:: GFACIRC1 semantic presentation
REAL
is
set
NAT
is non
empty
V9
()
V10
()
V11
()
V36
()
V51
()
V52
()
Element
of
K18
(
REAL
)
K18
(
REAL
) is
set
COMPLEX
is
set
RAT
is
set
INT
is
set
K19
(
COMPLEX
,
COMPLEX
) is
Relation-like
set
K18
(
K19
(
COMPLEX
,
COMPLEX
)) is
set
K19
(
K19
(
COMPLEX
,
COMPLEX
),
COMPLEX
) is
Relation-like
set
K18
(
K19
(
K19
(
COMPLEX
,
COMPLEX
),
COMPLEX
)) is
set
K19
(
REAL
,
REAL
) is
Relation-like
set
K18
(
K19
(
REAL
,
REAL
)) is
set
K19
(
K19
(
REAL
,
REAL
),
REAL
) is
Relation-like
set
K18
(
K19
(
K19
(
REAL
,
REAL
),
REAL
)) is
set
K19
(
RAT
,
RAT
) is
Relation-like
set
K18
(
K19
(
RAT
,
RAT
)) is
set
K19
(
K19
(
RAT
,
RAT
),
RAT
) is
Relation-like
set
K18
(
K19
(
K19
(
RAT
,
RAT
),
RAT
)) is
set
K19
(
INT
,
INT
) is
Relation-like
set
K18
(
K19
(
INT
,
INT
)) is
set
K19
(
K19
(
INT
,
INT
),
INT
) is
Relation-like
set
K18
(
K19
(
K19
(
INT
,
INT
),
INT
)) is
set
K19
(
NAT
,
NAT
) is
Relation-like
set
K19
(
K19
(
NAT
,
NAT
),
NAT
) is
Relation-like
set
K18
(
K19
(
K19
(
NAT
,
NAT
),
NAT
)) is
set
NAT
is non
empty
V9
()
V10
()
V11
()
V36
()
V51
()
V52
()
set
K18
(
NAT
) is
set
K18
(
NAT
) is
set
BOOLEAN
is non
empty
set
1 is non
empty
V9
()
V10
()
V11
()
V15
() non
pair
V119
()
Element
of
NAT
{}
is
set
the
empty
Relation-like
non-empty
empty-yielding
NAT
-defined
V9
()
V10
()
V11
()
V13
()
V14
()
V15
()
Function-like
one-to-one
constant
functional
non
pair
V36
()
FinSequence-like
FinSubsequence-like
FinSequence-membered
V48
()
V49
()
V51
() non
with_pair
set
is
empty
Relation-like
non-empty
empty-yielding
NAT
-defined
V9
()
V10
()
V11
()
V13
()
V14
()
V15
()
Function-like
one-to-one
constant
functional
non
pair
V36
()
FinSequence-like
FinSubsequence-like
FinSequence-membered
V48
()
V49
()
V51
() non
with_pair
set
{
{}
,1
}
is
set
K348
() is
set
K18
(
K348
()) is
set
K349
() is
Element
of
K18
(
K348
())
K389
() is non
empty
V95
()
L10
()
the
carrier
of
K389
() is non
empty
set
K352
( the
carrier
of
K389
()) is non
empty
M24
( the
carrier
of
K389
())
K388
(
K389
()) is
Element
of
K18
(
K352
( the
carrier
of
K389
()))
K18
(
K352
( the
carrier
of
K389
())) is
set
K19
(
K388
(
K389
()),
NAT
) is
Relation-like
set
K18
(
K19
(
K388
(
K389
()),
NAT
)) is
set
K19
(
NAT
,
K388
(
K389
())) is
Relation-like
set
K18
(
K19
(
NAT
,
K388
(
K389
()))) is
set
2 is non
empty
V9
()
V10
()
V11
()
V15
() non
pair
V119
()
Element
of
NAT
2
-tuples_on
BOOLEAN
is non
empty
functional
FinSequence-membered
FinSequenceSet
of
BOOLEAN
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
) is
Relation-like
set
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
)) is
set
3 is non
empty
V9
()
V10
()
V11
()
V15
() non
pair
V119
()
Element
of
NAT
3
-tuples_on
BOOLEAN
is non
empty
functional
FinSequence-membered
FinSequenceSet
of
BOOLEAN
K19
(
(
3
-tuples_on
BOOLEAN
)
,
BOOLEAN
) is
Relation-like
set
K18
(
K19
(
(
3
-tuples_on
BOOLEAN
)
,
BOOLEAN
)) is
set
'xor'
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
0
is
V9
()
V10
()
V11
()
V15
() non
pair
Element
of
NAT
Seg
1 is non
empty
V36
()
V43
(1)
V51
()
Element
of
K18
(
NAT
)
TRUE
is
boolean
Element
of
BOOLEAN
and2
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
and2a
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
and2b
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
nand2
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
or2
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
nor2a
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
xor2
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
xor2a
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
xor2b
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
nor3
is
Relation-like
Function-like
V27
(3
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
3
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
or3
is
Relation-like
Function-like
V27
(3
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
3
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
or3a
is
Relation-like
Function-like
V27
(3
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
3
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
or3b
is
Relation-like
Function-like
V27
(3
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
3
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
or3c
is
Relation-like
Function-like
V27
(3
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
3
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
K217
() is
set
1
-tuples_on
BOOLEAN
is non
empty
functional
FinSequence-membered
FinSequenceSet
of
BOOLEAN
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
) is
Relation-like
set
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
)) is
set
f1
is
Relation-like
Function-like
V27
(1
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f3
is
boolean
Element
of
BOOLEAN
<*
f3
*>
is non
empty
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
FinSequence
of
BOOLEAN
f2
is
Relation-like
Function-like
V27
(1
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f2
.
<*
f3
*>
is
boolean
set
f0
is
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
Element
of 1
-tuples_on
BOOLEAN
f0
.
1 is
set
F
1
(
(
f0
.
1
)
) is
boolean
Element
of
BOOLEAN
F
1
(
f3
) is
boolean
Element
of
BOOLEAN
1
-tuples_on
BOOLEAN
is non
empty
functional
FinSequence-membered
FinSequenceSet
of
BOOLEAN
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
) is
Relation-like
set
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
)) is
set
f1
is
Relation-like
Function-like
V27
(1
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f2
is
Relation-like
Function-like
V27
(1
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f3
is
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
Element
of 1
-tuples_on
BOOLEAN
f0
is
boolean
Element
of
BOOLEAN
<*
f0
*>
is non
empty
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
FinSequence
of
BOOLEAN
f1
.
f3
is
boolean
Element
of
BOOLEAN
F
1
(
f0
) is
boolean
Element
of
BOOLEAN
f2
.
f3
is
boolean
Element
of
BOOLEAN
1
-tuples_on
BOOLEAN
is non
empty
functional
FinSequence-membered
FinSequenceSet
of
BOOLEAN
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
) is
Relation-like
set
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
)) is
set
f1
is
Relation-like
Function-like
V27
(1
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f3
is
boolean
Element
of
BOOLEAN
<*
f3
*>
is non
empty
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
FinSequence
of
BOOLEAN
f2
is
Relation-like
Function-like
V27
(1
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f2
.
<*
f3
*>
is
boolean
set
f0
is
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
Element
of 1
-tuples_on
BOOLEAN
f0
.
1 is
set
F
1
(
(
f0
.
1
)
) is
boolean
Element
of
BOOLEAN
F
1
(
f3
) is
boolean
Element
of
BOOLEAN
f2
is
Relation-like
Function-like
V27
(1
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f3
is
Relation-like
Function-like
V27
(1
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f0
is
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
Element
of 1
-tuples_on
BOOLEAN
x
is
boolean
Element
of
BOOLEAN
<*
x
*>
is non
empty
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
FinSequence
of
BOOLEAN
f2
.
f0
is
boolean
Element
of
BOOLEAN
F
1
(
x
) is
boolean
Element
of
BOOLEAN
f3
.
f0
is
boolean
Element
of
BOOLEAN
1
-tuples_on
BOOLEAN
is non
empty
functional
FinSequence-membered
FinSequenceSet
of
BOOLEAN
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
) is
Relation-like
set
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
)) is
set
() is
Relation-like
Function-like
V27
(1
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
<*
0
*>
is non
empty
Relation-like
NAT
-defined
NAT
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
FinSequence
of
NAT
()
.
<*
0
*>
is
boolean
set
<*
1
*>
is non
empty
Relation-like
NAT
-defined
NAT
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
FinSequence
of
NAT
()
.
<*
1
*>
is
boolean
set
f1
is
boolean
Element
of
BOOLEAN
<*
f1
*>
is non
empty
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
FinSequence
of
BOOLEAN
()
.
<*
f1
*>
is
boolean
set
'not'
f1
is
boolean
Element
of
BOOLEAN
K114
(1,
f1
) is
set
<*
f1
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
nand2
.
<*
f1
,
f1
*>
is
boolean
set
f1
'&'
f1
is
boolean
Element
of
BOOLEAN
K111
(
f1
,
f1
) is
set
'not'
(
f1
'&'
f1
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
f1
'&'
f1
)
) is
set
FALSE
is
boolean
Element
of
BOOLEAN
'not'
FALSE
is
boolean
Element
of
BOOLEAN
K114
(1,
FALSE
) is
set
'not'
TRUE
is
boolean
Element
of
BOOLEAN
K114
(1,
TRUE
) is
set
() is
Relation-like
Function-like
V27
(1
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
1
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
()
.
<*
0
*>
is
boolean
set
()
.
<*
1
*>
is
boolean
set
f1
is
boolean
Element
of
BOOLEAN
<*
f1
*>
is non
empty
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
FinSequence
of
BOOLEAN
()
.
<*
f1
*>
is
boolean
set
<*
f1
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2
.
<*
f1
,
f1
*>
is
boolean
set
f1
'&'
f1
is
boolean
Element
of
BOOLEAN
K111
(
f1
,
f1
) is
set
FALSE
is
boolean
Element
of
BOOLEAN
() is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
<*
0
,
0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
()
.
<*
0
,
0
*>
is
boolean
set
<*
0
,1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
()
.
<*
0
,1
*>
is
boolean
set
<*
1,
0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
()
.
<*
1,
0
*>
is
boolean
set
<*
1,1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
()
.
<*
1,1
*>
is
boolean
set
f1
is
boolean
Element
of
BOOLEAN
f2
is
boolean
Element
of
BOOLEAN
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
f1
,
f2
*>
is
boolean
set
'not'
f2
is
boolean
Element
of
BOOLEAN
K114
(1,
f2
) is
set
f1
'&'
(
'not'
f2
)
is
boolean
Element
of
BOOLEAN
K111
(
f1
,
(
'not'
f2
)
) is
set
<*
f2
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2a
.
<*
f2
,
f1
*>
is
boolean
set
nor2a
.
<*
f1
,
f2
*>
is
boolean
set
'not'
f1
is
boolean
Element
of
BOOLEAN
K114
(1,
f1
) is
set
'not'
(
'not'
f2
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
'not'
f2
)
) is
set
(
'not'
f1
)
'or'
(
'not'
(
'not'
f2
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
'not'
f1
)
is
boolean
set
K114
(1,
(
'not'
f1
)
) is
set
'not'
(
'not'
(
'not'
f2
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f2
)
)
) is
set
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
(
'not'
(
'not'
f2
)
)
)
is
set
K111
(
(
'not'
(
'not'
f1
)
)
,
(
'not'
(
'not'
(
'not'
f2
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
(
'not'
(
'not'
f2
)
)
)
)
is
boolean
set
'not'
(
(
'not'
f1
)
'or'
(
'not'
(
'not'
f2
)
)
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
'not'
f1
)
'or'
(
'not'
(
'not'
f2
)
)
)
) is
set
FALSE
is
boolean
Element
of
BOOLEAN
'not'
FALSE
is
boolean
Element
of
BOOLEAN
K114
(1,
FALSE
) is
set
FALSE
'&'
(
'not'
FALSE
)
is
boolean
Element
of
BOOLEAN
K111
(
FALSE
,
(
'not'
FALSE
)
) is
set
'not'
TRUE
is
boolean
Element
of
BOOLEAN
K114
(1,
TRUE
) is
set
FALSE
'&'
(
'not'
TRUE
)
is
boolean
Element
of
BOOLEAN
K111
(
FALSE
,
(
'not'
TRUE
)
) is
set
TRUE
'&'
(
'not'
FALSE
)
is
boolean
Element
of
BOOLEAN
K111
(
TRUE
,
(
'not'
FALSE
)
) is
set
TRUE
'&'
(
'not'
TRUE
)
is
boolean
Element
of
BOOLEAN
K111
(
TRUE
,
(
'not'
TRUE
)
) is
set
() is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
()
.
<*
0
,
0
*>
is
boolean
set
()
.
<*
0
,1
*>
is
boolean
set
()
.
<*
1,
0
*>
is
boolean
set
()
.
