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Proofgold Term Root Disambiguation
∀ x0 : ο .
(
wceq
cinv
(
cmpt
(
λ x1 .
ccat
)
(
λ x1 .
cmpt2
(
λ x2 x3 .
cfv
(
cv
x1
)
cbs
)
(
λ x2 x3 .
cfv
(
cv
x1
)
cbs
)
(
λ x2 x3 .
cin
(
co
(
cv
x2
)
(
cv
x3
)
(
cfv
(
cv
x1
)
csect
)
)
(
ccnv
(
co
(
cv
x3
)
(
cv
x2
)
(
cfv
(
cv
x1
)
csect
)
)
)
)
)
)
⟶
wceq
ciso
(
cmpt
(
λ x1 .
ccat
)
(
λ x1 .
ccom
(
cmpt
(
λ x2 .
cvv
)
(
λ x2 .
cdm
(
cv
x2
)
)
)
(
cfv
(
cv
x1
)
cinv
)
)
)
⟶
wceq
ccic
(
cmpt
(
λ x1 .
ccat
)
(
λ x1 .
co
(
cfv
(
cv
x1
)
ciso
)
c0
csupp
)
)
⟶
wceq
cssc
(
copab
(
λ x1 x2 .
wex
(
λ x3 .
wa
(
wfn
(
cv
x2
)
(
cxp
(
cv
x3
)
(
cv
x3
)
)
)
(
wrex
(
λ x4 .
wcel
(
cv
x1
)
(
cixp
(
λ x5 .
cxp
(
cv
x4
)
(
cv
x4
)
)
(
λ x5 .
cpw
(
cfv
(
cv
x5
)
(
cv
x2
)
)
)
)
)
(
λ x4 .
cpw
(
cv
x3
)
)
)
)
)
)
⟶
wceq
cresc
(
cmpt2
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
co
(
co
(
cv
x1
)
(
cdm
(
cdm
(
cv
x2
)
)
)
cress
)
(
cop
(
cfv
cnx
chom
)
(
cv
x2
)
)
csts
)
)
⟶
wceq
csubc
(
cmpt
(
λ x1 .
ccat
)
(
λ x1 .
cab
(
λ x2 .
wa
(
wbr
(
cv
x2
)
(
cfv
(
cv
x1
)
chomf
)
cssc
)
(
wsbc
(
λ x3 .
wral
(
λ x4 .
wa
(
wcel
(
cfv
(
cv
x4
)
(
cfv
(
cv
x1
)
ccid
)
)
(
co
(
cv
x4
)
(
cv
x4
)
(
cv
x2
)
)
)
(
wral
(
λ x5 .
wral
(
λ x6 .
wral
(
λ x7 .
wral
(
λ x8 .
wcel
(
co
(
cv
x8
)
(
cv
x7
)
(
co
(
cop
(
cv
x4
)
(
cv
x5
)
)
(
cv
x6
)
(
cfv
(
cv
x1
)
cco
)
)
)
(
co
(
cv
x4
)
(
cv
x6
)
(
cv
x2
)
)
)
(
λ x8 .
co
(
cv
x5
)
(
cv
x6
)
(
cv
x2
)
)
)
(
λ x7 .
co
(
cv
x4
)
(
cv
x5
)
(
cv
x2
)
)
)
(
λ x6 .
cv
x3
)
)
(
λ x5 .
cv
x3
)
)
)
(
λ x4 .
cv
x3
)
)
(
cdm
(
cdm
(
cv
x2
)
)
)
)
)
)
)
⟶
wceq
cfunc
(
cmpt2
(
λ x1 x2 .
ccat
)
(
λ x1 x2 .
ccat
)
(
λ x1 x2 .
copab
(
λ x3 x4 .
wsbc
(
λ x5 .
w3a
(
wf
(
cv
x5
)
(
cfv
(
cv
x2
)
cbs
)
(
cv
x3
)
)
(
wcel
(
cv
x4
)
(
cixp
(
λ x6 .
cxp
(
cv
x5
)
(
cv
x5
)
)
(
λ x6 .
