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Proofgold Term Root Disambiguation
∀ x0 : ο .
(
wceq
cmndo
(
cin
csem
cexid
)
⟶
wceq
cghomOLD
(
cmpt2
(
λ x1 x2 .
cgr
)
(
λ x1 x2 .
cgr
)
(
λ x1 x2 .
cab
(
λ x3 .
wa
(
wf
(
crn
(
cv
x1
)
)
(
crn
(
cv
x2
)
)
(
cv
x3
)
)
(
wral
(
λ x4 .
wral
(
λ x5 .
wceq
(
co
(
cfv
(
cv
x4
)
(
cv
x3
)
)
(
cfv
(
cv
x5
)
(
cv
x3
)
)
(
cv
x2
)
)
(
cfv
(
co
(
cv
x4
)
(
cv
x5
)
(
cv
x1
)
)
(
cv
x3
)
)
)
(
λ x5 .
crn
(
cv
x1
)
)
)
(
λ x4 .
crn
(
cv
x1
)
)
)
)
)
)
⟶
wceq
crngo
(
copab
(
λ x1 x2 .
wa
(
wa
(
wcel
(
cv
x1
)
cablo
)
(
wf
(
cxp
(
crn
(
cv
x1
)
)
(
crn
(
cv
x1
)
)
)
(
crn
(
cv
x1
)
)
(
cv
x2
)
)
)
(
wa
(
wral
(
λ x3 .
wral
(
λ x4 .
wral
(
λ x5 .
w3a
(
wceq
(
co
(
co
(
cv
x3
)
(
cv
x4
)
(
cv
x2
)
)
(
cv
x5
)
(
cv
x2
)
)
(
co
(
cv
x3
)
(
co
(
cv
x4
)
(
cv
x5
)
(
cv
x2
)
)
(
cv
x2
)
)
)
(
wceq
(
co
(
cv
x3
)
(
co
(
cv
x4
)
(
cv
x5
)
(
cv
x1
)
)
(
cv
x2
)
)
(
co
(
co
(
cv
x3
)
(
cv
x4
)
(
cv
x2
)
)
(
co
(
cv
x3
)
(
cv
x5
)
(
cv
x2
)
)
(
cv
x1
)
)
)
(
wceq
(
co
(
co
(
cv
x3
)
(
cv
x4
)
(
cv
x1
)
)
(
cv
x5
)
(
cv
x2
)
)
(
co
(
co
(
cv
x3
)
(
cv
x5
)
(
cv
x2
)
)
(
co
(
cv
x4
)
(
cv
x5
)
(
cv
x2
)
)
(
cv
x1
)
)
)
)
(
λ x5 .
crn
(
cv
x1
)
)
)
(
λ x4 .
crn
(
cv
x1
)
)
)
(
λ x3 .
crn
(
cv
x1
)
)
)
(
wrex
(
λ x3 .
wral
(
λ x4 .
wa
(
wceq
(
co
(
cv
x3
)
(
cv
x4
)
(
cv
x2
)
)
(
cv
x4
)
)
(
wceq
(
co
(
cv
x4
)
(
cv
x3
)
(
cv
x2
)
)
(
cv
x4
)
)
)
(
λ x4 .
crn
(
cv
x1
)
)
)
(
λ x3 .
crn
(
cv
x1
)
)
)
)
)
)
⟶
wceq
cdrng
(
copab
(
λ x1 x2 .
wa
(
wcel
(
cop
(
cv
x1
)
(
cv
x2
)
)
crngo
)
(
wcel
(
cres
(
cv
x2
)
(
cxp
(
cdif
(
crn
(
cv
x1
)
)
(
csn
(
cfv
(
cv
x1
)
cgi
)
)
)
(
cdif
(
crn
(
cv
x1
)
)
(
csn
(
cfv
(
cv
x1
)
cgi
)
)
)
)
)
cgr
)
)
)
⟶
wceq
crnghom
(
cmpt2
(
λ x1 x2 .