<*
1,1
*>
is
boolean
set
f1
is
boolean
Element
of
BOOLEAN
f2
is
boolean
Element
of
BOOLEAN
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
f1
,
f2
*>
is
boolean
set
'not'
f2
is
boolean
Element
of
BOOLEAN
K114
(1,
f2
) is
set
f1
'xor'
(
'not'
f2
)
is
boolean
Element
of
BOOLEAN
K222
(
f1
,
(
'not'
f2
)
) is
set
K221
(
f1
,
(
'not'
f2
)
) is
set
'not'
f1
is
boolean
set
K114
(1,
f1
) is
set
K220
(
(
'not'
f1
)
,
(
'not'
f2
)
) is
set
'not'
(
'not'
f1
)
is
boolean
set
K114
(1,
(
'not'
f1
)
) is
set
'not'
(
'not'
f2
)
is
boolean
set
K114
(1,
(
'not'
f2
)
) is
set
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
(
'not'
f2
)
)
is
set
K111
(
(
'not'
(
'not'
f1
)
)
,
(
'not'
(
'not'
f2
)
)
) is
set
'not'
(
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
(
'not'
f2
)
)
)
is
boolean
set
K221
(
(
'not'
f2
)
,
f1
) is
set
K220
(
(
'not'
(
'not'
f2
)
)
,
f1
) is
set
'not'
(
'not'
(
'not'
f2
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f2
)
)
) is
set
(
'not'
(
'not'
(
'not'
f2
)
)
)
'&'
(
'not'
f1
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f2
)
)
)
,
(
'not'
f1
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f2
)
)
)
'&'
(
'not'
f1
)
)
is
boolean
set
K221
(
f1
,
(
'not'
f2
)
)
'&'
K221
(
(
'not'
f2
)
,
f1
) is
set
'not'
K222
(
f1
,
(
'not'
f2
)
) is
boolean
set
xor2a
.
<*
f1
,
f2
*>
is
boolean
set
and2b
.
<*
f1
,
f2
*>
is
boolean
set
and2
.
<*
f1
,
f2
*>
is
boolean
set
<*
(
and2b
.
<*
f1
,
f2
*>
)
,
(
and2
.
<*
f1
,
f2
*>
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
or2
.
<*
(
and2b
.
<*
f1
,
f2
*>
)
,
(
and2
.
<*
f1
,
f2
*>
)
*>
is
boolean
set
'not'
f1
is
boolean
Element
of
BOOLEAN
(
'not'
f1
)
'xor'
f2
is
boolean
Element
of
BOOLEAN
K222
(
(
'not'
f1
)
,
f2
) is
set
K221
(
(
'not'
f1
)
,
f2
) is
set
'not'
(
'not'
f1
)
is
boolean
set
K114
(1,
(
'not'
f1
)
) is
set
K220
(
(
'not'
(
'not'
f1
)
)
,
f2
) is
set
'not'
(
'not'
(
'not'
f1
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f1
)
)
) is
set
'not'
f2
is
boolean
set
(
'not'
(
'not'
(
'not'
f1
)
)
)
'&'
(
'not'
f2
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f1
)
)
)
,
(
'not'
f2
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f1
)
)
)
'&'
(
'not'
f2
)
)
is
boolean
set
K221
(
f2
,
(
'not'
f1
)
) is
set
K220
(
(
'not'
f2
)
,
(
'not'
f1
)
) is
set
'not'
(
'not'
f2
)
is
boolean
set
K114
(1,
(
'not'
f2
)
) is
set
(
'not'
(
'not'
f2
)
)
'&'
(
'not'
(
'not'
f1
)
)
is
set
K111
(
(
'not'
(
'not'
f2
)
)
,
(
'not'
(
'not'
f1
)
)
) is
set
'not'
(
(
'not'
(
'not'
f2
)
)
'&'
(
'not'
(
'not'
f1
)
)
)
is
boolean
set
K221
(
(
'not'
f1
)
,
f2
)
'&'
K221
(
f2
,
(
'not'
f1
)
) is
set
'not'
K222
(
(
'not'
f1
)
,
f2
) is
boolean
set
(
'not'
f1
)
'&'
(
'not'
f2
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
f1
)
,
(
'not'
f2
)
) is
set
'not'
(
'not'
f2
)
is
boolean
Element
of
BOOLEAN
f1
'&'
(
'not'
(
'not'
f2
)
)
is
boolean
Element
of
BOOLEAN
K111
(
f1
,
(
'not'
(
'not'
f2
)
)
) is
set
(
(
'not'
f1
)
'&'
(
'not'
f2
)
)
'or'
(
f1
'&'
(
'not'
(
'not'
f2
)
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
'not'
f1
)
'&'
(
'not'
f2
)
)
is
boolean
set
K114
(1,
(
(
'not'
f1
)
'&'
(
'not'
f2
)
)
) is
set
'not'
(
f1
'&'
(
'not'
(
'not'
f2
)
)
)
is
boolean
set
K114
(1,
(
f1
'&'
(
'not'
(
'not'
f2
)
)
)
) is
set
(
'not'
(
(
'not'
f1
)
'&'
(
'not'
f2
)
)
)
'&'
(
'not'
(
f1
'&'
(
'not'
(
'not'
f2
)
)
)
)
is
set
K111
(
(
'not'
(
(
'not'
f1
)
'&'
(
'not'
f2
)
)
)
,
(
'not'
(
f1
'&'
(
'not'
(
'not'
f2
)
)
)
)
) is
set
'not'
(
(
'not'
(
(
'not'
f1
)
'&'
(
'not'
f2
)
)
)
'&'
(
'not'
(
f1
'&'
(
'not'
(
'not'
f2
)
)
)
)
)
is
boolean
set
f1
'&'
f2
is
boolean
Element
of
BOOLEAN
K111
(
f1
,
f2
) is
set
<*
(
(
'not'
f1
)
'&'
(
'not'
f2
)
)
,
(
f1
'&'
f2
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
or2
.
<*
(
(
'not'
f1
)
'&'
(
'not'
f2
)
)
,
(
f1
'&'
f2
)
*>
is
boolean
set
<*
(
and2b
.
<*
f1
,
f2
*>
)
,
(
f1
'&'
f2
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
or2
.
<*
(
and2b
.
<*
f1
,
f2
*>
)
,
(
f1
'&'
f2
)
*>
is
boolean
set
FALSE
is
boolean
Element
of
BOOLEAN
'not'
FALSE
is
boolean
Element
of
BOOLEAN
K114
(1,
FALSE
) is
set
FALSE
'xor'
(
'not'
FALSE
)
is
boolean
Element
of
BOOLEAN
K222
(
FALSE
,
(
'not'
FALSE
)
) is
set
K221
(
FALSE
,
(
'not'
FALSE
)
) is
set
'not'
FALSE
is
boolean
set
K220
(
(
'not'
FALSE
)
,
(
'not'
FALSE
)
) is
set
'not'
(
'not'
FALSE
)
is
boolean
set
K114
(1,
(
'not'
FALSE
)
) is
set
'not'
(
'not'
FALSE
)
is
boolean
set
K114
(1,
(
'not'
FALSE
)
) is
set
(
'not'
(
'not'
FALSE
)
)
'&'
(
'not'
(
'not'
FALSE
)
)
is
set
K111
(
(
'not'
(
'not'
FALSE
)
)
,
(
'not'
(
'not'
FALSE
)
)
) is
set
'not'
(
(
'not'
(
'not'
FALSE
)
)
'&'
(
'not'
(
'not'
FALSE
)
)
)
is
boolean
set
K221
(
(
'not'
FALSE
)
,
FALSE
) is
set
K220
(
(
'not'
(
'not'
FALSE
)
)
,
FALSE
) is
set
'not'
(
'not'
(
'not'
FALSE
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
FALSE
)
)
) is
set
(
'not'
(
'not'
(
'not'
FALSE
)
)
)
'&'
(
'not'
FALSE
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
FALSE
)
)
)
,
(
'not'
FALSE
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
FALSE
)
)
)
'&'
(
'not'
FALSE
)
)
is
boolean
set
K221
(
FALSE
,
(
'not'
FALSE
)
)
'&'
K221
(
(
'not'
FALSE
)
,
FALSE
) is
set
'not'
K222
(
FALSE
,
(
'not'
FALSE
)
) is
boolean
set
'not'
TRUE
is
boolean
Element
of
BOOLEAN
K114
(1,
TRUE
) is
set
FALSE
'xor'
(
'not'
TRUE
)
is
boolean
Element
of
BOOLEAN
K222
(
FALSE
,
(
'not'
TRUE
)
) is
set
K221
(
FALSE
,
(
'not'
TRUE
)
) is
set
K220
(
(
'not'
FALSE
)
,
(
'not'
TRUE
)
) is
set
'not'
(
'not'
TRUE
)
is
boolean
set
K114
(1,
(
'not'
TRUE
)
) is
set
(
'not'
(
'not'
FALSE
)
)
'&'
(
'not'
(
'not'
TRUE
)
)
is
set
K111
(
(
'not'
(
'not'
FALSE
)
)
,
(
'not'
(
'not'
TRUE
)
)
) is
set
'not'
(
(
'not'
(
'not'
FALSE
)
)
'&'
(
'not'
(
'not'
TRUE
)
)
)
is
boolean
set
K221
(
(
'not'
TRUE
)
,
FALSE
) is
set
K220
(
(
'not'
(
'not'
TRUE
)
)
,
FALSE
) is
set
'not'
(
'not'
(
'not'
TRUE
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
TRUE
)
)
) is
set
(
'not'
(
'not'
(
'not'
TRUE
)
)
)
'&'
(
'not'
FALSE
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
TRUE
)
)
)
,
(
'not'
FALSE
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
TRUE
)
)
)
'&'
(
'not'
FALSE
)
)
is
boolean
set
K221
(
FALSE
,
(
'not'
TRUE
)
)
'&'
K221
(
(
'not'
TRUE
)
,
FALSE
) is
set
'not'
K222
(
FALSE
,
(
'not'
TRUE
)
) is
boolean
set
TRUE
'xor'
(
'not'
FALSE
)
is
boolean
Element
of
BOOLEAN
K222
(
TRUE
,
(
'not'
FALSE
)
) is
set
K221
(
TRUE
,
(
'not'
FALSE
)
) is
set
'not'
TRUE
is
boolean
set
K220
(
(
'not'
TRUE
)
,
(
'not'
FALSE
)
) is
set
'not'
(
'not'
TRUE
)
is
boolean
set
K114
(1,
(
'not'
TRUE
)
) is
set
(
'not'
(
'not'
TRUE
)
)
'&'
(
'not'
(
'not'
FALSE
)
)
is
set
K111
(
(
'not'
(
'not'
TRUE
)
)
,
(
'not'
(
'not'
FALSE
)
)
) is
set
'not'
(
(
'not'
(
'not'
TRUE
)
)
'&'
(
'not'
(
'not'
FALSE
)
)
)
is
boolean
set
K221
(
(
'not'
FALSE
)
,
TRUE
) is
set
K220
(
(
'not'
(
'not'
FALSE
)
)
,
TRUE
) is
set
(
'not'
(
'not'
(
'not'
FALSE
)
)
)
'&'
(
'not'
TRUE
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
FALSE
)
)
)
,
(
'not'
TRUE
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
FALSE
)
)
)
'&'
(
'not'
TRUE
)
)
is
boolean
set
K221
(
TRUE
,
(
'not'
FALSE
)
)
'&'
K221
(
(
'not'
FALSE
)
,
TRUE
) is
set
'not'
K222
(
TRUE
,
(
'not'
FALSE
)
) is
boolean
set
TRUE
'xor'
(
'not'
TRUE
)
is
boolean
Element
of
BOOLEAN
K222
(
TRUE
,
(
'not'
TRUE
)
) is
set
K221
(
TRUE
,
(
'not'
TRUE
)
) is
set
K220
(
(
'not'
TRUE
)
,
(
'not'
TRUE
)
) is
set
(
'not'
(
'not'
TRUE
)
)
'&'
(
'not'
(
'not'
TRUE
)
)
is
set
K111
(
(
'not'
(
'not'
TRUE
)
)
,
(
'not'
(
'not'
TRUE
)
)
) is
set
'not'
(
(
'not'
(
'not'
TRUE
)
)
'&'
(
'not'
(
'not'
TRUE
)
)
)
is
boolean
set
K221
(
(
'not'
TRUE
)
,
TRUE
) is
set
K220
(
(
'not'
(
'not'
TRUE
)
)
,
TRUE
) is
set
(
'not'
(
'not'
(
'not'
TRUE
)
)
)
'&'
(
'not'
TRUE
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
TRUE
)
)
)
,
(
'not'
TRUE
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
TRUE
)
)
)
'&'
(
'not'
TRUE
)
)
is
boolean
set
K221
(
TRUE
,
(
'not'
TRUE
)
)
'&'
K221
(
(
'not'
TRUE
)
,
TRUE
) is
set
'not'
K222
(
TRUE
,
(
'not'
TRUE
)
) is
boolean
set
f1
is
boolean
Element
of
BOOLEAN
f2
is
boolean
Element
of
BOOLEAN
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
f1
,
f2
*>
is
boolean
set
<*
(
xor2
.
