x33 x34 = x34) ⟶ x17 = 1 ⟶ x18 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x19 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x14 (x19 (add_SNo x33 (minus_SNo 1)) x34 x35) (x20 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x20 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x15 (x19 (add_SNo x33 (minus_SNo 1)) x34 x35) (x20 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x21 x33 x34 = x19 (x16 x33 x34) x17 x18) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x22 x33 x34 = add_SNo (add_SNo (x21 x33 x34) (mul_SNo 2 (add_SNo x33 x33))) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x23 x33 = x33) ⟶ x24 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x25 x33 x34 = If_i (SNoLe x33 0) x34 (x22 (x25 (add_SNo x33 (minus_SNo 1)) x34) x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x26 x33 = x25 (x23 x33) x24) ⟶ (∀ x33 . x33 ∈ int ⟶ x27 x33 = add_SNo x33 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x28 x33 = x33) ⟶ x29 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x30 x33 x34 = If_i (SNoLe x33 0) x34 (x27 (x30 (add_SNo x33 (minus_SNo 1)) x34))) ⟶ (∀ x33 . x33 ∈ int ⟶ x31 x33 = x30 (x28 x33) x29) ⟶ (∀ x33 . x33 ∈ int ⟶ x32 x33 = mul_SNo (x26 x33) (x31 x33)) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x13 x33 = x32 x33
Conjecture 22641..A19443 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ ∀ x21 : ι → ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x21 x22 x23 x24 ∈ int) ⟶ ∀ x22 : ι → ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x22 x23 x24 x25 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 : ι → ι . (∀ x30 . x30 ∈ int ⟶ x29 x30 ∈ int) ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x31 x32 x33 ∈ int) ⟶ ∀ x32 : ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x32 x33 x34 ∈ int) ⟶ ∀ x33 : ι → ι → ι . (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x33 x34 x35 ∈ int) ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι . (∀ x36 . x36 ∈ int ⟶ x35 x36 ∈ int) ⟶ ∀ x36 . x36 ∈ int ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι . (∀ x39 . x39 ∈ int ⟶ x38 x39 ∈ int) ⟶ ∀ x39 : ι → ι . (∀ x40 . x40 ∈ int ⟶ x39 x40 ∈ int) ⟶ (∀ x40 . x40 ∈ int ⟶ x0 x40 = add_SNo (add_SNo x40 x40) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x1 x40 x41 = add_SNo x41 x41) ⟶ x2 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x3 x40 x41 = If_i (SNoLe x40 0) x41 (x0 (x3 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x4 x40 x41 = x3 (x1 x40 x41) x2) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x5 x40 x41 = add_SNo (x4 x40 x41) (mul_SNo 2 (add_SNo (add_SNo x40 x40) x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x6 x40 x41 = x41) ⟶ x7 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x8 x40 x41 = If_i (SNoLe x40 0) x41 (x5 (x8 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x9 x40 x41 = x8 (x6 x40 x41) x7) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x10 x40 x41 = add_SNo (x9 x40 x41) (mul_SNo 2 (add_SNo x40 x40))) ⟶ (∀ x40 . x40 ∈ int ⟶ x11 x40 = x40) ⟶ x12 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x13 x40 x41 = If_i (SNoLe x40 0) x41 (x10 (x13 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x14 x40 = x13 (x11 x40) x12) ⟶ (∀ x40 . x40 ∈ int ⟶ x15 x40 = x14 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x16 x40 x41 = add_SNo (add_SNo (add_SNo x40 x40) x40) x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x17 x40 x41 = add_SNo x41 x41) ⟶ (∀ x40 . x40 ∈ int ⟶ x18 x40 = x40) ⟶ x19 = 1 ⟶ x20 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x21 x40 x41 x42 = If_i (SNoLe x40 0) x41 (x16 (x21 (add_SNo x40 (minus_SNo 1)) x41 x42) (x22 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 . x42 ∈ int ⟶ x22 x40 x41 x42 = If_i (SNoLe x40 0) x42 (x17 (x21 (add_SNo x40 (minus_SNo 1)) x41 x42) (x22 (add_SNo x40 (minus_SNo 1)) x41 x42))) ⟶ (∀ x40 . x40 ∈ int ⟶ x23 x40 = x21 (x18 x40) x19 x20) ⟶ (∀ x40 . x40 ∈ int ⟶ x24 x40 = add_SNo x40 x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x25 x40 = add_SNo x40 (minus_SNo 1)) ⟶ x26 = 2 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x27 x40 x41 = If_i (SNoLe x40 0) x41 (x24 (x27 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ x28 x40 = x27 (x25 x40) x26) ⟶ (∀ x40 . x40 ∈ int ⟶ x29 x40 = mul_SNo (x23 x40) (x28 x40)) ⟶ x30 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x31 x40 x41 = x41) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x32 x40 x41 = If_i (SNoLe x40 0) x41 (x29 (x32 (add_SNo x40 (minus_SNo 1)) x41))) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x33 x40 x41 = x32 x30 (x31 x40 x41)) ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x34 x40 x41 = add_SNo (add_SNo (x33 x40 x41) (mul_SNo 2 (mul_SNo 2 (add_SNo x40 x40)))) x40) ⟶ (∀ x40 . x40 ∈ int ⟶ x35 x40 = x40) ⟶ x36 = 1 ⟶ (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x37 x40 x41 = If_i (SNoLe x40 0) x41 (x34 (x37 (add_SNo x40 (minus_SNo 1)) x41) x40)) ⟶ (∀ x40 . x40 ∈ int ⟶ x38 x40 = x37 (x35 x40) x36) ⟶ (∀ x40 . x40 ∈ int ⟶ x39 x40 = x38 x40) ⟶ ∀ x40 . x40 ∈ int ⟶ SNoLe 0 x40 ⟶ x15 x40 = x39 x40
