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Proofgold Term Root Disambiguation
∀ x0 : ο .
(
wceq
chash
(
cun
(
ccom
(
cres
(
crdg
(
cmpt
(
λ x1 .
cvv
)
(
λ x1 .
co
(
cv
x1
)
c1
caddc
)
)
cc0
)
com
)
ccrd
)
(
cxp
(
cdif
cvv
cfn
)
(
csn
cpnf
)
)
)
⟶
(
∀ x1 :
ι → ο
.
wceq
(
cword
x1
)
(
cab
(
λ x2 .
wrex
(
λ x3 .
wf
(
co
cc0
(
cv
x3
)
cfzo
)
x1
(
cv
x2
)
)
(
λ x3 .
cn0
)
)
)
)
⟶
wceq
clsw
(
cmpt
(
λ x1 .
cvv
)
(
λ x1 .
cfv
(
co
(
cfv
(
cv
x1
)
chash
)
c1
cmin
)
(
cv
x1
)
)
)
⟶
wceq
cconcat
(
cmpt2
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
cmpt
(
λ x3 .
co
cc0
(
co
(
cfv
(
cv
x1
)
chash
)
(
cfv
(
cv
x2
)
chash
)
caddc
)
cfzo
)
(
λ x3 .
cif
(
wcel
(
cv
x3
)
(
co
cc0
(
cfv
(
cv
x1
)
chash
)
cfzo
)
)
(
cfv
(
cv
x3
)
(
cv
x1
)
)
(
cfv
(
co
(
cv
x3
)
(
cfv
(
cv
x1
)
chash
)
cmin
)
(
cv
x2
)
)
)
)
)
⟶
(
∀ x1 :
ι → ο
.
wceq
(
cs1
x1
)
(
csn
(
cop
cc0
(
cfv
x1
cid
)
)
)
)
⟶
wceq
csubstr
(
cmpt2
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
cxp
cz
cz
)
(
λ x1 x2 .
cif
(
wss
(
co
(
cfv
(
cv
x2
)
c1st
)
(
cfv
(
cv
x2
)
c2nd
)
cfzo
)
(
cdm
(
cv
x1
)
)
)
(
cmpt
(
λ x3 .
co
cc0
(
co
(
cfv
(
cv
x2
)
c2nd
)
(
cfv
(
cv
x2
)
c1st
)
cmin
)
cfzo
)
(
λ x3 .
cfv
(
co
(
cv
x3
)
(
cfv
(
cv
x2
)
c1st
)
caddc
)
(
cv
x1
)
)
)
c0
)
)
⟶
wceq
csplice
(
cmpt2
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
co
(
co
(
co
(
cv
x1
)
(
cop
cc0
(
cfv
(
cfv
(
cv
x2
)
c1st
)
c1st
)
)
csubstr
)
(
cfv
(
cv
x2
)
c2nd
)
cconcat
)
(
co
(
cv
x1
)
(
cop
(
cfv
(
cfv
(
cv
x2
)
c1st
)
c2nd
)
(
cfv
(
cv
x1
)
chash
)
)
csubstr
)
cconcat
)
)
⟶
wceq
creverse
(
cmpt
(
λ x1 .
cvv
)
(
λ x1 .
cmpt
(
λ x2 .
co
cc0
(
cfv
(
cv
x1
)
chash
)
cfzo
)
(
λ x2 .
cfv
(
co
(
co
(
cfv
(
cv
x1
)
chash
)
c1
cmin
)
(
cv
x2
)
cmin
)
(
cv
x1
)
)
)
)
⟶
wceq
creps
(
cmpt2
(
λ x1 x2 .
cvv
)
(
λ x1 x2 .
cn0
)
(
λ x1 x2 .
cmpt
(
λ x3 .
co
cc0
(
cv
x2
)
cfzo
)
(
λ x3 .
cv
x1
)
)
)
⟶
wceq
ccsh
(
cmpt2
(
λ x1 x2 .
cab
(
λ x3 .
wrex
(
λ x4 .
wfn
(
cv
x3
)
(
co
cc0
(
cv
x4
)
cfzo
)
)
(
λ x4 .
cn0
)
)
)
(
λ x1 x2 .
cz
)
(
λ x1 x2 .
cif
(
wceq
(
cv
x1
)
c0
)
c0
(
co
(
co
(
cv
x1
)
(
cop
(
co
(
cv
x2
)
(
cfv
(
cv
x1
)
chash
)
cmo
)
(
cfv
(
cv
x1
)
chash
)
)
csubstr
)
(
co
(
cv
x1
)
(
cop
cc0
(
co
(
cv
x2
)
(
cfv
(
cv
x1
)
chash
)
cmo
)
)
csubstr
)
cconcat
)
)
)
⟶
(
∀ x1 x2 :
ι → ο
.
wceq
(
cs2
x1
x2
)
(
co
(
cs1
x1
)
(
cs1
x2
)
cconcat
)
)
⟶
(
∀ x1 x2 x3 :
ι → ο
.
wceq
(
cs3
x1
x2
x3
)
(
co
(
cs2
x1
x2
)
(
cs1
x3
)
cconcat
)
)
⟶
(
∀ x1 x2 x3 x4 :
ι → ο
.
wceq
(
cs4
x1
x2
x3
x4
)
(
co
(
cs3
x1
x2
x3
)
(
cs1
x4
)
cconcat
)
)
⟶
(
∀ x1 x2 x3 x4 x5 :
ι → ο
.
wceq
(
cs5
x1
x2
x3
x4
x5
)
(
co
(
cs4
x1
x2
x3
x4
)
(
cs1
x5
)
cconcat
)
)
⟶
(
∀ x1 x2 x3 x4 x5 x6 :
ι → ο
.
wceq
(
cs6
x1
x2
x3
x4
x5
x6
)
(
co
(
cs5
x1
x2
x3
x4
x5
)
(
cs1
x6
)
cconcat
)
)
⟶
(
∀ x1 x2 x3 x4 x5 x6 x7 :
ι → ο
.
wceq
(
cs7
x1
x2
x3
x4
x5
x6
x7
)
(
co
(
cs6
x1
x2
x3
x4
x5
x6
)
(
cs1
x7
)
cconcat
)
)
⟶
(
∀ x1 x2 x3 x4 x5 x6 x7 x8 :
ι → ο
.
wceq
(
cs8
x1
x2
x3
x4
x5
x6
x7
x8
)
(
co
(
cs7
x1
x2
x3
x4
x5
x6
x7
)
(
cs1
x8
)
cconcat
)
)
⟶
wceq
ctcl
(
cmpt
(
λ x1 .
cvv
)
(
λ x1 .
cint
(
cab
(
λ x2 .
wa
(
wss
(
cv
x1
)
(
cv
x2
)
)
(
wss
(
ccom
(
cv
x2
)
(
cv
x2
)
)
(
cv
x2
)
)
)
)
)
)
⟶
x0
)
⟶
x0
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