crngo
)
(
λ x1 x2 .
crngo
)
(
λ x1 x2 .
crab
(
λ x3 .
wa
(
wceq
(
cfv
(
cfv
(
cfv
(
cv
x1
)
c2nd
)
cgi
)
(
cv
x3
)
)
(
cfv
(
cfv
(
cv
x2
)
c2nd
)
cgi
)
)
(
wral
(
λ x4 .
wral
(
λ x5 .
wa
(
wceq
(
cfv
(
co
(
cv
x4
)
(
cv
x5
)
(
cfv
(
cv
x1
)
c1st
)
)
(
cv
x3
)
)
(
co
(
cfv
(
cv
x4
)
(
cv
x3
)
)
(
cfv
(
cv
x5
)
(
cv
x3
)
)
(
cfv
(
cv
x2
)
c1st
)
)
)
(
wceq
(
cfv
(
co
(
cv
x4
)
(
cv
x5
)
(
cfv
(
cv
x1
)
c2nd
)
)
(
cv
x3
)
)
(
co
(
cfv
(
cv
x4
)
(
cv
x3
)
)
(
cfv
(
cv
x5
)
(
cv
x3
)
)
(
cfv
(
cv
x2
)
c2nd
)
)
)
)
(
λ x5 .
crn
(
cfv
(
cv
x1
)
c1st
)
)
)
(
λ x4 .
crn
(
cfv
(
cv
x1
)
c1st
)
)
)
)
(
λ x3 .
co
(
crn
(
cfv
(
cv
x2
)
c1st
)
)
(
crn
(
cfv
(
cv
x1
)
c1st
)
)
cmap
)
)
)
⟶
wceq
crngiso
(
cmpt2
(
λ x1 x2 .
crngo
)
(
λ x1 x2 .
crngo
)
(
λ x1 x2 .
crab
(
λ x3 .
wf1o
(
crn
(
cfv
(
cv
x1
)
c1st
)
)
(
crn
(
cfv
(
cv
x2
)
c1st
)
)
(
cv
x3
)
)
(
λ x3 .
co
(
cv
x1
)
(
cv
x2
)
crnghom
)
)
)
⟶
wceq
crisc
(
copab
(
λ x1 x2 .
wa
(
wa
(
wcel
(
cv
x1
)
crngo
)
(
wcel
(
cv
x2
)
crngo
)
)
(
wex
(
λ x3 .
wcel
(
cv
x3
)
(
co
(
cv
x1
)
(
cv
x2
)
crngiso
)
)
)
)
)
⟶
wceq
ccm2
(
copab
(
λ x1 x2 .
wral
(
λ x3 .
wral
(
λ x4 .
wceq
(
co
(
cv
x3
)
(
cv
x4
)
(
cv
x2
)
)
(
co
(
cv
x4
)
(
cv
x3
)
(
cv
x2
)
)
)
(
λ x4 .
crn
(
cv
x1
)
)
)
(
λ x3 .
crn
(
cv
x1
)
)
)
)
⟶
wceq
cfld
(
cin
cdrng
ccm2
)
⟶
wceq
ccring
(
cin
crngo
ccm2
)
⟶
wceq
cidl
(
cmpt
(
λ x1 .
crngo
)
(
λ x1 .
crab
(
λ x2 .
wa
(
wcel
(
cfv
(
cfv
(
cv
x1
)
c1st
)
cgi
)
(
cv
x2
)
)
(
wral
(
λ x3 .
wa
(
wral
(
λ x4 .
wcel
(
co
(
cv
x3
)
(
cv
x4
)
(
cfv
(
cv
x1
)
c1st
)
)
(
cv
x2
)
)
(
λ x4 .
cv
x2
)
)
(
wral
(
λ x4 .