Conjecture 01446..A193592 : ∀ 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 → 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 : 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 . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι → ι . (∀ x20 . x20 ∈ int ⟶ ∀ x21 . x21 ∈ int ⟶ x19 x20 x21 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ 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 ⟶ ∀ x30 : ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x30 x31 x32 ∈ int) ⟶ ∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 : ι → ι → ι . (∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x34 x35 x36 ∈ int) ⟶ ∀ x35 : ι → ι . (∀ x36 . x36 ∈ int ⟶ x35 x36 ∈ int) ⟶ ∀ x36 : ι → ι . (∀ x37 . x37 ∈ int ⟶ x36 x37 ∈ int) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x0 x37 x38 = add_SNo x38 (minus_SNo 1)) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x1 x37 x38 = add_SNo x37 (minus_SNo x38)) ⟶ (∀ x37 . x37 ∈ int ⟶ x2 x37 = x37) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x3 x37 x38 = If_i (SNoLe x37 0) x38 (x0 (x3 (add_SNo x37 (minus_SNo 1)) x38) x37)) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x4 x37 x38 = x3 (x1 x37 x38) (x2 x37)) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x5 x37 x38 = x4 x37 x38) ⟶ (∀ x37 . x37 ∈ int ⟶ x6 x37 = x37) ⟶ (∀ x37 . x37 ∈ int ⟶ x7 x37 = x37) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x8 x37 x38 = If_i (SNoLe x37 0) x38 (x5 (x8 (add_SNo x37 (minus_SNo 1)) x38) x37)) ⟶ (∀ x37 . x37 ∈ int ⟶ x9 x37 = x8 (x6 x37) (x7 x37)) ⟶ (∀ x37 . x37 ∈ int ⟶ x10 x37 = add_SNo (If_i (SNoLe (add_SNo (x9 x37) (minus_SNo 1)) 0) 0 1) x37) ⟶ (∀ x37 . x37 ∈ int ⟶ x11 x37 = x37) ⟶ (∀ x37 . x37 ∈ int ⟶ x12 x37 = x37) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x13 x37 x38 = If_i (SNoLe x37 0) x38 (x10 (x13 (add_SNo x37 (minus_SNo 1)) x38))) ⟶ (∀ x37 . x37 ∈ int ⟶ x14 x37 = x13 (x11 x37) (x12 x37)) ⟶ (∀ x37 . x37 ∈ int ⟶ x15 x37 = add_SNo (add_SNo (x14 x37) (minus_SNo x37)) 1) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x16 x37 x38 = x38) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x17 x37 x38 = add_SNo x37 (minus_SNo x38)) ⟶ (∀ x37 . x37 ∈ int ⟶ x18 x37 = x37) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x19 x37 x38 = If_i (SNoLe x37 0) x38 (x16 (x19 (add_SNo x37 (minus_SNo 1)) x38) x37)) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x20 x37 x38 = x19 (x17 x37 x38) (x18 x37)) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x21 x37 x38 = x20 x37 x38) ⟶ (∀ x37 . x37 ∈ int ⟶ x22 x37 = x37) ⟶ (∀ x37 . x37 ∈ int ⟶ x23 x37 = add_SNo 2 x37) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x24 x37 x38 = If_i (SNoLe x37 0) x38 (x21 (x24 (add_SNo x37 (minus_SNo 1)) x38) x37)) ⟶ (∀ x37 . x37 ∈ int ⟶ x25 x37 = x24 (x22 x37) (x23 x37)) ⟶ (∀ x37 . x37 ∈ int ⟶ x26 x37 = add_SNo (add_SNo (If_i (SNoLe (add_SNo (x25 x37) (minus_SNo 2)) 0) 1 2) (minus_SNo 1)) x37) ⟶ (∀ x37 . x37 ∈ int ⟶ x27 x37 = mul_SNo x37 x37) ⟶ x28 = 2 ⟶ x29 = 2 ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x30 x37 x38 = If_i (SNoLe x37 0) x38 (x27 (x30 (add_SNo x37 (minus_SNo 1)) x38))) ⟶ x31 = x30 x28 x29 ⟶ x32 = x31 ⟶ (∀ x37 . x37 ∈ int ⟶ x33 x37 = x37) ⟶ (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x34 x37 x38 = If_i (SNoLe x37 0) x38 (x26 (x34 (add_SNo x37 (minus_SNo 1)) x38))) ⟶ (∀ x37 . x37 ∈ int ⟶ x35 x37 = x34 x32 (x33 x37)) ⟶ (∀ x37 . x37 ∈ int ⟶ x36 x37 = add_SNo (add_SNo (x35 x37) (minus_SNo x37)) 1) ⟶ ∀ x37 . x37 ∈ int ⟶ SNoLe 0 x37 ⟶ x15 x37 = x36 x37