<*
f1
,
f2
*>
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
xor2
.
<*
f1
,
f2
*>
)
*>
is
boolean
set
xor2a
.
<*
f1
,
f2
*>
is
boolean
set
()
.
<*
f1
,
f2
*>
is
boolean
set
<*
f1
*>
is non
empty
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
FinSequence
of
BOOLEAN
()
.
<*
f1
*>
is
boolean
set
<*
f2
*>
is non
empty
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
FinSequence
of
BOOLEAN
()
.
<*
f2
*>
is
boolean
set
<*
(
()
.
<*
f1
*>
)
,
(
()
.
<*
f2
*>
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
(
()
.
<*
f1
*>
)
,
(
()
.
<*
f2
*>
)
*>
is
boolean
set
f1
'xor'
f2
is
boolean
Element
of
BOOLEAN
K222
(
f1
,
f2
) is
set
K221
(
f1
,
f2
) is
set
'not'
f1
is
boolean
set
K114
(1,
f1
) is
set
K220
(
(
'not'
f1
)
,
f2
) is
set
'not'
(
'not'
f1
)
is
boolean
set
K114
(1,
(
'not'
f1
)
) is
set
'not'
f2
is
boolean
set
K114
(1,
f2
) is
set
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
f2
)
is
set
K111
(
(
'not'
(
'not'
f1
)
)
,
(
'not'
f2
)
) is
set
'not'
(
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
f2
)
)
is
boolean
set
K221
(
f2
,
f1
) is
set
K220
(
(
'not'
f2
)
,
f1
) is
set
'not'
(
'not'
f2
)
is
boolean
set
K114
(1,
(
'not'
f2
)
) is
set
(
'not'
(
'not'
f2
)
)
'&'
(
'not'
f1
)
is
set
K111
(
(
'not'
(
'not'
f2
)
)
,
(
'not'
f1
)
) is
set
'not'
(
(
'not'
(
'not'
f2
)
)
'&'
(
'not'
f1
)
)
is
boolean
set
K221
(
f1
,
f2
)
'&'
K221
(
f2
,
f1
) is
set
'not'
K222
(
f1
,
f2
) is
boolean
set
<*
(
f1
'xor'
f2
)
*>
is non
empty
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
FinSequence
of
BOOLEAN
()
.
<*
(
f1
'xor'
f2
)
*>
is
boolean
set
'not'
(
f1
'xor'
f2
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
f1
'xor'
f2
)
) is
set
'not'
f1
is
boolean
Element
of
BOOLEAN
(
'not'
f1
)
'xor'
f2
is
boolean
Element
of
BOOLEAN
K222
(
(
'not'
f1
)
,
f2
) is
set
K221
(
(
'not'
f1
)
,
f2
) is
set
'not'
(
'not'
f1
)
is
boolean
set
K114
(1,
(
'not'
f1
)
) is
set
K220
(
(
'not'
(
'not'
f1
)
)
,
f2
) is
set
'not'
(
'not'
(
'not'
f1
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f1
)
)
) is
set
(
'not'
(
'not'
(
'not'
f1
)
)
)
'&'
(
'not'
f2
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f1
)
)
)
,
(
'not'
f2
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f1
)
)
)
'&'
(
'not'
f2
)
)
is
boolean
set
K221
(
f2
,
(
'not'
f1
)
) is
set
K220
(
(
'not'
f2
)
,
(
'not'
f1
)
) is
set
(
'not'
(
'not'
f2
)
)
'&'
(
'not'
(
'not'
f1
)
)
is
set
K111
(
(
'not'
(
'not'
f2
)
)
,
(
'not'
(
'not'
f1
)
)
) is
set
'not'
(
(
'not'
(
'not'
f2
)
)
'&'
(
'not'
(
'not'
f1
)
)
)
is
boolean
set
K221
(
(
'not'
f1
)
,
f2
)
'&'
K221
(
f2
,
(
'not'
f1
)
) is
set
'not'
K222
(
(
'not'
f1
)
,
f2
) is
boolean
set
<*
(
'not'
f1
)
,
(
()
.
<*
f2
*>
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
(
'not'
f1
)
,
(
()
.
<*
f2
*>
)
*>
is
boolean
set
'not'
f2
is
boolean
Element
of
BOOLEAN
<*
(
'not'
f1
)
,
(
'not'
f2
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
(
'not'
f1
)
,
(
'not'
f2
)
*>
is
boolean
set
(
'not'
f1
)
'xor'
(
'not'
f2
)
is
boolean
Element
of
BOOLEAN
K222
(
(
'not'
f1
)
,
(
'not'
f2
)
) is
set
K221
(
(
'not'
f1
)
,
(
'not'
f2
)
) is
set
K220
(
(
'not'
(
'not'
f1
)
)
,
(
'not'
f2
)
) is
set
'not'
(
'not'
f2
)
is
boolean
set
K114
(1,
(
'not'
f2
)
) is
set
(
'not'
(
'not'
(
'not'
f1
)
)
)
'&'
(
'not'
(
'not'
f2
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f1
)
)
)
,
(
'not'
(
'not'
f2
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f1
)
)
)
'&'
(
'not'
(
'not'
f2
)
)
)
is
boolean
set
K221
(
(
'not'
f2
)
,
(
'not'
f1
)
) is
set
K220
(
(
'not'
(
'not'
f2
)
)
,
(
'not'
f1
)
) is
set
'not'
(
'not'
(
'not'
f2
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f2
)
)
) is
set
(
'not'
(
'not'
(
'not'
f2
)
)
)
'&'
(
'not'
(
'not'
f1
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f2
)
)
)
,
(
'not'
(
'not'
f1
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f2
)
)
)
'&'
(
'not'
(
'not'
f1
)
)
)
is
boolean
set
K221
(
(
'not'
f1
)
,
(
'not'
f2
)
)
'&'
K221
(
(
'not'
f2
)
,
(
'not'
f1
)
) is
set
'not'
K222
(
(
'not'
f1
)
,
(
'not'
f2
)
) is
boolean
set
f1
is
boolean
Element
of
BOOLEAN
f2
is
boolean
Element
of
BOOLEAN
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
f1
,
f2
*>
is
boolean
set
f3
is
boolean
Element
of
BOOLEAN
<*
(
()
.
<*
f1
,
f2
*>
)
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
(
()
.
<*
f1
,
f2
*>
)
,
f3
*>
is
boolean
set
<*
(
xor2
.
<*
(
()
.
<*
f1
,
f2
*>
)
,
f3
*>
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
xor2
.
<*
(
()
.
<*
f1
,
f2
*>
)
,
f3
*>
)
*>
is
boolean
set
()
.
<*
(
()
.
<*
f1
,
f2
*>
)
,
f3
*>
is
boolean
set
'not'
f2
is
boolean
Element
of
BOOLEAN
K114
(1,
f2
) is
set
f1
'xor'
(
'not'
f2
)
is
boolean
Element
of
BOOLEAN
K222
(
f1
,
(
'not'
f2
)
) is
set
K221
(
f1
,
(
'not'
f2
)
) is
set
'not'
f1
is
boolean
set
K114
(1,
f1
) is
set
K220
(
(
'not'
f1
)
,
(
'not'
f2
)
) is
set
'not'
(
'not'
f1
)
is
boolean
set
K114
(1,
(
'not'
f1
)
) is
set
'not'
(
'not'
f2
)
is
boolean
set
K114
(1,
(
'not'
f2
)
) is
set
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
(
'not'
f2
)
)
is
set
K111
(
(
'not'
(
'not'
f1
)
)
,
(
'not'
(
'not'
f2
)
)
) is
set
'not'
(
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
(
'not'
f2
)
)
)
is
boolean
set
K221
(
(
'not'
f2
)
,
f1
) is
set
K220
(
(
'not'
(
'not'
f2
)
)
,
f1
) is
set
'not'
(
'not'
(
'not'
f2
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f2
)
)
) is
set
(
'not'
(
'not'
(
'not'
f2
)
)
)
'&'
(
'not'
f1
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f2
)
)
)
,
(
'not'
f1
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f2
)
)
)
'&'
(
'not'
f1
)
)
is
boolean
set
K221
(
f1
,
(
'not'
f2
)
)
'&'
K221
(
(
'not'
f2
)
,
f1
) is
set
'not'
K222
(
f1
,
(
'not'
f2
)
) is
boolean
set
<*
(
f1
'xor'
(
'not'
f2
)
)
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
(
f1
'xor'
(
'not'
f2
)
)
,
f3
*>
is
boolean
set
<*
(
xor2
.
<*
(
f1
'xor'
(
'not'
f2
)
)
,
f3
*>
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
xor2
.
<*
(
f1
'xor'
(
'not'
f2
)
)
,
f3
*>
)
*>
is
boolean
set
(
f1
'xor'
(
'not'
f2
)
)
'xor'
f3
is
boolean
Element
of
BOOLEAN
K222
(
(
f1
'xor'
(
'not'
f2
)
)
,
f3
) is
set
K221
(
(
f1
'xor'
(
'not'
f2
)
)
,
f3
) is
set
'not'
(
f1
'xor'
(
'not'
f2
)
)
is
boolean
set
K114
(1,
(
f1
'xor'
(
'not'
f2
)
)
) is
set
K220
(
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
,
f3
) is
set
'not'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
is
boolean
set
K114
(1,
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
) is
set
'not'
f3
is
boolean
set
K114
(1,
f3
) is
set
(
'not'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
'&'
(
'not'
f3
)
is
set
K111
(
(
'not'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
,
(
'not'
f3
)
) is
set
'not'
(
(
'not'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
'&'
(
'not'
f3
)
)
is
boolean
set
K221
(
f3
,
(
f1
'xor'
(
'not'
f2
)
)
) is
set
K220
(
(
'not'
f3
)
,
(
f1
'xor'
(
'not'
f2
)
)
) is
set
'not'
(
'not'
f3
)
is
boolean
set
K114
(1,
(
'not'
f3
)
) is
set
(
'not'
(
'not'
f3
)
)
'&'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
is
set
K111
(
(
'not'
(
'not'
f3
)
)
,
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
f3
)
)
'&'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
is
boolean
set
K221
(
(
f1
'xor'
(
'not'
f2
)
)
,
f3
)
'&'
K221
(
f3
,
(
f1
'xor'
(
'not'
f2
)
)
) is
set
'not'
K222
(
(
f1
'xor'
(
'not'
f2
)
)
,
f3
) is
boolean
set
<*
(
(
f1
'xor'
(
'not'
f2
)
)
'xor'
f3
)
*>
is non
empty
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
FinSequence
of
BOOLEAN
()
.
<*
(
(
f1
'xor'
(
'not'
f2
)
)
'xor'
f3
)
*>
is
boolean
set
'not'
(
(
f1
'xor'
(
'not'
f2
)
)
'xor'
f3
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
f1
'xor'
(
'not'
f2
)
)
'xor'
f3
)
) is
set
'not'
f3
is
boolean
Element
of
BOOLEAN
(
f1
'xor'
(
'not'
f2
)
)
'xor'
(
'not'
f3
)
is
boolean
Element
of
BOOLEAN
K222
(
(
f1
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
) is
set
K221
(
(
f1
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
) is
set
K220
(
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
,
(
'not'
f3
)
) is
set
'not'
(
'not'
f3
)
is
boolean
set
K114
(1,
(
'not'
f3
)
) is
set
(
'not'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
'&'
(
'not'
(
'not'
f3
)
)
is
set
K111
(
(
'not'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
,
(
'not'
(
'not'
f3
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
'&'
(
'not'
(
'not'
f3
)
)
)
is
boolean
set
K221
(
(
'not'
f3
)
,
(
f1
'xor'
(
'not'
f2
)
)
) is
set
K220
(
(
'not'
(
'not'
f3
)
)
,
(
f1
'xor'
(
'not'
f2
)
)
) is
set
'not'
(
'not'
(
'not'
f3
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f3
)
)
) is
set
(
'not'
(
'not'
(
'not'
f3
)
)
)
'&'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f3
)
)
)
,
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f3
)
)
)
'&'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
is
boolean
set
K221
(
(
f1
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
)
'&'
K221
(
(
'not'
f3
)
,
(
f1
'xor'
(
'not'
f2
)
)
) is
set
'not'
K222
(
(
f1
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
) is
boolean
set
()
.