co
(
co
(
cfv
(
cfv
(
cv
x6
)
c1st
)
(
cv
x3
)
)
(
cfv
(
cfv
(
cv
x6
)
c2nd
)
(
cv
x3
)
)
(
cfv
(
cv
x2
)
chom
)
)
(
cfv
(
cv
x6
)
(
cfv
(
cv
x1
)
chom
)
)
cmap
)
)
)
(
wral
(
λ x6 .
wa
(
wceq
(
cfv
(
cfv
(
cv
x6
)
(
cfv
(
cv
x1
)
ccid
)
)
(
co
(
cv
x6
)
(
cv
x6
)
(
cv
x4
)
)
)
(
cfv
(
cfv
(
cv
x6
)
(
cv
x3
)
)
(
cfv
(
cv
x2
)
ccid
)
)
)
(
wral
(
λ x7 .
wral
(
λ x8 .
wral
(
λ x9 .
wral
(
λ x10 .
wceq
(
cfv
(
co
(
cv
x10
)
(
cv
x9
)
(
co
(
cop
(
cv
x6
)
(
cv
x7
)
)
(
cv
x8
)
(
cfv
(
cv
x1
)
cco
)
)
)
(
co
(
cv
x6
)
(
cv
x8
)
(
cv
x4
)
)
)
(
co
(
cfv
(
cv
x10
)
(
co
(
cv
x7
)
(
cv
x8
)
(
cv
x4
)
)
)
(
cfv
(
cv
x9
)
(
co
(
cv
x6
)
(
cv
x7
)
(
cv
x4
)
)
)
(
co
(
cop
(
cfv
(
cv
x6
)
(
cv
x3
)
)
(
cfv
(
cv
x7
)
(
cv
x3
)
)
)
(
cfv
(
cv
x8
)
(
cv
x3
)
)
(
cfv
(
cv
x2
)
cco
)
)
)
)
(
λ x10 .
co
(
cv
x7
)
(
cv
x8
)
(
cfv
(
cv
x1
)
chom
)
)
)
(
λ x9 .
co
(
cv
x6
)
(
cv
x7
)
(
cfv
(
cv
x1
)
chom
)
)
)
(
λ x8 .
cv
x5
)
)
(
λ x7 .
cv
x5
)
)
)
(
λ x6 .
cv
x5
)
)
)
(
cfv
(
cv
x1
)
cbs
)
)
)
)
⟶
wceq
cidfu
(
cmpt
(
λ x1 .
ccat
)
(
λ x1 .
csb
(
cfv
(
cv
x1
)
cbs
)
(
λ x2 .
cop
(
cres
cid
(
cv
x2
)
)
(
cmpt
(
λ x3 .
cxp
(
cv
x2
)
(
cv
x2
)
)
(
λ x3 .
cres
cid
(
cfv
(
cv
x3
)
(
cfv
(
cv
x1
)
chom
)
)
)
)
)
)
)
⟶
wceq
ccofu
(
cmpt2
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
cop
(
ccom
(
cfv
(
cv
x1
)
c1st
)
(
cfv
(
cv
x2
)
c1st
)
)
(
cmpt2
(
λ x3 x4 .
cdm
(
cdm
(
cfv
(
cv
x2
)
c2nd
)
)
)
(
λ x3 x4 .
cdm
(
cdm
(
cfv
(
cv
x2
)
c2nd
)
)
)
(
λ x3 x4 .
ccom
(
co
(
cfv
(
cv
x3
)
(
cfv
(
cv
x2
)
c1st
)
)
(
cfv
(
cv
x4
)
(
cfv
(
cv
x2
)
c1st
)
)
(
cfv
(
cv
x1
)
c2nd
)
)
(
co
(
cv
x3
)
(
cv
x4
)
(
cfv
(
cv
x2
)
c2nd
)
)
)
)
)
)
⟶
wceq
cresf
(
cmpt2
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
cop
(
cres
(
cfv
(
cv
x1
)
c1st
)
(
cdm
(
cdm
(
cv
x2
)
)
)
)
(
cmpt
(
λ x3 .