Conjecture 5526e..A193577 : ∀ 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 (mul_SNo 2 (add_SNo (add_SNo x15 x15) x15)) x15) ⟶ (∀ x15 . x15 ∈ int ⟶ x1 x15 = x15) ⟶ x2 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x3 x15 x16 = If_i (SNoLe x15 0) x16 (x0 (x3 (add_SNo x15 (minus_SNo 1)) x16))) ⟶ (∀ x15 . x15 ∈ int ⟶ x4 x15 = x3 (x1 x15) x2) ⟶ (∀ x15 . x15 ∈ int ⟶ x5 x15 = x4 x15) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x6 x15 x16 = mul_SNo x15 x16) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x7 x15 x16 = x16) ⟶ (∀ x15 . x15 ∈ int ⟶ x8 x15 = x15) ⟶ x9 = add_SNo 1 (add_SNo 2 2) ⟶ x10 = add_SNo 1 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x11 x15 x16 x17 = If_i (SNoLe x15 0) x16 (x6 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x12 x15 x16 x17 = If_i (SNoLe x15 0) x17 (x7 (x11 (add_SNo x15 (minus_SNo 1)) x16 x17) (x12 (add_SNo x15 (minus_SNo 1)) x16 x17))) ⟶ (∀ x15 . x15 ∈ int ⟶ x13 x15 = x11 (x8 x15) x9 x10) ⟶ (∀ x15 . x15 ∈ int ⟶ x14 x15 = x13 x15) ⟶ ∀ x15 . x15 ∈ int ⟶ SNoLe 0 x15 ⟶ x5 x15 = x14 x15
Conjecture 9893f..A192796 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι . (∀ x4 . x4 ∈ int ⟶ x3 x4 ∈ int) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x0 x17 x18 = add_SNo x17 x18) ⟶ (∀ x17 . x17 ∈ int ⟶ x1 x17 = add_SNo 1 (add_SNo x17 x17)) ⟶ x2 = 2 ⟶ (∀ x17 . x17 ∈ int ⟶ x3 x17 = x17) ⟶ (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x4 x17 x18 = If_i (SNoLe x17 0) x18 (x1 (x4 (add_SNo x17 (minus_SNo 1)) x18))) ⟶ (∀ x17 . x17 ∈ int ⟶ x5 x17 = x4 x2 (x3 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x6 x17 = x5 x17) ⟶ x7 = 0 ⟶ (∀ 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 . x17 ∈ int ⟶ x9 x17 = x8 (x6 x17) x7) ⟶ (∀ x17 . x17 ∈ int ⟶ x10 x17 = mul_SNo (x9 x17) x17) ⟶ (∀ x17 . x17 ∈ int ⟶ x11 x17 = add_SNo (mul_SNo 2 (mul_SNo x17 x17)) (minus_SNo x17)) ⟶ x12 = 1 ⟶ (∀ x17 . x17 ∈ int ⟶ x13 x17 = add_SNo 2 (add_SNo x17 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 (x13 x17)) ⟶ (∀ x17 . x17 ∈ int ⟶ x16 x17 = mul_SNo (x15 x17) x17) ⟶ ∀ x17 . x17 ∈ int ⟶ SNoLe 0 x17 ⟶ x10 x17 = x16 x17
Conjecture 56bf7..A192475 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 : 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 → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x13 x14 x15 x16 ∈ int) ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x17 x18 x19 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 : ι → ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x25 x26 x27 x28 ∈ int) ⟶ ∀ x26 : ι → ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x26 x27 x28 x29 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 : ι → ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ x30 x31 x32 x33 ∈ int) ⟶ ∀ x31 : ι → ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x31 x32 x33 x34 ∈ int) ⟶ ∀ x32 : ι → ι . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x0 x34 x35 = add_SNo x34 x35) ⟶ (∀ x34 . x34 ∈ int ⟶ x1 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x2 x34 x35 = x35) ⟶ x3 = 1 ⟶ (∀ x34 . x34 ∈ int ⟶ x4 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x5 x34 x35 x36 = If_i (SNoLe x34 0) x35 (x0 (x5 (add_SNo x34 (minus_SNo 1)) x35 x36) (x6 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x6 x34 x35 x36 = If_i (SNoLe x34 0) x36 (x1 (x5 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x7 x34 x35 = x5 (x2 x34 x35) x3 (x4 x34)) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x8 x34 x35 = x7 x34 x35) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x9 x34 x35 = add_SNo 1 x35) ⟶ x10 = 2 ⟶ x11 = 2 ⟶ (∀ x34 . x34 ∈ int ⟶ x12 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x13 x34 x35 x36 = If_i (SNoLe x34 0) x35 (x8 (x13 (add_SNo x34 (minus_SNo 1)) x35 x36) (x14 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x14 x34 x35 x36 = If_i (SNoLe x34 0) x36 (x9 (x13 (add_SNo x34 (minus_SNo 1)) x35 x36) (x14 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ x15 x34 = x13 x10 x11 (x12 x34)) ⟶ (∀ x34 . x34 ∈ int ⟶ x16 x34 = x15 x34) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x17 x34 x35 = add_SNo x34 x35) ⟶ (∀ x34 . x34 ∈ int ⟶ x18 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ x19 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x20 x34 x35 = add_SNo x34 x35) ⟶ (∀ x34 . x34 ∈ int ⟶ x21 x34 = x34) ⟶ (∀ x34 . x34 ∈ int ⟶ x22 x34 = x34) ⟶ x23 = 1 ⟶ x24 = 2 ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x25 x34 x35 x36 = If_i (SNoLe x34 0) x35 (x20 (x25 (add_SNo x34 (minus_SNo 1)) x35 x36) (x26 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x26 x34 x35 x36 = If_i (SNoLe x34 0) x36 (x21 (x25 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ x27 x34 = x25 (x22 x34) x23 x24) ⟶ (∀ x34 . x34 ∈ int ⟶ x28 x34 = add_SNo 1 (x27 x34)) ⟶ x29 = 1 ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x30 x34 x35 x36 = If_i (SNoLe x34 0) x35 (x17 (x30 (add_SNo x34 (minus_SNo 1)) x35 x36) (x31 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 . x36 ∈ int ⟶ x31 x34 x35 x36 = If_i (SNoLe x34 0) x36 (x18 (x30 (add_SNo x34 (minus_SNo 1)) x35 x36))) ⟶ (∀ x34 . x34 ∈ int ⟶ x32 x34 = x30 (x19 x34) (x28 x34) x29) ⟶ (∀ x34 . x34 ∈ int ⟶ x33 x34 = x32 x34) ⟶ ∀ x34 . x34 ∈ int ⟶ SNoLe 0 x34 ⟶ x16 x34 = x33 x34