<*
(
f1
'xor'
(
'not'
f2
)
)
,
f3
*>
is
boolean
set
f1
is
boolean
Element
of
BOOLEAN
'not'
f1
is
boolean
Element
of
BOOLEAN
K114
(1,
f1
) is
set
f2
is
boolean
Element
of
BOOLEAN
(
'not'
f1
)
'xor'
f2
is
boolean
Element
of
BOOLEAN
K222
(
(
'not'
f1
)
,
f2
) is
set
K221
(
(
'not'
f1
)
,
f2
) is
set
'not'
(
'not'
f1
)
is
boolean
set
K114
(1,
(
'not'
f1
)
) is
set
K220
(
(
'not'
(
'not'
f1
)
)
,
f2
) is
set
'not'
(
'not'
(
'not'
f1
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f1
)
)
) is
set
'not'
f2
is
boolean
set
K114
(1,
f2
) is
set
(
'not'
(
'not'
(
'not'
f1
)
)
)
'&'
(
'not'
f2
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f1
)
)
)
,
(
'not'
f2
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f1
)
)
)
'&'
(
'not'
f2
)
)
is
boolean
set
K221
(
f2
,
(
'not'
f1
)
) is
set
K220
(
(
'not'
f2
)
,
(
'not'
f1
)
) is
set
'not'
(
'not'
f2
)
is
boolean
set
K114
(1,
(
'not'
f2
)
) is
set
(
'not'
(
'not'
f2
)
)
'&'
(
'not'
(
'not'
f1
)
)
is
set
K111
(
(
'not'
(
'not'
f2
)
)
,
(
'not'
(
'not'
f1
)
)
) is
set
'not'
(
(
'not'
(
'not'
f2
)
)
'&'
(
'not'
(
'not'
f1
)
)
)
is
boolean
set
K221
(
(
'not'
f1
)
,
f2
)
'&'
K221
(
f2
,
(
'not'
f1
)
) is
set
'not'
K222
(
(
'not'
f1
)
,
f2
) is
boolean
set
f3
is
boolean
Element
of
BOOLEAN
'not'
f3
is
boolean
Element
of
BOOLEAN
K114
(1,
f3
) is
set
(
(
'not'
f1
)
'xor'
f2
)
'xor'
(
'not'
f3
)
is
boolean
Element
of
BOOLEAN
K222
(
(
(
'not'
f1
)
'xor'
f2
)
,
(
'not'
f3
)
) is
set
K221
(
(
(
'not'
f1
)
'xor'
f2
)
,
(
'not'
f3
)
) is
set
'not'
(
(
'not'
f1
)
'xor'
f2
)
is
boolean
set
K114
(1,
(
(
'not'
f1
)
'xor'
f2
)
) is
set
K220
(
(
'not'
(
(
'not'
f1
)
'xor'
f2
)
)
,
(
'not'
f3
)
) is
set
'not'
(
'not'
(
(
'not'
f1
)
'xor'
f2
)
)
is
boolean
set
K114
(1,
(
'not'
(
(
'not'
f1
)
'xor'
f2
)
)
) is
set
'not'
(
'not'
f3
)
is
boolean
set
K114
(1,
(
'not'
f3
)
) is
set
(
'not'
(
'not'
(
(
'not'
f1
)
'xor'
f2
)
)
)
'&'
(
'not'
(
'not'
f3
)
)
is
set
K111
(
(
'not'
(
'not'
(
(
'not'
f1
)
'xor'
f2
)
)
)
,
(
'not'
(
'not'
f3
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
(
'not'
f1
)
'xor'
f2
)
)
)
'&'
(
'not'
(
'not'
f3
)
)
)
is
boolean
set
K221
(
(
'not'
f3
)
,
(
(
'not'
f1
)
'xor'
f2
)
) is
set
K220
(
(
'not'
(
'not'
f3
)
)
,
(
(
'not'
f1
)
'xor'
f2
)
) is
set
'not'
(
'not'
(
'not'
f3
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f3
)
)
) is
set
(
'not'
(
'not'
(
'not'
f3
)
)
)
'&'
(
'not'
(
(
'not'
f1
)
'xor'
f2
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f3
)
)
)
,
(
'not'
(
(
'not'
f1
)
'xor'
f2
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f3
)
)
)
'&'
(
'not'
(
(
'not'
f1
)
'xor'
f2
)
)
)
is
boolean
set
K221
(
(
(
'not'
f1
)
'xor'
f2
)
,
(
'not'
f3
)
)
'&'
K221
(
(
'not'
f3
)
,
(
(
'not'
f1
)
'xor'
f2
)
) is
set
'not'
K222
(
(
(
'not'
f1
)
'xor'
f2
)
,
(
'not'
f3
)
) is
boolean
set
'not'
f2
is
boolean
Element
of
BOOLEAN
f1
'xor'
(
'not'
f2
)
is
boolean
Element
of
BOOLEAN
K222
(
f1
,
(
'not'
f2
)
) is
set
K221
(
f1
,
(
'not'
f2
)
) is
set
'not'
f1
is
boolean
set
K220
(
(
'not'
f1
)
,
(
'not'
f2
)
) is
set
'not'
(
'not'
f1
)
is
boolean
set
K114
(1,
(
'not'
f1
)
) is
set
'not'
(
'not'
f2
)
is
boolean
set
K114
(1,
(
'not'
f2
)
) is
set
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
(
'not'
f2
)
)
is
set
K111
(
(
'not'
(
'not'
f1
)
)
,
(
'not'
(
'not'
f2
)
)
) is
set
'not'
(
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
(
'not'
f2
)
)
)
is
boolean
set
K221
(
(
'not'
f2
)
,
f1
) is
set
K220
(
(
'not'
(
'not'
f2
)
)
,
f1
) is
set
'not'
(
'not'
(
'not'
f2
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f2
)
)
) is
set
(
'not'
(
'not'
(
'not'
f2
)
)
)
'&'
(
'not'
f1
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f2
)
)
)
,
(
'not'
f1
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f2
)
)
)
'&'
(
'not'
f1
)
)
is
boolean
set
K221
(
f1
,
(
'not'
f2
)
)
'&'
K221
(
(
'not'
f2
)
,
f1
) is
set
'not'
K222
(
f1
,
(
'not'
f2
)
) is
boolean
set
(
f1
'xor'
(
'not'
f2
)
)
'xor'
(
'not'
f3
)
is
boolean
Element
of
BOOLEAN
K222
(
(
f1
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
) is
set
K221
(
(
f1
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
) is
set
'not'
(
f1
'xor'
(
'not'
f2
)
)
is
boolean
set
K114
(1,
(
f1
'xor'
(
'not'
f2
)
)
) is
set
K220
(
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
,
(
'not'
f3
)
) is
set
'not'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
is
boolean
set
K114
(1,
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
) is
set
(
'not'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
'&'
(
'not'
(
'not'
f3
)
)
is
set
K111
(
(
'not'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
,
(
'not'
(
'not'
f3
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
'&'
(
'not'
(
'not'
f3
)
)
)
is
boolean
set
K221
(
(
'not'
f3
)
,
(
f1
'xor'
(
'not'
f2
)
)
) is
set
K220
(
(
'not'
(
'not'
f3
)
)
,
(
f1
'xor'
(
'not'
f2
)
)
) is
set
(
'not'
(
'not'
(
'not'
f3
)
)
)
'&'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f3
)
)
)
,
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f3
)
)
)
'&'
(
'not'
(
f1
'xor'
(
'not'
f2
)
)
)
)
is
boolean
set
K221
(
(
f1
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
)
'&'
K221
(
(
'not'
f3
)
,
(
f1
'xor'
(
'not'
f2
)
)
) is
set
'not'
K222
(
(
f1
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
) is
boolean
set
f1
is
boolean
Element
of
BOOLEAN
f2
is
boolean
Element
of
BOOLEAN
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2a
.
<*
f1
,
f2
*>
is
boolean
set
f3
is
boolean
Element
of
BOOLEAN
<*
(
xor2a
.
<*
f1
,
f2
*>
)
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
xor2a
.
<*
f1
,
f2
*>
)
,
f3
*>
is
boolean
set
()
.
<*
f1
,
f2
*>
is
boolean
set
<*
(
()
.
<*
f1
,
f2
*>
)
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
()
.
<*
f1
,
f2
*>
)
,
f3
*>
is
boolean
set
f1
is
boolean
Element
of
BOOLEAN
f2
is
boolean
Element
of
BOOLEAN
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2b
.
<*
f1
,
f2
*>
is
boolean
set
f3
is
boolean
Element
of
BOOLEAN
<*
(
xor2b
.
<*
f1
,
f2
*>
)
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
xor2b
.
<*
f1
,
f2
*>
)
,
f3
*>
is
boolean
set
<*
(
()
.
<*
(
xor2b
.
<*
f1
,
f2
*>
)
,
f3
*>
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
()
.
<*
(
xor2b
.
<*
f1
,
f2
*>
)
,
f3
*>
)
*>
is
boolean
set
xor2
.
<*
f1
,
f2
*>
is
boolean
set
<*
(
xor2
.
<*
f1
,
f2
*>
)
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
(
xor2
.
<*
f1
,
f2
*>
)
,
f3
*>
is
boolean
set
'not'
f1
is
boolean
Element
of
BOOLEAN
K114
(1,
f1
) is
set
'not'
f2
is
boolean
Element
of
BOOLEAN
K114
(1,
f2
) is
set
(
'not'
f1
)
'xor'
(
'not'
f2
)
is
boolean
Element
of
BOOLEAN
K222
(
(
'not'
f1
)
,
(
'not'
f2
)
) is
set
K221
(
(
'not'
f1
)
,
(
'not'
f2
)
) is
set
'not'
(
'not'
f1
)
is
boolean
set
K114
(1,
(
'not'
f1
)
) is
set
K220
(
(
'not'
(
'not'
f1
)
)
,
(
'not'
f2
)
) is
set
'not'
(
'not'
(
'not'
f1
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f1
)
)
) is
set
'not'
(
'not'
f2
)
is
boolean
set
K114
(1,
(
'not'
f2
)
) is
set
(
'not'
(
'not'
(
'not'
f1
)
)
)
'&'
(
'not'
(
'not'
f2
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f1
)
)
)
,
(
'not'
(
'not'
f2
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f1
)
)
)
'&'
(
'not'
(
'not'
f2
)
)
)
is
boolean
set
K221
(
(
'not'
f2
)
,
(
'not'
f1
)
) is
set
K220
(
(
'not'
(
'not'
f2
)
)
,
(
'not'
f1
)
) is
set
'not'
(
'not'
(
'not'
f2
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f2
)
)
) is
set
(
'not'
(
'not'
(
'not'
f2
)
)
)
'&'
(
'not'
(
'not'
f1
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f2
)
)
)
,
(
'not'
(
'not'
f1
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f2
)
)
)
'&'
(
'not'
(
'not'
f1
)
)
)
is
boolean
set
K221
(
(
'not'
f1
)
,
(
'not'
f2
)
)
'&'
K221
(
(
'not'
f2
)
,
(
'not'
f1
)
) is
set
'not'
K222
(
(
'not'
f1
)
,
(
'not'
f2
)
) is
boolean
set
<*
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
,
f3
*>
is
boolean
set
<*
(
()
.
<*
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
,
f3
*>
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
()
.
<*
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
,
f3
*>
)
*>
is
boolean
set
'not'
f3
is
boolean
Element
of
BOOLEAN
K114
(1,
f3
) is
set
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
'xor'
(
'not'
f3
)
is
boolean
Element
of
BOOLEAN
K222
(
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
) is
set
K221
(
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
) is
set
'not'
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
is
boolean
set
K114
(1,
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
) is
set
K220
(
(
'not'
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
)
,
(
'not'
f3
)
) is
set
'not'
(
'not'
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
)
is
boolean
set
K114
(1,
(
'not'
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
)
) is
set
'not'
(
'not'
f3
)
is
boolean
set
K114
(1,
(
'not'
f3
)
) is
set
(
'not'
(
'not'
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
)
)
'&'
(
'not'
(
'not'
f3
)
)
is
set
K111
(
(
'not'
(
'not'
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
)
)
,
(
'not'
(
'not'
f3
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
)
)
'&'
(
'not'
(
'not'
f3
)
)
)
is
boolean
set
K221
(
(
'not'
f3
)
,
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
) is
set
K220
(
(
'not'
(
'not'
f3
)
)
,
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
) is
set
'not'
(
'not'
(
'not'
f3
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
f3
)
)
) is
set
(
'not'
(
'not'
(
'not'
f3
)
)
)
'&'
(
'not'
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
f3
)
)
)
,
(
'not'
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
f3
)
)
)
'&'
(
'not'
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
)
)
is
boolean
set
K221
(
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
)
'&'
K221
(
(
'not'
f3
)
,
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
) is
set
'not'
K222
(
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
,
(
'not'
f3
)
) is
boolean
set
<*
(
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
'xor'
(
'not'
f3
)
)
*>
is non
empty
Relation-like
NAT
-defined
BOOLEAN
-valued
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
FinSequence
of
BOOLEAN
()
.