cdm
(
cv
x2
)
)
(
λ x3 .
cres
(
cfv
(
cv
x3
)
(
cfv
(
cv
x1
)
c2nd
)
)
(
cfv
(
cv
x3
)
(
cv
x2
)
)
)
)
)
)
⟶
wceq
cful
(
cmpt2
(
λ x1 x2 .
ccat
)
(
λ x1 x2 .
ccat
)
(
λ x1 x2 .
copab
(
λ x3 x4 .
wa
(
wbr
(
cv
x3
)
(
cv
x4
)
(
co
(
cv
x1
)
(
cv
x2
)
cfunc
)
)
(
wral
(
λ x5 .
wral
(
λ x6 .
wceq
(
crn
(
co
(
cv
x5
)
(
cv
x6
)
(
cv
x4
)
)
)
(
co
(
cfv
(
cv
x5
)
(
cv
x3
)
)
(
cfv
(
cv
x6
)
(
cv
x3
)
)
(
cfv
(
cv
x2
)
chom
)
)
)
(
λ x6 .
cfv
(
cv
x1
)
cbs
)
)
(
λ x5 .
cfv
(
cv
x1
)
cbs
)
)
)
)
)
⟶
wceq
cfth
(
cmpt2
(
λ x1 x2 .
ccat
)
(
λ x1 x2 .
ccat
)
(
λ x1 x2 .
copab
(
λ x3 x4 .
wa
(
wbr
(
cv
x3
)
(
cv
x4
)
(
co
(
cv
x1
)
(
cv
x2
)
cfunc
)
)
(
wral
(
λ x5 .
wral
(
λ x6 .
wfun
(
ccnv
(
co
(
cv
x5
)
(
cv
x6
)
(
cv
x4
)
)
)
)
(
λ x6 .
cfv
(
cv
x1
)
cbs
)
)
(
λ x5 .
cfv
(
cv
x1
)
cbs
)
)
)
)
)
⟶
wceq
cnat
(
cmpt2
(
λ x1 x2 .
ccat
)
(
λ x1 x2 .
ccat
)
(
λ x1 x2 .
cmpt2
(
λ x3 x4 .
co
(
cv
x1
)
(
cv
x2
)
cfunc
)
(
λ x3 x4 .
co
(
cv
x1
)
(
cv
x2
)
cfunc
)
(
λ x3 x4 .
csb
(
cfv
(
cv
x3
)
c1st
)
(
λ x5 .
csb
(
cfv
(
cv
x4
)
c1st
)
(
λ x6 .
crab
(
λ x7 .
wral
(
λ x8 .
wral
(
λ x9 .
wral
(
λ x10 .
wceq
(
co
(
cfv
(
cv
x9
)
(
cv
x7
)
)
(
cfv
(
cv
x10
)
(
co
(
cv
x8
)
(
cv
x9
)
(
cfv
(
cv
x3
)
c2nd
)
)
)
(
co
(
cop
(
cfv
(
cv
x8
)
(
cv
x5
)
)
(
cfv
(
cv
x9
)
(
cv
x5
)
)
)
(
cfv
(
cv
x9
)
(
cv
x6
)
)
(
cfv
(
cv
x2
)
cco
)
)
)
(
co
(
cfv
(
cv
x10
)
(
co
(
cv
x8
)
(
cv
x9
)
(
cfv
(
cv
x4
)
c2nd
)
)
)
(
cfv
(
cv
x8
)
(
cv
x7
)
)
(
co
(
cop
(
cfv
(
cv
x8
)
(
cv
x5
)
)
(
cfv
(
cv
x8
)
(
cv
x6
)
)
)
(
cfv
(
cv
x9
)
(
cv
x6
)
)
(
cfv
(
cv
x2
)
cco
)
)
)
)
(
λ x10 .
co
(
cv
x8
)
(
cv
x9
)
(
cfv
(
cv
x1
)
chom
)
)
)
(
λ x9 .
cfv
(
cv
x1
)
cbs
)
)
(
λ x8 .