Conjecture 78a25..A1923 : ∀ 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 → ι . (∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ x2 x3 x4 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ int ⟶ ∀ x6 . x6 ∈ int ⟶ x4 x5 x6 ∈ int) ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι → ι → 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 → 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 : 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 ⟶ ∀ x29 . x29 ∈ int ⟶ x1 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x2 x28 x29 = x29) ⟶ x3 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x4 x28 x29 = x29) ⟶ (∀ 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 ⟶ ∀ x29 . x29 ∈ int ⟶ x7 x28 x29 = x5 (x2 x28 x29) x3 (x4 x28 x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x8 x28 x29 = add_SNo x28 (x7 x28 x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = x28) ⟶ x10 = 0 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = If_i (SNoLe x28 0) x29 (x8 (x11 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x11 (x9 x28) x10) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x14 x28 x29 = mul_SNo x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x15 x28 x29 = x29) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x16 x28 x29 = add_SNo x29 (minus_SNo 2)) ⟶ x17 = 1 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x18 x28 x29 = x29) ⟶ (∀ 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 ⟶ ∀ x29 . x29 ∈ int ⟶ x21 x28 x29 = x19 (x16 x28 x29) x17 (x18 x28 x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x22 x28 x29 = add_SNo (mul_SNo (x21 x28 x29) (mul_SNo x29 x29)) x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x23 x28 = x28) ⟶ x24 = 0 ⟶ (∀ 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 = x26 x28) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture e6091..A190966 : ∀ 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 : 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 → 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 ⟶ ∀ x24 . x24 ∈ int ⟶ x1 x23 x24 = mul_SNo 2 (mul_SNo 2 (add_SNo (add_SNo x24 (minus_SNo x23)) (minus_SNo x23)))) ⟶ (∀ x23 . x23 ∈ int ⟶ x2 x23 = x23) ⟶ x3 = 0 ⟶ x4 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x5 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x0 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x6 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x1 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x5 (x2 x23) x3 x4) ⟶ (∀ x23 . x23 ∈ int ⟶ x8 x23 = x7 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x9 x23 x24 = add_SNo x23 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x10 x23 x24 = add_SNo x24 (minus_SNo x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x11 x23 = x23) ⟶ x12 = 0 ⟶ (∀ x23 . x23 ∈ int ⟶ x13 x23 = add_SNo x23 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x14 x23 = add_SNo x23 (minus_SNo 1)) ⟶ x15 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x16 x23 x24 = If_i (SNoLe x23 0) x24 (x13 (x16 (add_SNo x23 (minus_SNo 1)) x24))) ⟶ (∀ x23 . x23 ∈ int ⟶ x17 x23 = x16 (x14 x23) x15) ⟶ (∀ x23 . x23 ∈ int ⟶ x18 x23 = x17 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x19 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x9 (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 (x10 (x19 (add_SNo x23 (minus_SNo 1)) x24 x25) (x20 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x21 x23 = x19 (x11 x23) x12 (x18 x23)) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = x21 x23) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x8 x23 = x22 x23
Conjecture b8b63..A190576 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x0 x7 x8 = add_SNo 2 (add_SNo x7 x8)) ⟶ (∀ x7 . x7 ∈ int ⟶ x1 x7 = x7) ⟶ (∀ x7 . x7 ∈ int ⟶ x2 x7 = x7) ⟶ (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x3 x7 x8 = If_i (SNoLe x7 0) x8 (x0 (x3 (add_SNo x7 (minus_SNo 1)) x8) x7)) ⟶ (∀ x7 . x7 ∈ int ⟶ x4 x7 = x3 (x1 x7) (x2 x7)) ⟶ (∀ x7 . x7 ∈ int ⟶ x5 x7 = add_SNo 1 (mul_SNo 2 (x4 x7))) ⟶ (∀ x7 . x7 ∈ int ⟶ x6 x7 = add_SNo 1 (add_SNo (mul_SNo (add_SNo 2 (add_SNo 2 (add_SNo 2 x7))) x7) x7)) ⟶ ∀ x7 . x7 ∈ int ⟶ SNoLe 0 x7 ⟶ x5 x7 = x6 x7