wa
(
wcel
(
co
(
cv
x4
)
(
cv
x3
)
(
cfv
(
cv
x1
)
c2nd
)
)
(
cv
x2
)
)
(
wcel
(
co
(
cv
x3
)
(
cv
x4
)
(
cfv
(
cv
x1
)
c2nd
)
)
(
cv
x2
)
)
)
(
λ x4 .
crn
(
cfv
(
cv
x1
)
c1st
)
)
)
)
(
λ x3 .
cv
x2
)
)
)
(
λ x2 .
cpw
(
crn
(
cfv
(
cv
x1
)
c1st
)
)
)
)
)
⟶
wceq
cpridl
(
cmpt
(
λ x1 .
crngo
)
(
λ x1 .
crab
(
λ x2 .
wa
(
wne
(
cv
x2
)
(
crn
(
cfv
(
cv
x1
)
c1st
)
)
)
(
wral
(
λ x3 .
wral
(
λ x4 .
wral
(
λ x5 .
wral
(
λ x6 .
wcel
(
co
(
cv
x5
)
(
cv
x6
)
(
cfv
(
cv
x1
)
c2nd
)
)
(
cv
x2
)
)
(
λ x6 .
cv
x4
)
)
(
λ x5 .
cv
x3
)
⟶
wo
(
wss
(
cv
x3
)
(
cv
x2
)
)
(
wss
(
cv
x4
)
(
cv
x2
)
)
)
(
λ x4 .
cfv
(
cv
x1
)
cidl
)
)
(
λ x3 .
cfv
(
cv
x1
)
cidl
)
)
)
(
λ x2 .
cfv
(
cv
x1
)
cidl
)
)
)
⟶
wceq
cmaxidl
(
cmpt
(
λ x1 .
crngo
)
(
λ x1 .
crab
(
λ x2 .
wa
(
wne
(
cv
x2
)
(
crn
(
cfv
(
cv
x1
)
c1st
)
)
)
(
wral
(
λ x3 .
wss
(
cv
x2
)
(
cv
x3
)
⟶
wo
(
wceq
(
cv
x3
)
(
cv
x2
)
)
(
wceq
(
cv
x3
)
(
crn
(
cfv
(
cv
x1
)
c1st
)
)
)
)
(
λ x3 .
cfv
(
cv
x1
)
cidl
)
)
)
(
λ x2 .
cfv
(
cv
x1
)
cidl
)
)
)
⟶
wceq
cprrng
(
crab
(
λ x1 .
wcel
(
csn
(
cfv
(
cfv
(
cv
x1
)
c1st
)
cgi
)
)
(
cfv
(
cv
x1
)
cpridl
)
)
(
λ x1 .
crngo
)
)
⟶
wceq
cdmn
(
cin
cprrng
ccm2
)
⟶
wceq
cigen
(
cmpt2
(
λ x1 x2 .
crngo
)
(
λ x1 x2 .
cpw
(
crn
(
cfv
(
cv
x1
)
c1st
)
)
)
(
λ x1 x2 .
cint
(
crab
(
λ x3 .
wss
(
cv
x2
)
(
cv
x3
)
)
(
λ x3 .
cfv
(
cv
x1
)
cidl
)
)
)
)
⟶
(
∀ x1 x2 :
ι → ο
.
wceq
(
cxrn
x1
x2
)
(
cin
(
ccom
(
ccnv
(
cres
c1st
(
cxp
cvv
cvv
)
)
)
x1
)
(
ccom
(
ccnv
(
cres
c2nd
(
cxp
cvv
cvv
)
)
)
x2
)
)
)
⟶
(
∀ x1 :
ι → ο
.
wceq
(
ccoss
x1
)
(
copab
(
λ x2 x3 .
wex
(
λ x4 .
wa
(
wbr
(
cv
x4
)
(
cv
x2
)
x1
)
(
wbr
(
cv
x4
)
(
cv
x3
)
x1
)
)
)
)
)
⟶
x0
)
⟶
x0
as obj
-
as prop
cc009..
theory
SetMM
stx
ebbdd..
address
TMMoV..