<*
(
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
'xor'
(
'not'
f3
)
)
*>
is
boolean
set
'not'
(
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
'xor'
(
'not'
f3
)
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
(
'not'
f1
)
'xor'
(
'not'
f2
)
)
'xor'
(
'not'
f3
)
)
) is
set
f1
'xor'
f2
is
boolean
Element
of
BOOLEAN
K222
(
f1
,
f2
) is
set
K221
(
f1
,
f2
) is
set
'not'
f1
is
boolean
set
K220
(
(
'not'
f1
)
,
f2
) is
set
'not'
(
'not'
f1
)
is
boolean
set
K114
(1,
(
'not'
f1
)
) is
set
'not'
f2
is
boolean
set
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
f2
)
is
set
K111
(
(
'not'
(
'not'
f1
)
)
,
(
'not'
f2
)
) is
set
'not'
(
(
'not'
(
'not'
f1
)
)
'&'
(
'not'
f2
)
)
is
boolean
set
K221
(
f2
,
f1
) is
set
K220
(
(
'not'
f2
)
,
f1
) is
set
'not'
(
'not'
f2
)
is
boolean
set
K114
(1,
(
'not'
f2
)
) is
set
(
'not'
(
'not'
f2
)
)
'&'
(
'not'
f1
)
is
set
K111
(
(
'not'
(
'not'
f2
)
)
,
(
'not'
f1
)
) is
set
'not'
(
(
'not'
(
'not'
f2
)
)
'&'
(
'not'
f1
)
)
is
boolean
set
K221
(
f1
,
f2
)
'&'
K221
(
f2
,
f1
) is
set
'not'
K222
(
f1
,
f2
) is
boolean
set
(
f1
'xor'
f2
)
'xor'
f3
is
boolean
Element
of
BOOLEAN
K222
(
(
f1
'xor'
f2
)
,
f3
) is
set
K221
(
(
f1
'xor'
f2
)
,
f3
) is
set
'not'
(
f1
'xor'
f2
)
is
boolean
set
K114
(1,
(
f1
'xor'
f2
)
) is
set
K220
(
(
'not'
(
f1
'xor'
f2
)
)
,
f3
) is
set
'not'
(
'not'
(
f1
'xor'
f2
)
)
is
boolean
set
K114
(1,
(
'not'
(
f1
'xor'
f2
)
)
) is
set
'not'
f3
is
boolean
set
(
'not'
(
'not'
(
f1
'xor'
f2
)
)
)
'&'
(
'not'
f3
)
is
set
K111
(
(
'not'
(
'not'
(
f1
'xor'
f2
)
)
)
,
(
'not'
f3
)
) is
set
'not'
(
(
'not'
(
'not'
(
f1
'xor'
f2
)
)
)
'&'
(
'not'
f3
)
)
is
boolean
set
K221
(
f3
,
(
f1
'xor'
f2
)
) is
set
K220
(
(
'not'
f3
)
,
(
f1
'xor'
f2
)
) is
set
'not'
(
'not'
f3
)
is
boolean
set
K114
(1,
(
'not'
f3
)
) is
set
(
'not'
(
'not'
f3
)
)
'&'
(
'not'
(
f1
'xor'
f2
)
)
is
set
K111
(
(
'not'
(
'not'
f3
)
)
,
(
'not'
(
f1
'xor'
f2
)
)
) is
set
'not'
(
(
'not'
(
'not'
f3
)
)
'&'
(
'not'
(
f1
'xor'
f2
)
)
)
is
boolean
set
K221
(
(
f1
'xor'
f2
)
,
f3
)
'&'
K221
(
f3
,
(
f1
'xor'
f2
)
) is
set
'not'
K222
(
(
f1
'xor'
f2
)
,
f3
) is
boolean
set
<*
(
f1
'xor'
f2
)
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
(
f1
'xor'
f2
)
,
f3
*>
is
boolean
set
f2
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f3
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f1
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
f2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
f2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
f2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
f3
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
f3
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
f3
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,
f1
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
f1
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
f1
}
,
{
<*
f0
,
x
*>
}
}
is
set
{
x
,
y
}
is
set
{
[
<*
f0
,
x
*>
,
f1
]
,
[
<*
x
,
y
*>
,
f2
]
}
is
Relation-like
set
{
f0
,
x
,
y
}
is
set
dom
<*
f0
,
x
*>
is non
empty
V51
()
Element
of
K18
(
NAT
)
Seg
2 is non
empty
V36
()
V43
(2)
V51
()
Element
of
K18
(
NAT
)
<*
f0
,
x
*>
.
2 is
set
[
2,
x
]
is non
empty
pair
set
{
2,
x
}
is
set
{
2
}
is non
with_pair
set
{
{
2,
x
}
,
{
2
}
}
is
set
{
2,
y
}
is
set
[
2,
y
]
is non
empty
pair
set
{
{
2,
y
}
,
{
2
}
}
is
set
<*
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
set
[
1,
y
]
is non
empty
pair
set
{
1,
y
}
is
set
{
1
}
is non
with_pair
set
{
{
1,
y
}
,
{
1
}
}
is
set
{
[
1,
y
]
}
is
Relation-like
Function-like
set
<*
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
set
[
1,
f0
]
is non
empty
pair
set
{
1,
f0
}
is
set
{
{
1,
f0
}
,
{
1
}
}
is
set
{
[
1,
f0
]
}
is
Relation-like
Function-like
set
dom
<*
y
,
f0
*>
is non
empty
V51
()
Element
of
K18
(
NAT
)
<*
y
,
f0
*>
.
2 is
set
[
2,
f0
]
is non
empty
pair
set
{
2,
f0
}
is
set
{
{
2,
f0
}
,
{
2
}
}
is
set
<*
y
*>
^
<*
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(1
+
1)
FinSequence-like
FinSubsequence-like
V51
()
set
1
+
1 is
V9
()
V10
()
V11
()
V15
() non
pair
Element
of
NAT
dom
<*
x
,
y
*>
is non
empty
V51
()
Element
of
K18
(
NAT
)
<*
x
,
y
*>
.
2 is
set
<*
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(1)
FinSequence-like
FinSubsequence-like
V51
()
set
<*
f0
*>
^
<*
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(1
+
1)
FinSequence-like
FinSubsequence-like
V51
()
set
f1
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f2
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f3
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f0
is
Relation-like
Function-like
V27
(3
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
3
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
x
is
set
y
is
set
z
is
set
{
x
,
y
,
z
}
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
f1
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
f1
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
f1
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
f2
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
f2
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
f2
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
f3
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
f3
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
f3
}
,
{
<*
z
,
x
*>
}
}
is
set
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
,
f0
]
is non
empty
pair
set
{
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
,
f0
}
is
functional
set
{
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
,
f0
}
,
{
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
}
}
is
set
{
[
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
,
f0
]
}
is
Relation-like
Function-like
set
{
x
,
y
,
z
}
\
{
[
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
,
f0
]
}
is
Element
of
K18
(
{
x
,
y
,
z
}
)
K18
(
{
x
,
y
,
z
}
) is
set
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
.
3 is
set
len
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
is
V9
()
V10
()
V11
()
V15
() non
pair
Element
of
NAT
Seg
3 is non
empty
V36
()
V43
(3)
V51
()
Element
of
K18
(
NAT
)
dom
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
is non
empty
V51
()
Element
of
K18
(
NAT
)
[
3,
[
<*
z
,
x
*>
,
f3
]
]
is non
empty
pair
set
{
3,
[
<*
z
,
x
*>
,
f3
]
}
is
set
{
3
}
is non
with_pair
set
{
{
3,
[
<*
z
,
x
*>
,
f3
]
}
,
{
3
}
}
is
set
proj2
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
is non
empty
set
the_rank_of
[
<*
z
,
x
*>
,
f3
]
is
V9
()
V10
()
V11
()
set
the_rank_of
[
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
,
f0
]
is
V9
()
V10
()
V11
()
set
proj2
<*
y
,
z
*>
is non
empty
set
{
y
,
z
}
is
set
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
.
2 is
set
A1
is
set
<*
[
<*
x
,
y
*>
,
f1
]
,
[
<*
y
,
z
*>
,
f2
]
,
[
<*
z
,
x
*>
,
f3
]
*>
.
1 is
set
[
1,
[
<*
x
,
y
*>
,
f1
]
]
is non
empty
pair
set
{
1,
[
<*
x
,
y
*>
,
f1
]
}
is
set
{
1
}
is non
with_pair
set
{
{
1,
[
<*
x
,
y
*>
,
f1
]
}
,
{
1
}
}
is
set
the_rank_of
[
<*
x
,
y
*>
,
f1
]
is
V9
()
V10
()
V11
()
set
proj2
<*
z
,
x
*>
is non
empty
set
{
z
,
x
}
is
set
[
2,
[
<*
y
,
z
*>
,
f2
]
]
is non
empty
pair
set
{
2,
[
<*
y
,
z
*>
,
f2
]
}
is
set
{
2
}
is non
with_pair
set
{
{
2,
[
<*
y
,
z
*>
,
f2
]
}
,
{
2
}
}
is
set
the_rank_of
[
<*
y
,
z
*>
,
f2
]
is
V9
()
V10
()
V11
()
set
proj2
<*
x
,
y
*>
is non
empty
set
{
x
,
y
}
is
set
f1
is
Relation-like
Function-like
V27
(2
-tuples_on
BOOLEAN
,
BOOLEAN
)
boolean-valued
Element
of
K18
(
K19
(
(
2
-tuples_on
BOOLEAN
)
,
BOOLEAN
))
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
f1
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
f1
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
f1
}
,
{
<*
f2
,
f3
*>
}
}
is
set
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircuit
(
f2
,
f3
,
f0
,
f1
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
1GateCircuit
(
f2
,
f3
,
f1
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
1GateCircuit
(
<*
f2
,
f3
*>
,
f1
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
1GateCircuit
(
[
<*
f2
,
f3
*>
,
f1
]
,
f0
,
f1
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
(
1GateCircuit
(
f2
,
f3
,
f1
)
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
f1
]
,
f0
,
f1
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
the
Sorts
of
(
2GatesCircuit
(
f2
,
f3
,
f0
,
f1
)
)
is
Relation-like
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
-defined
Function-like
V23
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
)
set
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
is non
empty
set
K230
( the
Sorts
of
(
2GatesCircuit
(
f2
,
f3
,
f0
,
f1
)
)
) is
functional
V49
()
V50
()
set
2GatesCircOutput
(
f2
,
f3
,
f0
,
f1
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
)
[
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
}
,
{
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
}
}
is
set
InputVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
\
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
)
{
f2
,
f3
,
f0
}
is
set
{
[
<*
f2
,
f3
*>
,
f1
]
,
(
2GatesCircOutput
(
f2
,
f3
,
f0
,
f1
)
)
}
is
Relation-like
set
A1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
2GatesCircuit
(
f2
,
f3
,
f0
,
f1
)
)
)
Following
A1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
2GatesCircuit
(
f2
,
f3
,
f0
,
f1
)
)
)
(
Following
A1
)
.
(
2GatesCircOutput
(
f2
,
f3
,
f0
,
f1
)
)
is
boolean
Element
of
BOOLEAN
A1
.
[
<*
f2
,
f3
*>
,
f1
]
is
set
A1
.
f0
is
set
<*
(
A1
.
[
<*
f2
,
f3
*>
,
f1
]
)
,
(
A1
.
f0
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
f1
.
<*
(
A1
.
[
<*
f2
,
f3
*>
,
f1
]
)
,
(
A1
.
f0
)
*>
is
boolean
set
(
Following
A1
)
.
[
<*
f2
,
f3
*>
,
f1
]
is
set
A1
.
f2
is
set
A1
.
f3
is
set
<*
(
A1
.
f2
)
,
(
A1
.
f3
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
f1
.
<*
(
A1
.
f2
)
,
(
A1
.
f3
)
*>
is
boolean
set
(
Following
A1
)
.
f2
is
set
(
Following
A1
)
.
f3
is
set
(
Following
A1
)
.
f0
is
set
the
Sorts
of
(
1GateCircuit
(
f2
,
f3
,
f1
)
)
is
Relation-like
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
-defined
Function-like
V23
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
)
set
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
is non
empty
set
K230
( the
Sorts
of
(
1GateCircuit
(
f2
,
f3
,
f1
)
)
) is
functional
V49
()
V50
()
set
A1
|
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
is
Relation-like
Function-like
set
the
Sorts
of
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
f1
]
,
f0
,
f1
)
)
is
Relation-like
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
-defined
Function-like
V23
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
)
set
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
is non
empty
set
K230
( the
Sorts
of
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
f1
]
,
f0
,
f1
)
)
) is
functional
V49
()
V50
()
set
A1
|
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
is
Relation-like
Function-like
set
t
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
f1
]
,
f0
,
f1
)
)
)
proj1
t
is
set
proj2
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
is non
empty
set
S2
is
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
f1
)
)
{
S2
,
f0
}
is
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
)
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
)
InnerVertices
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
)
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
)
s2
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
1GateCircuit
(
f2
,
f3
,
f1
)
)
)
proj1
s2
is
set
Following
t
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
f1
]
,
f0
,
f1
)
)
)
s2
is
Element
of
InnerVertices
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
(
Following
t
)
.
s2
is
boolean
Element
of
BOOLEAN
S
is
Element
of the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
t
.