Conjecture 17b02..A190542 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ int ⟶ ∀ x11 . x11 ∈ int ⟶ x9 x10 x11 ∈ int) ⟶ ∀ x10 : ι → ι → ι . (∀ x11 . x11 ∈ int ⟶ ∀ x12 . x12 ∈ int ⟶ x10 x11 x12 ∈ int) ⟶ ∀ x11 : ι → ι . (∀ x12 . x12 ∈ int ⟶ x11 x12 ∈ int) ⟶ ∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ ∀ x14 : ι → ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x14 x15 x16 x17 ∈ int) ⟶ ∀ x15 : ι → ι → ι → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x15 x16 x17 x18 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 : ι → ι . (∀ x18 . x18 ∈ int ⟶ x17 x18 ∈ int) ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 . x21 ∈ int ⟶ ∀ x22 : ι → ι → ι . (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x22 x23 x24 ∈ int) ⟶ ∀ x23 : ι → ι . (∀ x24 . x24 ∈ int ⟶ x23 x24 ∈ int) ⟶ ∀ x24 : ι → ι . (∀ x25 . x25 ∈ int ⟶ x24 x25 ∈ int) ⟶ ∀ x25 : ι → ι → ι . (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x25 x26 x27 ∈ int) ⟶ ∀ x26 : ι → ι . (∀ x27 . x27 ∈ int ⟶ x26 x27 ∈ int) ⟶ ∀ x27 : ι → ι . (∀ x28 . x28 ∈ int ⟶ x27 x28 ∈ int) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x0 x28 x29 = add_SNo (mul_SNo (add_SNo 1 2) (add_SNo (add_SNo x28 x28) x29)) x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x1 x28 x29 = mul_SNo 2 (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 (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 19074..A190540 : ∀ x0 : ι → ι . (∀ x1 . x1 ∈ int ⟶ x0 x1 ∈ int) ⟶ ∀ x1 : ι → ι . (∀ x2 . x2 ∈ int ⟶ x1 x2 ∈ int) ⟶ ∀ x2 . x2 ∈ int ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ int ⟶ ∀ x5 . x5 ∈ int ⟶ x3 x4 x5 ∈ int) ⟶ ∀ x4 : ι → ι . (∀ x5 . x5 ∈ int ⟶ x4 x5 ∈ int) ⟶ ∀ x5 : ι → ι . (∀ x6 . x6 ∈ int ⟶ x5 x6 ∈ int) ⟶ ∀ x6 : ι → ι . (∀ x7 . x7 ∈ int ⟶ x6 x7 ∈ int) ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ ∀ x16 : ι → ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ x16 x17 x18 x19 ∈ int) ⟶ ∀ x17 : ι → ι → ι → ι . (∀ x18 . x18 ∈ int ⟶ ∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x17 x18 x19 x20 ∈ int) ⟶ ∀ x18 : ι → ι . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : 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 . x25 ∈ int ⟶ x0 x25 = add_SNo (mul_SNo 2 (add_SNo (add_SNo x25 x25) x25)) x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x1 x25 = x25) ⟶ x2 = 1 ⟶ (∀ 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 x25) x2) ⟶ (∀ x25 . x25 ∈ int ⟶ x5 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x6 x25 = x25) ⟶ x7 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x8 x25 x26 = If_i (SNoLe x25 0) x26 (x5 (x8 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x9 x25 = x8 (x6 x25) x7) ⟶ (∀ x25 . x25 ∈ int ⟶ x10 x25 = add_SNo (x4 x25) (minus_SNo (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 ⟶ x15 = add_SNo 1 (add_SNo 2 (add_SNo 2 2)) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x16 x25 x26 x27 = If_i (SNoLe x25 0) x26 (x11 (x16 (add_SNo x25 (minus_SNo 1)) x26 x27) (x17 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x17 x25 x26 x27 = If_i (SNoLe x25 0) x27 (x12 (x16 (add_SNo x25 (minus_SNo 1)) x26 x27) (x17 (add_SNo x25 (minus_SNo 1)) x26 x27))) ⟶ (∀ x25 . x25 ∈ int ⟶ x18 x25 = x16 (x13 x25) x14 x15) ⟶ (∀ x25 . x25 ∈ int ⟶ x19 x25 = add_SNo x25 x25) ⟶ (∀ x25 . x25 ∈ int ⟶ x20 x25 = x25) ⟶ x21 = 1 ⟶ (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x22 x25 x26 = If_i (SNoLe x25 0) x26 (x19 (x22 (add_SNo x25 (minus_SNo 1)) x26))) ⟶ (∀ x25 . x25 ∈ int ⟶ x23 x25 = x22 (x20 x25) x21) ⟶ (∀ x25 . x25 ∈ int ⟶ x24 x25 = add_SNo (x18 x25) (minus_SNo (x23 x25))) ⟶ ∀ x25 . x25 ∈ int ⟶ SNoLe 0 x25 ⟶ x10 x25 = x24 x25
Conjecture 14452..A190535 : ∀ 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 → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ int) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ int ⟶ ∀ x10 . x10 ∈ int ⟶ x8 x9 x10 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 . x10 ∈ int ⟶ ∀ x11 : ι → ι → ι . (∀ x12 . x12 ∈ int ⟶ ∀ x13 . x13 ∈ int ⟶ x11 x12 x13 ∈ int) ⟶ ∀ x12 : ι → ι . (∀ x13 . x13 ∈ int ⟶ x12 x13 ∈ int) ⟶ ∀ x13 : ι → ι . (∀ x14 . x14 ∈ int ⟶ x13 x14 ∈ int) ⟶ ∀ x14 : ι → ι → ι . (∀ x15 . x15 ∈ int ⟶ ∀ x16 . x16 ∈ int ⟶ x14 x15 x16 ∈ int) ⟶ ∀ x15 : ι → ι . (∀ x16 . x16 ∈ int ⟶ x15 x16 ∈ int) ⟶ ∀ x16 : ι → ι → ι . (∀ x17 . x17 ∈ int ⟶ ∀ x18 . x18 ∈ int ⟶ x16 x17 x18 ∈ 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 → 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 : 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 x28 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x1 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x2 x28 x29 = add_SNo 2 x29) ⟶ (∀ x28 . x28 ∈ int ⟶ x3 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x4 x28 = x28) ⟶ (∀ 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))) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x7 