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Proofgold Proof
pf
Apply df_ifs__df_cgr3__df_fs__df_segle__df_outsideof__df_line2__df_ray__df_lines2__df_fwddif__df_fwddifn__df_hf__df_fne__df_3nand__df_gcdOLD__ax_prv1__ax_prv2__ax_prv3__df_ssb with
∀ x0 x1 x2 : ο .
wb
(
w3nand
x0
x1
x2
)
(
x0
⟶
x1
⟶
wn
x2
)
.
Assume H0:
wceq
cifs
(
copab
(
λ x0 x1 .
wrex
(
λ x2 .
wrex
(
λ x3 .
wrex
(
λ x4 .
wrex
(
λ x5 .
wrex
(
λ x6 .
wrex
(
λ x7 .
wrex
(
λ x8 .
wrex
(
λ x9 .
wrex
(
λ x10 .
w3a
(
wceq
(
cv
x0
)
(
cop
(
cop
(
cv
x3
)
(
cv
x4
)
)
(
cop
(
cv
x5
)
(
cv
x6
)
)
)
)
(
wceq
(
cv
x1
)
(
cop
(
cop
(
cv
x7
)
(
cv
x8
)
)
(
cop
(
cv
x9
)
(
cv
x10
)
)
)
)
(
w3a
(
wa
(
wbr
(
cv
x4
)
(
cop
(
cv
x3
)
(
cv
x5
)
)
cbtwn
)
(
wbr
(
cv
x8
)
(
cop
(
cv
x7
)
(
cv
x9
)
)
cbtwn
)
)
(
wa
(
wbr
(
cop
(
cv
x3
)
(
cv
x5
)
)
(
cop
(
cv
x7
)
(
cv
x9
)
)
ccgr
)
(
wbr
(
cop
(
cv
x4
)
(
cv
x5
)
)
(
cop
(
cv
x8
)
(
cv
x9
)
)
ccgr
)
)
(
wa
(
wbr
(
cop
(
cv
x3
)
(
cv
x6
)
)
(
cop
(
cv
x7
)
(
cv
x10
)
)
ccgr
)
(
wbr
(
cop
(
cv
x5
)
(
cv
x6
)
)
(
cop
(
cv
x9
)
(
cv
x10
)
)
ccgr
)
)
)
)
(
λ x10 .
cfv
(
cv
x2
)
cee
)
)
(
λ x9 .
cfv
(
cv
x2
)
cee
)
)
(
λ x8 .
cfv
(
cv
x2
)
cee
)
)
(
λ x7 .
cfv
(
cv
x2
)
cee
)
)
(
λ x6 .
cfv
(
cv
x2
)
cee
)
)
(
λ x5 .
cfv
(
cv
x2
)
cee
)
)
(
λ x4 .
cfv
(
cv
x2
)
cee
)
)
(
λ x3 .
cfv
(
cv
x2
)
cee
)
)
(
λ x2 .
cn
)
)
)
.
Assume H1:
wceq
ccgr3
(
copab
(
λ x0 x1 .
wrex
(
λ x2 .
wrex
(
λ x3 .
wrex
(
λ x4 .
wrex
(
λ x5 .
wrex
(
λ x6 .
wrex
(
λ x7 .
wrex
(
λ x8 .
w3a
(
wceq
(
cv
x0
)
(
cop
(
cv
x3
)
(
cop
(
cv
x4
)
(
cv
x5
)
)
)
)
(
wceq
(
cv
x1
)
(
cop
(
cv
x6
)
(
cop
(
cv
x7
)
(
cv
x8
)
)
)
)
(
w3a
(
wbr
(
cop
(
cv
x3
)
(
cv
x4
)
)
(
cop
(
cv
x6
)
(
cv
x7
)
)
ccgr
)
(
wbr
(
cop
(
cv
x3
)
(
cv
x5
)
)
(
cop
(
cv
x6
)
(
cv
x8
)
)
ccgr
)
(
wbr
(
cop
(
cv
x4
)
(
cv
x5
)
)
(
cop
(
cv
x7
)
(
cv
x8
)
)
ccgr
)
)
)
(
λ x8 .
cfv
...
...
)
)
...
)
...
)
...
)
...
)
...
)
...
)
)
.
...
■