S
is
boolean
Element
of
BOOLEAN
a
is
Element
of the
carrier
of
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
f1
]
,
f0
*>
,
f1
)
)
t
.
a
is
boolean
Element
of
BOOLEAN
<*
(
t
.
S
)
,
(
t
.
a
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
f1
.
<*
(
t
.
S
)
,
(
t
.
a
)
*>
is
boolean
set
<*
(
A1
.
[
<*
f2
,
f3
*>
,
f1
]
)
,
(
t
.
a
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
f1
.
<*
(
A1
.
[
<*
f2
,
f3
*>
,
f1
]
)
,
(
t
.
a
)
*>
is
boolean
set
Following
s2
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
1GateCircuit
(
f2
,
f3
,
f1
)
)
)
a
is
Element
of
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
(
Following
s2
)
.
a
is
boolean
Element
of
BOOLEAN
v
is
Element
of the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
s2
.
v
is
boolean
Element
of
BOOLEAN
vy
is
Element
of the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
f1
)
)
s2
.
vy
is
boolean
Element
of
BOOLEAN
<*
(
s2
.
v
)
,
(
s2
.
vy
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
f1
.
<*
(
s2
.
v
)
,
(
s2
.
vy
)
*>
is
boolean
set
<*
(
A1
.
f2
)
,
(
s2
.
vy
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
f1
.
<*
(
A1
.
f2
)
,
(
s2
.
vy
)
*>
is
boolean
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircuit
(
f1
,
f2
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
1GateCircuit
(
f2
,
f3
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
(
1GateCircuit
(
f1
,
f2
,
and2
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
1GateCircuit
(
f3
,
f1
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
(
(
1GateCircuit
(
f1
,
f2
,
and2
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
1GateCircuit
(
f2
,
f3
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
(
1GateCircuit
(
f1
,
f2
,
and2
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
1GateCircuit
(
f3
,
f1
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
(
(
1GateCircuit
(
f1
,
f2
,
and2
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Function-like
set
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\/
(
InnerVertices
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
set
the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
))
the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
InnerVertices
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
set
the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
))
the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
(
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
(
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
(
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Function-like
set
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is
set
{
f2
,
f3
}
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
set
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
set
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
)
is
set
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
Function-like
set
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
}
is
Relation-like
Function-like
set
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Function-like
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
)
is
set
{
f1
,
f2
}
is
set
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Element
of
K18
(
{
f1
,
f2
}
)
K18
(
{
f1
,
f2
}
) is
set
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
is
set
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
)
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
)
is
set
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
is
Element
of
K18
(
{
f2
,
f3
}
)
K18
(
{
f2
,
f3
}
) is
set
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
is
set
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
)
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
)
is
set
{
f3
,
f1
}
is
set
{
f3
,
f1
}
\
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
is
Element
of
K18
(
{
f3
,
f1
}
)
K18
(
{
f3
,
f1
}
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
{
f3
,
f1
}
\
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
)
is
set
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
is
Element
of
K18
(
{
f3
,
f1
}
)
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
)
is
set
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
is
set
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
)
K18
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
) is
set
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
)
is
set
{
f1
,
f2
}
\/
{
f2
,
f3
}
is
set
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
)
K18
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
) is
set
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
)
is
set
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f2
,
f3
}
is
set
{
f1
,
f2
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f2
,
f3
}
) is
set
(
{
f1
,
f2
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
f3
,
f1
}
is
set
{
f2
,
f2
,
f1
,
f3
}
is
set
{
f2
,
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
{
f2
,
f2
,
f1
,
f3
}
)
K18
(
{
f2
,
f2
,
f1
,
f3
}
) is
set
(
{
f2
,
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
f3
,
f1
}
is
set
{
f2
,
f1
,
f3
}
is
set
{
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
{
f2
,
f1
,
f3
}
)
K18
(
{
f2
,
f1
,
f3
}
) is
set
(
{
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f3
}
) is
set
(
{
f1
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
}
is
set
{
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
}
\/
{
f1
}
is
set
{
f3
,
f3
,
f1
,
f2
}
is
set
{
f3
,
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
}
is
set
{
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
,
f1
}
is
set
{
f1
,
f1
,
f2
,
f3
}
is
set
f1
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is
set
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
proj2
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
{
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
}
is
Relation-like
Function-like
set
{
f1
,
f2
,
f3
}
\
{
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f3
}
) is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Element
of
K18
(
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
)
K18
(
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
) is
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
f1
,
f2
,
f3
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
(
(
InputVertices
(
f1
,
f2
,
f3
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Relation-like
Element
of
K18
(
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
)
{
f1
,
f2
,
f3
}
\/
(
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
{
f1
,
f2
,
f3
}
\/
{}
is
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
S
is non
empty
pair
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
{
[
<*
f1
,
f2
*>
,
and2
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
Function-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
(
InputVertices
(
f1
,
f2
,
f3
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
set
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
proj2
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
set
{
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
}
is
Relation-like
Function-like
set
(
proj2
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
)
\/
{
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
}
is
set
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
,(
f1
,
f2
,
f3
)
}
is
set
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
and2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
and2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,
and2
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
and2
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
and2
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
{
f0
,
x
,
y
}
is
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
{
f1
,
f2
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
{
f2
,
f3
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
{
f3
,
f1
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
{
[
<*
f1
,
f2
*>
,
and2
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Function-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
{
[
<*
f1
,
f2
*>
,
and2
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
f1
,
f2
,
f3
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
is
set
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
{
f1
,
f2
,
f2
,
f3
}
is
set
{
f1
,
f2
,
f2
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f2
,
f2
,
f1
,
f3
}
is
set
{
f2
,
f2
,
f1
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f2
,
f1
,
f3
}
is non
with_pair
set
{
f2
,
f1
,
f3
}
\/
{
f3
,
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f3
,
f1
}
is non
with_pair
set
{
f3
}
is non
with_pair
set
{
f1
}
is non
with_pair
set
{
f3
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
(
{
f3
}
\/
{
f1
}
)
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f3
}
is non
with_pair
set
(
{
f1
,
f2
,
f3
}
\/
{
f3
}
)
\/
{
f1
}
is non
with_pair
set
{
f3
,
f1
,
f2
}
is non
with_pair
set
{
f3
,
f1
,
f2
}
\/
{
f3
}
is non
with_pair
set
(
{
f3
,
f1
,
f2
}
\/
{
f3
}
)
\/
{
f1
}
is non
with_pair
set
{
f3
,
f3
,
f1
,
f2
}
is
set
{
f3
,
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f1
,
f2
,
f3
}
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
1GateCircuit
(
f2
,
f3
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
(
1GateCircuit
(
f1
,
f2
,
and2
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
1GateCircuit
(
f3
,
f1
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
(
(
1GateCircuit
(
f1
,
f2
,
and2
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
the
Sorts
of (
f1
,
f2
,
f3
) is
Relation-like
the
carrier
of (
f1
,
f2
,
f3
)
-defined
Function-like
V23
( the
carrier
of (
f1
,
f2
,
f3
))
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K230
( the
Sorts
of (
f1
,
f2
,
f3
)) is
functional
V49
()
V50
()
set
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
z
.
f1
is
set
z
.
f2
is
set
z
.
f3
is
set
Following
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
(
Following
z
)
.
[
<*
f1
,
f2
*>
,
and2
]
is
set
(
Following
z
)
.
[
<*
f2
,
f3
*>
,
and2
]
is
set
(
Following
z
)
.
[
<*
f3
,
f1
*>
,
and2
]
is
set
S1
is
boolean
Element
of
BOOLEAN
A1
is
boolean
Element
of
BOOLEAN
s1
is
boolean
Element
of
BOOLEAN
S1
'&'
A1
is
boolean
Element
of
BOOLEAN
K111
(
S1
,
A1
) is
set
A1
'&'
s1
is
boolean
Element
of
BOOLEAN
K111
(
A1
,
s1
) is
set
s1
'&'
S1
is
boolean
Element
of
BOOLEAN
K111
(
s1
,
S1
) is
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
proj1
z
is
set
<*
f1
,
f2
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
and2
.
(
<*
f1
,
f2
*>
*
z
)
is
boolean
set
<*
S1
,
A1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2
.
<*
S1
,
A1
*>
is
boolean
set
<*
f2
,
f3
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
and2
.
(
<*
f2
,
f3
*>
*
z
)
is
boolean
set
<*
A1
,
s1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2
.
<*
A1
,
s1
*>
is
boolean
set
<*
f3
,
f1
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
and2
.
(
<*
f3
,
f1
*>
*
z
)
is
boolean
set
<*
s1
,
S1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2
.
<*
s1
,
S1
*>
is
boolean
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
1GateCircuit
(
f2
,
f3
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
(
1GateCircuit
(
f1
,
f2
,
and2
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
1GateCircuit
(
f3
,
f1
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
(
(
1GateCircuit
(
f1
,
f2
,
and2
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
the
Sorts
of (
f1
,
f2
,
f3
) is
Relation-like
the
carrier
of (
f1
,
f2
,
f3
)
-defined
Function-like
V23
( the
carrier
of (
f1
,
f2
,
f3
))
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K230
( the
Sorts
of (
f1
,
f2
,
f3
)) is
functional
V49
()
V50
()
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
A
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
A
.
[
<*
f1
,
f2
*>
,
and2
]
is
set
A
.
[
<*
f2
,
f3
*>
,
and2
]
is
set
A
.
[
<*
f3
,
f1
*>
,
and2
]
is
set
Following
A
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
(
Following
A
)
.
(
f1
,
f2
,
f3
) is
boolean
Element
of
BOOLEAN
A1
is
boolean
Element
of
BOOLEAN
s1
is
boolean
Element
of
BOOLEAN
A2
is
boolean
Element
of
BOOLEAN
A1
'or'
s1
is
boolean
Element
of
BOOLEAN
'not'
A1
is
boolean
set
K114
(1,
A1
) is
set
'not'
s1
is
boolean
set
K114
(1,
s1
) is
set
(
'not'
A1
)
'&'
(
'not'
s1
)
is
set
K111
(
(
'not'
A1
)
,
(
'not'
s1
)
) is
set
'not'
(
(
'not'
A1
)
'&'
(
'not'
s1
)
)
is
boolean
set
(
A1
'or'
s1
)
'or'
A2
is
boolean
Element
of
BOOLEAN
'not'
(
A1
'or'
s1
)
is
boolean
set
K114
(1,
(
A1
'or'
s1
)
) is
set
'not'
A2
is
boolean
set
K114
(1,
A2
) is
set
(
'not'
(
A1
'or'
s1
)
)
'&'
(
'not'
A2
)
is
set
K111
(
(
'not'
(
A1
'or'
s1
)
)
,
(
'not'
A2
)
) is
set
'not'
(
(
'not'
(
A1
'or'
s1
)
)
'&'
(
'not'
A2
)
)
is
boolean
set
proj1
A
is
set
t
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
S
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
a
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
<*
t
,
S
,
a
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
<*
t
,
S
,
a
*>
*
A
is
Relation-like
NAT
-defined
Function-like
set
or3
.
(
<*
t
,
S
,
a
*>
*
A
)
is
boolean
set
<*
A1
,
s1
,
A2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
or3
.
<*
A1
,
s1
,
A2
*>
is
boolean
set
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
and2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
and2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,
and2
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
and2
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
and2
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
1GateCircuit
(
f0
,
x
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
1GateCircuit
(
<*
f0
,
x
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
1GateCircuit
(
x
,
y
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
1GateCircuit
(
<*
x
,
y
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
(
1GateCircuit
(
f0
,
x
,
and2
)
)
+*
(
1GateCircuit
(
x
,
y
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
1GateCircuit
(
y
,
f0
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
1GateCircuit
(
<*
y
,
f0
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
(
(
1GateCircuit
(
f0
,
x
,
and2
)
)
+*
(
1GateCircuit
(
x
,
y
,
and2
)
)
)
+*
(
1GateCircuit
(
y
,
f0
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
(
f0
,
x
,
y
)
+*
(
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
the
Sorts
of (
f0
,
x
,
y
) is
Relation-like
the
carrier
of (
f0
,
x
,
y
)
-defined
Function-like
V23
( the
carrier
of (
f0
,
x
,
y
))
set
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K230
( the
Sorts
of (
f0
,
x
,
y
)) is
functional
V49
()
V50
()
set
(
f0
,
x
,
y
) is
Element
of
InnerVertices
(
f0
,
x
,
y
)
InnerVertices
(
f0
,
x
,
y
) is non
empty
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
[
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
}
}
is
set
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
S1
.
f0
is
set
S1
.
x
is
set
S1
.
y
is
set
Following
(
S1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
(
Following
(
S1
,2)
)
.