x28 x29 = x5 (x2 x28 x29) (x3 x28) (x4 x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x8 x28 x29 = add_SNo (x7 x28 x29) (minus_SNo x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x9 x28 = add_SNo 2 x28) ⟶ x10 = 2 ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x11 x28 x29 = If_i (SNoLe x28 0) x29 (x8 (x11 (add_SNo x28 (minus_SNo 1)) x29) x28)) ⟶ (∀ x28 . x28 ∈ int ⟶ x12 x28 = x11 (x9 x28) x10) ⟶ (∀ x28 . x28 ∈ int ⟶ x13 x28 = x12 x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x14 x28 x29 = add_SNo 1 (add_SNo x28 x29)) ⟶ (∀ x28 . x28 ∈ int ⟶ x15 x28 = x28) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x16 x28 x29 = x29) ⟶ x17 = 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 ⟶ ∀ x29 . x29 ∈ int ⟶ x21 x28 x29 = x19 (x16 x28 x29) x17 x18) ⟶ (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x22 x28 x29 = mul_SNo (x21 x28 x29) x28) ⟶ (∀ x28 . x28 ∈ int ⟶ x23 x28 = add_SNo 2 x28) ⟶ x24 = 2 ⟶ (∀ 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 = x26 x28) ⟶ ∀ x28 . x28 ∈ int ⟶ SNoLe 0 x28 ⟶ x13 x28 = x27 x28
Conjecture 1509f..A19040 : ∀ 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 → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ x5 x6 x7 ∈ int) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x6 x7 x8 ∈ int) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x7 x8 x9 ∈ 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 → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ int) ⟶ ∀ x13 : ι → ι → ι . (∀ x14 . x14 ∈ int ⟶ ∀ x15 . x15 ∈ int ⟶ x13 x14 x15 ∈ int) ⟶ ∀ x14 : ι → ι . (∀ x15 . x15 ∈ int ⟶ x14 x15 ∈ int) ⟶ ∀ x15 . 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 → ι . (∀ x21 . x21 ∈ int ⟶ ∀ x22 . x22 ∈ int ⟶ x20 x21 x22 ∈ int) ⟶ ∀ x21 : ι → ι → ι . (∀ x22 . x22 ∈ int ⟶ ∀ x23 . x23 ∈ int ⟶ x21 x22 x23 ∈ int) ⟶ ∀ x22 . 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 → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ int) ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 : ι → ι → ι . (∀ x31 . x31 ∈ int ⟶ ∀ x32 . x32 ∈ int ⟶ x30 x31 x32 ∈ int) ⟶ ∀ x31 : ι → ι . (∀ x32 . x32 ∈ int ⟶ x31 x32 ∈ int) ⟶ ∀ x32 : ι → ι . (∀ x33 . x33 ∈ int ⟶ x32 x33 ∈ int) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x0 x33 x34 = mul_SNo (add_SNo 2 x34) x33) ⟶ x1 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ x2 x33 = x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x3 x33 x34 = If_i (SNoLe x33 0) x34 (x0 (x3 (add_SNo x33 (minus_SNo 1)) x34) x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x4 x33 = x3 x1 (x2 x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x5 x33 x34 = add_SNo (add_SNo (x4 x33) (minus_SNo x33)) (mul_SNo x34 x34)) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x6 x33 x34 = add_SNo x34 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x7 x33 x34 = x34) ⟶ x8 = 1 ⟶ x9 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x10 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x5 (x10 (add_SNo x33 (minus_SNo 1)) x34 x35) (x11 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x11 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x6 (x10 (add_SNo x33 (minus_SNo 1)) x34 x35) (x11 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x12 x33 x34 = x10 (x7 x33 x34) x8 x9) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x13 x33 x34 = add_SNo (add_SNo (x12 x33 x34) (mul_SNo 2 (add_SNo x33 x33))) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x14 x33 = x33) ⟶ x15 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x16 x33 x34 = If_i (SNoLe x33 0) x34 (x13 (x16 (add_SNo x33 (minus_SNo 1)) x34) x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x17 x33 = x16 (x14 x33) x15) ⟶ (∀ x33 . x33 ∈ int ⟶ x18 x33 = x17 x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x19 x33 x34 = add_SNo (add_SNo (mul_SNo 2 (add_SNo x33 x33)) (mul_SNo x34 x34)) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x20 x33 x34 = add_SNo x34 x34) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x21 x33 x34 = x34) ⟶ x22 = 1 ⟶ x23 = 2 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x24 x33 x34 x35 = If_i (SNoLe x33 0) x34 (x19 (x24 (add_SNo x33 (minus_SNo 1)) x34 x35) (x25 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x25 x33 x34 x35 = If_i (SNoLe x33 0) x35 (x20 (x24 (add_SNo x33 (minus_SNo 1)) x34 x35) (x25 (add_SNo x33 (minus_SNo 1)) x34 x35))) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x26 x33 x34 = x24 (x21 x33 x34) x22 x23) ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x27 x33 x34 = add_SNo (add_SNo (x26 x33 x34) (mul_SNo 2 (add_SNo (mul_SNo 2 (add_SNo x33 x33)) x33))) x33) ⟶ (∀ x33 . x33 ∈ int ⟶ x28 x33 = x33) ⟶ x29 = 1 ⟶ (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x30 x33 x34 = If_i (SNoLe x33 0) x34 (x27 (x30 (add_SNo x33 (minus_SNo 1)) x34) x33)) ⟶ (∀ x33 . x33 ∈ int ⟶ x31 x33 = x30 (x28 x33) x29) ⟶ (∀ x33 . x33 ∈ int ⟶ x32 x33 = x31 x33) ⟶ ∀ x33 . x33 ∈ int ⟶ SNoLe 0 x33 ⟶ x18 x33 = x32 x33
