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Proofgold Proof
pf
Apply df_ordt__df_xrs__df_qtop__df_imas__df_qus__df_xps__df_mre__df_mrc__df_mri__df_acs__df_cat__df_cid__df_homf__df_comf__df_oppc__df_mon__df_epi__df_sect with
wceq
ccat
(
cab
(
λ x0 .
wsbc
(
λ x1 .
wsbc
(
λ x2 .
wsbc
(
λ x3 .
wral
(
λ x4 .
wa
(
wrex
(
λ x5 .
wral
(
λ x6 .
wa
(
wral
(
λ x7 .
wceq
(
co
(
cv
x5
)
(
cv
x7
)
(
co
(
cop
(
cv
x6
)
(
cv
x4
)
)
(
cv
x4
)
(
cv
x3
)
)
)
(
cv
x7
)
)
(
λ x7 .
co
(
cv
x6
)
(
cv
x4
)
(
cv
x2
)
)
)
(
wral
(
λ x7 .
wceq
(
co
(
cv
x7
)
(
cv
x5
)
(
co
(
cop
(
cv
x4
)
(
cv
x4
)
)
(
cv
x6
)
(
cv
x3
)
)
)
(
cv
x7
)
)
(
λ x7 .
co
(
cv
x4
)
(
cv
x6
)
(
cv
x2
)
)
)
)
(
λ x6 .
cv
x1
)
)
(
λ x5 .
co
(
cv
x4
)
(
cv
x4
)
(
cv
x2
)
)
)
(
wral
(
λ x5 .
wral
(
λ x6 .
wral
(
λ x7 .
wral
(
λ x8 .
wa
(
wcel
(
co
(
cv
x8
)
(
cv
x7
)
(
co
(
cop
(
cv
x4
)
(
cv
x5
)
)
(
cv
x6
)
(
cv
x3
)
)
)
(
co
(
cv
x4
)
(
cv
x6
)
(
cv
x2
)
)
)
(
wral
(
λ x9 .
wral
(
λ x10 .
wceq
(
co
(
co
(
cv
x10
)
(
cv
x8
)
(
co
(
cop
(
cv
x5
)
(
cv
x6
)
)
(
cv
x9
)
(
cv
x3
)
)
)
(
cv
x7
)
(
co
(
cop
(
cv
x4
)
(
cv
x5
)
)
(
cv
x9
)
(
cv
x3
)
)
)
(
co
(
cv
x10
)
(
co
(
cv
x8
)
(
cv
x7
)
(
co
(
cop
(
cv
x4
)
(
cv
x5
)
)
(
cv
x6
)
(
cv
x3
)
)
)
(
co
(
cop
(
cv
x4
)
(
cv
x6
)
)
(
cv
x9
)
(
cv
x3
)
)
)
)
(
λ x10 .
co
(
cv
x6
)
(
cv
x9
)
(
cv
x2
)
)
)
(
λ x9 .
cv
x1
)
)
)
(
λ x8 .
co
(
cv
x5
)
(
cv
x6
)
(
cv
x2
)
)
)
(
λ x7 .
co
(
cv
x4
)
(
cv
x5
)
(
cv
x2
)
)
)
(
λ x6 .
cv
x1
)
)
(
λ x5 .
cv
x1
)
)
)
(
λ x4 .
cv
x1
)
)
(
cfv
(
cv
x0
)
cco
)
)
(
cfv
(
cv
x0
)
chom
)
)
(
cfv
(
cv
x0
)
cbs
)
)
)
.
Assume H0:
wceq
cordt
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cfv
(
cfv
(
cun
(
csn
(
cdm
(
cv
x0
)
)
)
(
crn
(
cun
(
cmpt
(
λ x1 .
cdm
(
cv
x0
)
)
(
λ x1 .
crab
(
λ x2 .
wn
(
wbr
...
...
...
)
)
...
)
)
...
)
)
)
...
)
...
)
)
.
...
■