(
f0
,
x
,
y
) is
boolean
Element
of
BOOLEAN
(
Following
(
S1
,2)
)
.
[
<*
f0
,
x
*>
,
and2
]
is
set
(
Following
(
S1
,2)
)
.
[
<*
x
,
y
*>
,
and2
]
is
set
(
Following
(
S1
,2)
)
.
[
<*
y
,
f0
*>
,
and2
]
is
set
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
Following
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
s
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
s
is
boolean
Element
of
BOOLEAN
S2
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
S2
is
boolean
Element
of
BOOLEAN
Following
(
Following
S1
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
s2
is
boolean
Element
of
BOOLEAN
t
is
boolean
Element
of
BOOLEAN
S
is
boolean
Element
of
BOOLEAN
s2
'&'
t
is
boolean
Element
of
BOOLEAN
K111
(
s2
,
t
) is
set
t
'&'
S
is
boolean
Element
of
BOOLEAN
K111
(
t
,
S
) is
set
(
s2
'&'
t
)
'or'
(
t
'&'
S
)
is
boolean
Element
of
BOOLEAN
'not'
(
s2
'&'
t
)
is
boolean
set
K114
(1,
(
s2
'&'
t
)
) is
set
'not'
(
t
'&'
S
)
is
boolean
set
K114
(1,
(
t
'&'
S
)
) is
set
(
'not'
(
s2
'&'
t
)
)
'&'
(
'not'
(
t
'&'
S
)
)
is
set
K111
(
(
'not'
(
s2
'&'
t
)
)
,
(
'not'
(
t
'&'
S
)
)
) is
set
'not'
(
(
'not'
(
s2
'&'
t
)
)
'&'
(
'not'
(
t
'&'
S
)
)
)
is
boolean
set
S
'&'
s2
is
boolean
Element
of
BOOLEAN
K111
(
S
,
s2
) is
set
(
(
s2
'&'
t
)
'or'
(
t
'&'
S
)
)
'or'
(
S
'&'
s2
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
s2
'&'
t
)
'or'
(
t
'&'
S
)
)
is
boolean
set
K114
(1,
(
(
s2
'&'
t
)
'or'
(
t
'&'
S
)
)
) is
set
'not'
(
S
'&'
s2
)
is
boolean
set
K114
(1,
(
S
'&'
s2
)
) is
set
(
'not'
(
(
s2
'&'
t
)
'or'
(
t
'&'
S
)
)
)
'&'
(
'not'
(
S
'&'
s2
)
)
is
set
K111
(
(
'not'
(
(
s2
'&'
t
)
'or'
(
t
'&'
S
)
)
)
,
(
'not'
(
S
'&'
s2
)
)
) is
set
'not'
(
(
'not'
(
(
s2
'&'
t
)
'or'
(
t
'&'
S
)
)
)
'&'
(
'not'
(
S
'&'
s2
)
)
)
is
boolean
set
(
Following
S1
)
.
[
<*
y
,
f0
*>
,
and2
]
is
set
(
Following
S1
)
.
[
<*
f0
,
x
*>
,
and2
]
is
set
(
Following
S1
)
.
[
<*
x
,
y
*>
,
and2
]
is
set
A
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
A
is
boolean
Element
of
BOOLEAN
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
and2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
and2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,
and2
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
and2
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
and2
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
1GateCircuit
(
f0
,
x
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
1GateCircuit
(
<*
f0
,
x
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
1GateCircuit
(
x
,
y
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
1GateCircuit
(
<*
x
,
y
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
(
1GateCircuit
(
f0
,
x
,
and2
)
)
+*
(
1GateCircuit
(
x
,
y
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
1GateCircuit
(
y
,
f0
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
1GateCircuit
(
<*
y
,
f0
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
(
(
1GateCircuit
(
f0
,
x
,
and2
)
)
+*
(
1GateCircuit
(
x
,
y
,
and2
)
)
)
+*
(
1GateCircuit
(
y
,
f0
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
(
f0
,
x
,
y
)
+*
(
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
the
Sorts
of (
f0
,
x
,
y
) is
Relation-like
the
carrier
of (
f0
,
x
,
y
)
-defined
Function-like
V23
( the
carrier
of (
f0
,
x
,
y
))
set
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K230
( the
Sorts
of (
f0
,
x
,
y
)) is
functional
V49
()
V50
()
set
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
(
S1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
A
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
A
is
boolean
Element
of
BOOLEAN
s
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
s
is
boolean
Element
of
BOOLEAN
S2
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
S2
is
boolean
Element
of
BOOLEAN
Following
(
Following
(
S1
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
(
Following
S1
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
(
Following
S1
)
.
y
is
set
(
Following
(
S1
,2)
)
.
y
is
set
(
Following
S1
)
.
x
is
set
(
Following
(
S1
,2)
)
.
x
is
set
(
Following
S1
)
.
f0
is
set
(
Following
(
S1
,2)
)
.
f0
is
set
S1
.
y
is
set
(
Following
(
S1
,2)
)
.
[
<*
f0
,
x
*>
,
and2
]
is
set
(
S1
.
A
)
'&'
(
S1
.
s
)
is
boolean
Element
of
BOOLEAN
K111
(
(
S1
.
A
)
,
(
S1
.
s
)
) is
set
S1
.
x
is
set
(
Following
(
S1
,2)
)
.
[
<*
y
,
f0
*>
,
and2
]
is
set
(
S1
.
A
)
'&'
(
S1
.
S2
)
is
boolean
Element
of
BOOLEAN
K111
(
(
S1
.
A
)
,
(
S1
.
S2
)
) is
set
S1
.
f0
is
set
(
Following
(
S1
,2)
)
.
[
<*
x
,
y
*>
,
and2
]
is
set
(
S1
.
s
)
'&'
(
S1
.
S2
)
is
boolean
Element
of
BOOLEAN
K111
(
(
S1
.
s
)
,
(
S1
.
S2
)
) is
set
(
f0
,
x
,
y
) is
Element
of
InnerVertices
(
f0
,
x
,
y
)
InnerVertices
(
f0
,
x
,
y
) is non
empty
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
[
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
}
}
is
set
(
Following
(
S1
,2)
)
.
(
f0
,
x
,
y
) is
boolean
Element
of
BOOLEAN
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
is
boolean
set
K114
(1,
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
) is
set
'not'
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
is
boolean
set
K114
(1,
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
) is
set
(
'not'
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
)
'&'
(
'not'
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
)
is
set
K111
(
(
'not'
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
)
,
(
'not'
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
)
) is
set
'not'
(
(
'not'
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
)
'&'
(
'not'
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
)
)
is
boolean
set
(
S1
.
S2
)
'&'
(
S1
.
A
)
is
boolean
Element
of
BOOLEAN
K111
(
(
S1
.
S2
)
,
(
S1
.
A
)
) is
set
(
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
)
'or'
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
)
is
boolean
set
K114
(1,
(
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
)
) is
set
'not'
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
is
boolean
set
K114
(1,
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
) is
set
(
'not'
(
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
)
)
'&'
(
'not'
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
)
is
set
K111
(
(
'not'
(
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
)
)
,
(
'not'
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
)
) is
set
'not'
(
(
'not'
(
(
(
S1
.
A
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
S1
.
S2
)
)
)
)
'&'
(
'not'
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
)
)
is
boolean
set
a
is
set
v
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
InputVertices
(
f0
,
x
,
y
)
)
\/
(
InnerVertices
(
f0
,
x
,
y
)
)
is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
(
Following
(
S1
,2)
)
.
a
is
set
(
Following
(
Following
(
S1
,2)
)
)
.
a
is
set
{
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
}
is
Relation-like
set
{
(
f0
,
x
,
y
)
}
is
set
{
[
<*
f0
,
x
*>
,
and2
]
,
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
f0
*>
,
and2
]
}
\/
{
(
f0
,
x
,
y
)
}
is
set
proj1
(
Following
(
Following
(
S1
,2)
)
)
is
set
proj1
(
Following
(
S1
,2)
)
is
set
f1
is
set
f2
is
set
f3
is
set
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
2GatesCircuit
(
f1
,
f2
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircuit
(
f1
,
f2
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
1GateCircuit
(
<*
f1
,
f2
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
(
1GateCircuit
(
f1
,
f2
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,
xor2
]
}
is
Relation-like
Function-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
)
}
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
x
is
set
f0
is
set
y
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f0
,
x
,
y
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f0
,
x
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f0
,
x
*>
,
xor2
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
xor2
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
xor2
}
,
{
<*
f0
,
x
*>
}
}
is
set
<*
[
<*
f0
,
x
*>
,
xor2
]
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
xor2
]
,
y
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
xor2
]
,
y
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
s
is
set
z
is
set
A
is
set
(
z
,
A
,
s
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
z
,
A
,
s
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
z
,
A
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
z
,
A
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
z
,
A
*>
,
xor2
]
is non
empty
pair
set
{
<*
z
,
A
*>
,
xor2
}
is
functional
set
{
<*
z
,
A
*>
}
is
functional
V49
()
set
{
{
<*
z
,
A
*>
,
xor2
}
,
{
<*
z
,
A
*>
}
}
is
set
<*
[
<*
z
,
A
*>
,
xor2
]
,
s
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
z
,
A
*>
,
xor2
]
,
s
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
z
,
A
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
z
,
A
*>
,
xor2
]
,
s
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
z
,
A
,
s
) is non
empty
set
S2
is
set
S1
is
set
<*
S2
,
S1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
S2
,
S1
*>
,
xor2
]
is non
empty
pair
set
{
<*
S2
,
S1
*>
,
xor2
}
is
functional
set
{
<*
S2
,
S1
*>
}
is
functional
V49
()
set
{
{
<*
S2
,
S1
*>
,
xor2
}
,
{
<*
S2
,
S1
*>
}
}
is
set
A1
is
set
(
S2
,
S1
,
A1
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
S2
,
S1
,
A1
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
S2
,
S1
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
S2
,
S1
*>
,
xor2
]
,
A1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
S2
,
S1
*>
,
xor2
]
,
A1
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
S2
,
S1
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
S2
,
S1
*>
,
xor2
]
,
A1
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
S2
,
S1
,
A1
) is non
empty
set
s1
is
set
A2
is
set
<*
s1
,
A2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
s1
,
A2
*>
,
xor2
]
is non
empty
pair
set
{
<*
s1
,
A2
*>
,
xor2
}
is
functional
set
{
<*
s1
,
A2
*>
}
is
functional
V49
()
set
{
{
<*
s1
,
A2
*>
,
xor2
}
,
{
<*
s1
,
A2
*>
}
}
is
set
s2
is
set
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
,
xor2
}
is
functional
set
{
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
,
xor2
}
,
{
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
}
}
is
set
(
s1
,
A2
,
s2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
s1
,
A2
,
s2
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
s1
,
A2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
s1
,
A2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
s1
,
A2
,
s2
) is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
}
is
Relation-like
Function-like
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
)
}
is
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
xor2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
xor2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f2
,
f3
,
f0
) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
the
carrier
of (
f2
,
f3
,
f0
)
\
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
{
f2
,
f3
,
f0
}
is
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
xor2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
xor2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
1GateCircuit
(
f2
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
(
1GateCircuit
(
f2
,
f3
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
z
.
f2
is
set
z
.
f3
is
set
z
.
f0
is
set
Following
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
z
)
.
[
<*
f2
,
f3
*>
,
xor2
]
is
set
(
Following
z
)
.
f2
is
set
(
Following
z
)
.
f3
is
set
(
Following
z
)
.
f0
is
set
A
is
boolean
Element
of
BOOLEAN
s
is
boolean
Element
of
BOOLEAN
S2
is
boolean
Element
of
BOOLEAN
A
'xor'
s
is
boolean
Element
of
BOOLEAN
K222
(
A
,
s
) is
set
K221
(
A
,
s
) is
set
'not'
A
is
boolean
set
K114
(1,
A
) is
set
K220
(
(
'not'
A
)
,
s
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
'not'
s
is
boolean
set
K114
(1,
s
) is
set
(
'not'
(
'not'
A
)
)
'&'
(
'not'
s
)
is
set
K111
(
(
'not'
(
'not'
A
)
)
,
(
'not'
s
)
) is
set
'not'
(
(
'not'
(
'not'
A
)
)
'&'
(
'not'
s
)
)
is
boolean
set
K221
(
s
,
A
) is
set
K220
(
(
'not'
s
)
,
A
) is
set
'not'
(
'not'
s
)
is
boolean
set
K114
(1,
(
'not'
s
)
) is
set
(
'not'
(
'not'
s
)
)
'&'
(
'not'
A
)
is
set
K111
(
(
'not'
(
'not'
s
)
)
,
(
'not'
A
)
) is
set
'not'
(
(
'not'
(
'not'
s
)
)
'&'
(
'not'
A
)
)
is
boolean
set
K221
(
A
,
s
)
'&'
K221
(
s
,
A
) is
set
'not'
K222
(
A
,
s
) is
boolean
set
<*
A
,
s
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
A
,
s
*>
is
boolean
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
xor2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
xor2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
1GateCircuit
(
f2
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
(
1GateCircuit
(
f2
,
f3
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
2GatesCircOutput
(
f2
,
f3
,
f0
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
[
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
}
,
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
}
}
is
set
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
z
.