Conjecture f1c7a..A189356 : ∀ 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 . 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 . (∀ x19 . x19 ∈ int ⟶ x18 x19 ∈ 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 → 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 (mul_SNo 2 (add_SNo x26 x26)) (minus_SNo x27)) ⟶ (∀ x26 . x26 ∈ int ⟶ x1 x26 = x26) ⟶ (∀ x26 . x26 ∈ int ⟶ x2 x26 = add_SNo 1 (add_SNo x26 x26)) ⟶ x3 = 1 ⟶ 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))) ⟶ (∀ 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 (mul_SNo 2 (add_SNo x26 x26)) (minus_SNo x27)) ⟶ (∀ x26 . x26 ∈ int ⟶ x10 x26 = x26) ⟶ (∀ x26 . x26 ∈ int ⟶ x11 x26 = x26) ⟶ x12 = 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 x13) ⟶ (∀ x26 . x26 ∈ int ⟶ ∀ x27 . x27 ∈ int ⟶ x17 x26 x27 = add_SNo (mul_SNo 2 (add_SNo x26 x26)) (minus_SNo x27)) ⟶ (∀ x26 . x26 ∈ int ⟶ x18 x26 = x26) ⟶ (∀ x26 . x26 ∈ int ⟶ x19 x26 = add_SNo x26 (minus_SNo 1)) ⟶ (∀ x26 . x26 ∈ int ⟶ x20 x26 = add_SNo (If_i (SNoLe x26 0) 0 2) 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 x26) x21) ⟶ (∀ x26 . x26 ∈ int ⟶ x25 x26 = add_SNo (mul_SNo (mul_SNo (x16 x26) (x24 x26)) 2) (minus_SNo 1)) ⟶ ∀ x26 . x26 ∈ int ⟶ SNoLe 0 x26 ⟶ x8 x26 = x25 x26
Conjecture f6bdf..A189318 : ∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ int ⟶ ∀ x2 . x2 ∈ int ⟶ x0 x1 x2 ∈ int) ⟶ ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ int ⟶ ∀ x3 . x3 ∈ int ⟶ x1 x2 x3 ∈ int) ⟶ ∀ x2 : ι → ι . (∀ x3 . x3 ∈ int ⟶ x2 x3 ∈ int) ⟶ ∀ x3 . x3 ∈ int ⟶ ∀ x4 . x4 ∈ int ⟶ ∀ x5 : ι → ι → ι → ι . (∀ x6 . x6 ∈ int ⟶ ∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ x5 x6 x7 x8 ∈ int) ⟶ ∀ x6 : ι → ι → ι → ι . (∀ x7 . x7 ∈ int ⟶ ∀ x8 . x8 ∈ int ⟶ ∀ x9 . x9 ∈ int ⟶ x6 x7 x8 x9 ∈ int) ⟶ ∀ x7 : ι → ι . (∀ x8 . x8 ∈ int ⟶ x7 x8 ∈ int) ⟶ ∀ x8 : ι → ι . (∀ x9 . x9 ∈ int ⟶ x8 x9 ∈ int) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ int ⟶ x9 x10 ∈ int) ⟶ ∀ x10 : ι → ι . (∀ x11 . x11 ∈ int ⟶ x10 x11 ∈ int) ⟶ ∀ x11 . x11 ∈ 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 → 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 . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x0 x23 x24 = add_SNo x24 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x1 x23 x24 = mul_SNo 2 (add_SNo x23 x24)) ⟶ (∀ x23 . x23 ∈ int ⟶ x2 x23 = x23) ⟶ x3 = 2 ⟶ x4 = 1 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x5 x23 x24 x25 = If_i (SNoLe x23 0) x24 (x0 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ ∀ x25 . x25 ∈ int ⟶ x6 x23 x24 x25 = If_i (SNoLe x23 0) x25 (x1 (x5 (add_SNo x23 (minus_SNo 1)) x24 x25) (x6 (add_SNo x23 (minus_SNo 1)) x24 x25))) ⟶ (∀ x23 . x23 ∈ int ⟶ x7 x23 = x5 (x2 x23) x3 x4) ⟶ (∀ x23 . x23 ∈ int ⟶ x8 x23 = add_SNo 1 (mul_SNo 2 (x7 x23))) ⟶ (∀ x23 . x23 ∈ int ⟶ x9 x23 = add_SNo x23 x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x10 x23 = add_SNo x23 (minus_SNo 1)) ⟶ x11 = 2 ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x12 x23 x24 = If_i (SNoLe x23 0) x24 (x9 (x12 (add_SNo x23 (minus_SNo 1)) x24))) ⟶ (∀ x23 . x23 ∈ int ⟶ x13 x23 = x12 (x10 x23) x11) ⟶ (∀ x23 . x23 ∈ int ⟶ ∀ x24 . x24 ∈ int ⟶ x14 x23 x24 = add_SNo x23 x24) ⟶ (∀ x23 . x23 ∈ int ⟶ x15 x23 = x23) ⟶ (∀ x23 . x23 ∈ int ⟶ x16 x23 = add_SNo x23 (minus_SNo 1)) ⟶ x17 = 1 ⟶ x18 = 2 ⟶ (∀ 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 x18) ⟶ (∀ x23 . x23 ∈ int ⟶ x22 x23 = add_SNo (mul_SNo (mul_SNo 2 (x13 x23)) (x21 x23)) 1) ⟶ ∀ x23 . x23 ∈ int ⟶ SNoLe 0 x23 ⟶ x8 x23 = x22 x23