cfv
(
cv
x1
)
cbs
)
)
(
λ x7 .
cixp
(
λ x8 .
cfv
(
cv
x1
)
cbs
)
(
λ x8 .
co
(
cfv
(
cv
x8
)
(
cv
x5
)
)
(
cfv
(
cv
x8
)
(
cv
x6
)
)
(
cfv
(
cv
x2
)
chom
)
)
)
)
)
)
)
)
⟶
wceq
cfuc
(
cmpt2
(
λ x1 x2 .
ccat
)
(
λ x1 x2 .
ccat
)
(
λ x1 x2 .
ctp
(
cop
(
cfv
cnx
cbs
)
(
co
(
cv
x1
)
(
cv
x2
)
cfunc
)
)
(
cop
(
cfv
cnx
chom
)
(
co
(
cv
x1
)
(
cv
x2
)
cnat
)
)
(
cop
(
cfv
cnx
cco
)
(
cmpt2
(
λ x3 x4 .
cxp
(
co
(
cv
x1
)
(
cv
x2
)
cfunc
)
(
co
(
cv
x1
)
(
cv
x2
)
cfunc
)
)
(
λ x3 x4 .
co
(
cv
x1
)
(
cv
x2
)
cfunc
)
(
λ x3 x4 .
csb
(
cfv
(
cv
x3
)
c1st
)
(
λ x5 .
csb
(
cfv
(
cv
x3
)
c2nd
)
(
λ x6 .
cmpt2
(
λ x7 x8 .
co
(
cv
x6
)
(
cv
x4
)
(
co
(
cv
x1
)
(
cv
x2
)
cnat
)
)
(
λ x7 x8 .
co
(
cv
x5
)
(
cv
x6
)
(
co
(
cv
x1
)
(
cv
x2
)
cnat
)
)
(
λ x7 x8 .
cmpt
(
λ x9 .
cfv
(
cv
x1
)
cbs
)
(
λ x9 .
co
(
cfv
(
cv
x9
)
(
cv
x7
)
)
(
cfv
(
cv
x9
)
(
cv
x8
)
)
(
co
(
cop
(
cfv
(
cv
x9
)
(
cfv
(
cv
x5
)
c1st
)
)
(
cfv
(
cv
x9
)
(
cfv
(
cv
x6
)
c1st
)
)
)
(
cfv
(
cv
x9
)
(
cfv
(
cv
x4
)
c1st
)
)
(
cfv
(
cv
x2
)
cco
)
)
)
)
)
)
)
)
)
)
)
⟶
wceq
cinito
(
cmpt
(
λ x1 .
ccat
)
(
λ x1 .
crab
(
λ x2 .
wral
(
λ x3 .
weu
(
λ x4 .
wcel
(
cv
x4
)
(
co
(
cv
x2
)
(
cv
x3
)
(
cfv
(
cv
x1
)
chom
)
)
)
)
(
λ x3 .
cfv
(
cv
x1
)
cbs
)
)
(
λ x2 .
cfv
(
cv
x1
)
cbs
)
)
)
⟶
wceq
ctermo
(
cmpt
(
λ x1 .
ccat
)
(
λ x1 .
crab
(
λ x2 .
wral
(
λ x3 .
weu
(
λ x4 .
wcel
(
cv
x4
)
(
co
(
cv
x3
)
(
cv
x2
)
(
cfv
(
cv
x1
)
chom
)
)
)
)
(
λ x3 .
cfv
(
cv
x1
)
cbs
)
)
(
λ x2 .
cfv
(
cv
x1
)
cbs
)
)
)
⟶
wceq
czeroo
(
cmpt
(
λ x1 .
ccat
)
(
λ x1 .
cin
(
cfv
(
cv
x1
)
cinito
)
(
cfv
(
cv
x1
)
ctermo
)
)
)
⟶
wceq
cdoma
(
ccom
c1st
c1st
)
⟶
x0
)
⟶
x0
as obj
-
as prop
43c2a..
theory
SetMM
stx
ebbdd..
address
TMGkY..