Conjecture 6c3a0..A18912 : ∀ 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 . x11 ∈ int ⟶ ∀ x12 : ι → ι → ι . (∀ x13 . x13 ∈ int ⟶ ∀ x14 . x14 ∈ int ⟶ x12 x13 x14 ∈ 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 → ι . (∀ x16 . x16 ∈ int ⟶ ∀ x17 . x17 ∈ int ⟶ x15 x16 x17 ∈ int) ⟶ ∀ x16 : ι → ι . (∀ x17 . x17 ∈ int ⟶ x16 x17 ∈ int) ⟶ ∀ x17 . x17 ∈ int ⟶ ∀ x18 : ι → ι → ι . (∀ x19 . x19 ∈ int ⟶ ∀ x20 . x20 ∈ int ⟶ x18 x19 x20 ∈ int) ⟶ ∀ x19 : ι → ι . (∀ x20 . x20 ∈ int ⟶ x19 x20 ∈ int) ⟶ ∀ x20 : ι → ι . (∀ x21 . x21 ∈ int ⟶ x20 x21 ∈ int) ⟶ ∀ x21 : ι → ι . (∀ x22 . x22 ∈ int ⟶ x21 x22 ∈ int) ⟶ ∀ x22 : ι → ι . (∀ x23 . x23 ∈ int ⟶ x22 x23 ∈ int) ⟶ ∀ x23 . x23 ∈ int ⟶ ∀ x24 : ι → ι → ι . (∀ x25 . x25 ∈ int ⟶ ∀ x26 . x26 ∈ int ⟶ x24 x25 x26 ∈ int) ⟶ ∀ x25 : ι → ι . (∀ x26 . x26 ∈ int ⟶ x25 x26 ∈ int) ⟶ ∀ x26 : ι → ι → ι . (∀ x27 . x27 ∈ int ⟶ ∀ x28 . x28 ∈ int ⟶ x26 x27 x28 ∈ int) ⟶ ∀ x27 : ι → ι → ι . (∀ x28 . x28 ∈ int ⟶ ∀ x29 . x29 ∈ int ⟶ x27 x28 x29 ∈ int) ⟶ ∀ x28 : ι → ι . (∀ x29 . x29 ∈ int ⟶ x28 x29 ∈ int) ⟶ ∀ x29 . x29 ∈ int ⟶ ∀ x30 . x30 ∈ int ⟶ ∀ x31 : ι → ι → ι → ι . (∀ x32 . x32 ∈ int ⟶ ∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ x31 x32 x33 x34 ∈ int) ⟶ ∀ x32 : ι → ι → ι → ι . (∀ x33 . x33 ∈ int ⟶ ∀ x34 . x34 ∈ int ⟶ ∀ x35 . x35 ∈ int ⟶ x32 x33 x34 x35 ∈ int) ⟶ ∀ x33 : ι → ι . (∀ x34 . x34 ∈ int ⟶ x33 x34 ∈ int) ⟶ ∀ x34 : ι → ι . (∀ x35 . x35 ∈ int ⟶ x34 x35 ∈ int) ⟶ ∀ x35 . x35 ∈ int ⟶ ∀ x36 : ι → ι → ι . (∀ x37 . x37 ∈ int ⟶ ∀ x38 . x38 ∈ int ⟶ x36 x37 x38 ∈ int) ⟶ ∀ x37 : ι → ι → ι . (∀ x38 . x38 ∈ int ⟶ ∀ x39 . x39 ∈ int ⟶ x37 x38 x39 ∈ int) ⟶ ∀ x38 : ι → ι → ι . (∀ x39 . x39 ∈ int ⟶ ∀ x40 . x40 ∈ int ⟶ x38 x39 x40 ∈ int) ⟶ ∀ x39 : ι → ι → ι . (∀ x40 . x40 ∈ int ⟶ ∀ x41 . x41 ∈ int ⟶ x39 x40 x41 ∈ int) ⟶ ∀ x40 : ι → ι . (∀ x41 . x41 ∈ int ⟶ x40 x41 ∈ int) ⟶ ∀ x41 . x41 ∈ int ⟶ ∀ x42 : ι → ι → ι . (∀ x43 . x43 ∈ int ⟶ ∀ x44 . x44 ∈ int ⟶ x42 x43 x44 ∈ int) ⟶ ∀ x43 : ι → ι . (∀ x44 . x44 ∈ int ⟶ x43 x44 ∈ int) ⟶ ∀ x44 : ι → ι . (∀ x45 . x45 ∈ int ⟶ x44 x45 ∈ int) ⟶ (∀ x45 . x45 ∈ int ⟶ x0 x45 = add_SNo (mul_SNo 2 (add_SNo x45 x45)) x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x1 x45 = x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x2 x45 = add_SNo x45 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x3 x45 = x45) ⟶ x4 = 2 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x5 x45 x46 = If_i (SNoLe x45 0) x46 (x2 (x5 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ x6 x45 = x5 (x3 x45) x4) ⟶ (∀ x45 . x45 ∈ int ⟶ x7 x45 = add_SNo (x6 x45) (minus_SNo 1)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x8 x45 x46 = If_i (SNoLe x45 0) x46 (x0 (x8 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ x9 x45 = x8 (x1 x45) (x7 x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x10 x45 = x9 x45) ⟶ x11 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x12 x45 x46 = x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x13 x45 x46 = If_i (SNoLe x45 0) x46 (x10 (x13 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x14 x45 x46 = x13 x11 (x12 x45 x46)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x15 x45 x46 = add_SNo (x14 x45 x46) (mul_SNo 2 (add_SNo x45 x45))) ⟶ (∀ x45 . x45 ∈ int ⟶ x16 x45 = x45) ⟶ x17 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x18 x45 x46 = If_i (SNoLe x45 0) x46 (x15 (x18 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x19 x45 = x18 (x16 x45) x17) ⟶ (∀ x45 . x45 ∈ int ⟶ x20 x45 = x19 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x21 x45 = add_SNo x45 x45) ⟶ (∀ x45 . x45 ∈ int ⟶ x22 x45 = x45) ⟶ x23 = 2 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x24 x45 x46 = If_i (SNoLe x45 0) x46 (x21 (x24 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ x25 x45 = x24 (x22 x45) x23) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x26 x45 x46 = mul_SNo x45 x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x27 x45 x46 = x46) ⟶ (∀ x45 . x45 ∈ int ⟶ x28 x45 = x45) ⟶ x29 = 1 ⟶ x30 = add_SNo 1 (add_SNo 2 2) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x31 x45 x46 x47 = If_i (SNoLe x45 0) x46 (x26 (x31 (add_SNo x45 (minus_SNo 1)) x46 x47) (x32 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ ∀ x47 . x47 ∈ int ⟶ x32 x45 x46 x47 = If_i (SNoLe x45 0) x47 (x27 (x31 (add_SNo x45 (minus_SNo 1)) x46 x47) (x32 (add_SNo x45 (minus_SNo 1)) x46 x47))) ⟶ (∀ x45 . x45 ∈ int ⟶ x33 x45 = x31 (x28 x45) x29 x30) ⟶ (∀ x45 . x45 ∈ int ⟶ x34 x45 = mul_SNo (add_SNo (x25 x45) (minus_SNo 1)) (x33 x45)) ⟶ x35 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x36 x45 x46 = x46) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x37 x45 x46 = If_i (SNoLe x45 0) x46 (x34 (x37 (add_SNo x45 (minus_SNo 1)) x46))) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x38 x45 x46 = x37 x35 (x36 x45 x46)) ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x39 x45 x46 = add_SNo (x38 x45 x46) (mul_SNo 2 (add_SNo x45 x45))) ⟶ (∀ x45 . x45 ∈ int ⟶ x40 x45 = x45) ⟶ x41 = 1 ⟶ (∀ x45 . x45 ∈ int ⟶ ∀ x46 . x46 ∈ int ⟶ x42 x45 x46 = If_i (SNoLe x45 0) x46 (x39 (x42 (add_SNo x45 (minus_SNo 1)) x46) x45)) ⟶ (∀ x45 . x45 ∈ int ⟶ x43 x45 = x42 (x40 x45) x41) ⟶ (∀ x45 . x45 ∈ int ⟶ x44 x45 = x43 x45) ⟶ ∀ x45 . x45 ∈ int ⟶ SNoLe 0 x45 ⟶ x20 x45 = x44 x45