[
<*
f2
,
f3
*>
,
xor2
]
is
set
z
.
f0
is
set
Following
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
z
)
.
(
f2
,
f3
,
f0
) is
boolean
Element
of
BOOLEAN
A
is
boolean
Element
of
BOOLEAN
S1
is
boolean
Element
of
BOOLEAN
A
'xor'
S1
is
boolean
Element
of
BOOLEAN
K222
(
A
,
S1
) is
set
K221
(
A
,
S1
) is
set
'not'
A
is
boolean
set
K114
(1,
A
) is
set
K220
(
(
'not'
A
)
,
S1
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
'not'
S1
is
boolean
set
K114
(1,
S1
) is
set
(
'not'
(
'not'
A
)
)
'&'
(
'not'
S1
)
is
set
K111
(
(
'not'
(
'not'
A
)
)
,
(
'not'
S1
)
) is
set
'not'
(
(
'not'
(
'not'
A
)
)
'&'
(
'not'
S1
)
)
is
boolean
set
K221
(
S1
,
A
) is
set
K220
(
(
'not'
S1
)
,
A
) is
set
'not'
(
'not'
S1
)
is
boolean
set
K114
(1,
(
'not'
S1
)
) is
set
(
'not'
(
'not'
S1
)
)
'&'
(
'not'
A
)
is
set
K111
(
(
'not'
(
'not'
S1
)
)
,
(
'not'
A
)
) is
set
'not'
(
(
'not'
(
'not'
S1
)
)
'&'
(
'not'
A
)
)
is
boolean
set
K221
(
A
,
S1
)
'&'
K221
(
S1
,
A
) is
set
'not'
K222
(
A
,
S1
) is
boolean
set
<*
(
z
.
[
<*
f2
,
f3
*>
,
xor2
]
)
,
(
z
.
f0
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
(
z
.
[
<*
f2
,
f3
*>
,
xor2
]
)
,
(
z
.
f0
)
*>
is
boolean
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
xor2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
xor2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
1GateCircuit
(
f2
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
(
1GateCircuit
(
f2
,
f3
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
2GatesCircOutput
(
f2
,
f3
,
f0
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
[
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
}
,
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
}
}
is
set
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
z
.
f2
is
set
z
.
f3
is
set
z
.
f0
is
set
Following
(
z
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
(
z
,2)
)
.
(
f2
,
f3
,
f0
) is
boolean
Element
of
BOOLEAN
(
Following
(
z
,2)
)
.
[
<*
f2
,
f3
*>
,
xor2
]
is
set
(
Following
(
z
,2)
)
.
f2
is
set
(
Following
(
z
,2)
)
.
f3
is
set
(
Following
(
z
,2)
)
.
f0
is
set
A
is
boolean
Element
of
BOOLEAN
s
is
boolean
Element
of
BOOLEAN
S2
is
boolean
Element
of
BOOLEAN
A
'xor'
s
is
boolean
Element
of
BOOLEAN
K222
(
A
,
s
) is
set
K221
(
A
,
s
) is
set
'not'
A
is
boolean
set
K114
(1,
A
) is
set
K220
(
(
'not'
A
)
,
s
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
'not'
s
is
boolean
set
K114
(1,
s
) is
set
(
'not'
(
'not'
A
)
)
'&'
(
'not'
s
)
is
set
K111
(
(
'not'
(
'not'
A
)
)
,
(
'not'
s
)
) is
set
'not'
(
(
'not'
(
'not'
A
)
)
'&'
(
'not'
s
)
)
is
boolean
set
K221
(
s
,
A
) is
set
K220
(
(
'not'
s
)
,
A
) is
set
'not'
(
'not'
s
)
is
boolean
set
K114
(1,
(
'not'
s
)
) is
set
(
'not'
(
'not'
s
)
)
'&'
(
'not'
A
)
is
set
K111
(
(
'not'
(
'not'
s
)
)
,
(
'not'
A
)
) is
set
'not'
(
(
'not'
(
'not'
s
)
)
'&'
(
'not'
A
)
)
is
boolean
set
K221
(
A
,
s
)
'&'
K221
(
s
,
A
) is
set
'not'
K222
(
A
,
s
) is
boolean
set
(
A
'xor'
s
)
'xor'
S2
is
boolean
Element
of
BOOLEAN
K222
(
(
A
'xor'
s
)
,
S2
) is
set
K221
(
(
A
'xor'
s
)
,
S2
) is
set
'not'
(
A
'xor'
s
)
is
boolean
set
K114
(1,
(
A
'xor'
s
)
) is
set
K220
(
(
'not'
(
A
'xor'
s
)
)
,
S2
) is
set
'not'
(
'not'
(
A
'xor'
s
)
)
is
boolean
set
K114
(1,
(
'not'
(
A
'xor'
s
)
)
) is
set
'not'
S2
is
boolean
set
K114
(1,
S2
) is
set
(
'not'
(
'not'
(
A
'xor'
s
)
)
)
'&'
(
'not'
S2
)
is
set
K111
(
(
'not'
(
'not'
(
A
'xor'
s
)
)
)
,
(
'not'
S2
)
) is
set
'not'
(
(
'not'
(
'not'
(
A
'xor'
s
)
)
)
'&'
(
'not'
S2
)
)
is
boolean
set
K221
(
S2
,
(
A
'xor'
s
)
) is
set
K220
(
(
'not'
S2
)
,
(
A
'xor'
s
)
) is
set
'not'
(
'not'
S2
)
is
boolean
set
K114
(1,
(
'not'
S2
)
) is
set
(
'not'
(
'not'
S2
)
)
'&'
(
'not'
(
A
'xor'
s
)
)
is
set
K111
(
(
'not'
(
'not'
S2
)
)
,
(
'not'
(
A
'xor'
s
)
)
) is
set
'not'
(
(
'not'
(
'not'
S2
)
)
'&'
(
'not'
(
A
'xor'
s
)
)
)
is
boolean
set
K221
(
(
A
'xor'
s
)
,
S2
)
'&'
K221
(
S2
,
(
A
'xor'
s
)
) is
set
'not'
K222
(
(
A
'xor'
s
)
,
S2
) is
boolean
set
<*
A
,
s
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
A
,
s
*>
is
boolean
set
<*
(
xor2
.
<*
A
,
s
*>
)
,
S2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
(
xor2
.
<*
A
,
s
*>
)
,
S2
*>
is
boolean
set
<*
(
A
'xor'
s
)
,
S2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
xor2
.
<*
(
A
'xor'
s
)
,
S2
*>
is
boolean
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
2GatesCircuit
(
f1
,
f2
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
1GateCircuit
(
f1
,
f2
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
1GateCircuit
(
<*
f1
,
f2
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
(
1GateCircuit
(
f1
,
f2
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
1GateCircuit
(
f2
,
f3
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
(
1GateCircuit
(
f1
,
f2
,
and2
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
1GateCircuit
(
f3
,
f1
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
(
(
1GateCircuit
(
f1
,
f2
,
and2
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,
xor2
]
}
is
Relation-like
Function-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
(
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
InnerVertices
(
f1
,
f2
,
f3
)
)
\/
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
(
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
xor2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
xor2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
xor2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
\/
{
f1
,
f2
,
f3
}
is non
with_pair
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
}
is
Relation-like
Function-like
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
(
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
)
}
\/
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
set
(
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
)
}
\/
{
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
,(
f1
,
f2
,
f3
)
}
is
set
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
xor2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
xor2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
xor2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2
]
,
[
<*
f2
,
f3
*>
,
and2
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
xor2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
xor2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
xor2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
2GatesCircuit
(
x
,
y
,
z
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
1GateCircuit
(
x
,
y
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
1GateCircuit
(
<*
x
,
y
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
1GateCircuit
(
[
<*
x
,
y
*>
,
xor2
]
,
z
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
(
1GateCircuit
(
x
,
y
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,
xor2
]
,
z
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
1GateCircuit
(
x
,
y
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
1GateCircuit
(
<*
x
,
y
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
1GateCircuit
(
y
,
z
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
1GateCircuit
(
<*
y
,
z
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
(
1GateCircuit
(
x
,
y
,
and2
)
)
+*
(
1GateCircuit
(
y
,
z
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
1GateCircuit
(
z
,
x
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
1GateCircuit
(
<*
z
,
x
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
(
(
1GateCircuit
(
x
,
y
,
and2
)
)
+*
(
1GateCircuit
(
y
,
z
,
and2
)
)
)
+*
(
1GateCircuit
(
z
,
x
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
1GateCircuit
(
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
(
x
,
y
,
z
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
(
x
,
y
,
z
) is
Element
of
InnerVertices
(
x
,
y
,
z
)
the
carrier
of (
x
,
y
,
z
) is non
empty
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
2GatesCircOutput
(
x
,
y
,
z
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
)
[
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
}
is
functional
set
{
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
}
,
{
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
}
}
is
set
(
x
,
y
,
z
) is
Element
of
InnerVertices
(
x
,
y
,
z
)
the
carrier
of (
x
,
y
,
z
) is non
empty
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
[
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
}
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
s1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
s1
.
x
is
set
s1
.
y
is
set
s1
.
z
is
set
Following
(
s1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
s1
,2)
)
.
(
x
,
y
,
z
) is
set
(
Following
(
s1
,2)
)
.
(
x
,
y
,
z
) is
set
A2
is
boolean
Element
of
BOOLEAN
s2
is
boolean
Element
of
BOOLEAN
t
is
boolean
Element
of
BOOLEAN
A2
'xor'
s2
is
boolean
Element
of
BOOLEAN
K222
(
A2
,
s2
) is
set
K221
(
A2
,
s2
) is
set
'not'
A2
is
boolean
set
K114
(1,
A2
) is
set
K220
(
(
'not'
A2
)
,
s2
) is
set
'not'
(
'not'
A2
)
is
boolean
set
K114
(1,
(
'not'
A2
)
) is
set
'not'
s2
is
boolean
set
K114
(1,
s2
) is
set
(
'not'
(
'not'
A2
)
)
'&'
(
'not'
s2
)
is
set
K111
(
(
'not'
(
'not'
A2
)
)
,
(
'not'
s2
)
) is
set
'not'
(
(
'not'
(
'not'
A2
)
)
'&'
(
'not'
s2
)
)
is
boolean
set
K221
(
s2
,
A2
) is
set
K220
(
(
'not'
s2
)
,
A2
) is
set
'not'
(
'not'
s2
)
is
boolean
set
K114
(1,
(
'not'
s2
)
) is
set
(
'not'
(
'not'
s2
)
)
'&'
(
'not'
A2
)
is
set
K111
(
(
'not'
(
'not'
s2
)
)
,
(
'not'
A2
)
) is
set
'not'
(
(
'not'
(
'not'
s2
)
)
'&'
(
'not'
A2
)
)
is
boolean
set
K221
(
A2
,
s2
)
'&'
K221
(
s2
,
A2
) is
set
'not'
K222
(
A2
,
s2
) is
boolean
set
(
A2
'xor'
s2
)
'xor'
t
is
boolean
Element
of
BOOLEAN
K222
(
(
A2
'xor'
s2
)
,
t
) is
set
K221
(
(
A2
'xor'
s2
)
,
t
) is
set
'not'
(
A2
'xor'
s2
)
is
boolean
set
K114
(1,
(
A2
'xor'
s2
)
) is
set
K220
(
(
'not'
(
A2
'xor'
s2
)
)
,
t
) is
set
'not'
(
'not'
(
A2
'xor'
s2
)
)
is
boolean
set
K114
(1,
(
'not'
(
A2
'xor'
s2
)
)
) is
set
'not'
t
is
boolean
set
K114
(1,
t
) is
set
(
'not'
(
'not'
(
A2
'xor'
s2
)
)
)
'&'
(
'not'
t
)
is
set
K111
(
(
'not'
(
'not'
(
A2
'xor'
s2
)
)
)
,
(
'not'
t
)
) is
set
'not'
(
(
'not'
(
'not'
(
A2
'xor'
s2
)
)
)
'&'
(
'not'
t
)
)
is
boolean
set
K221
(
t
,
(
A2
'xor'
s2
)
) is
set
K220
(
(
'not'
t
)
,
(
A2
'xor'
s2
)
) is
set
'not'
(
'not'
t
)
is
boolean
set
K114
(1,
(
'not'
t
)
) is
set
(
'not'
(
'not'
t
)
)
'&'
(
'not'
(
A2
'xor'
s2
)
)
is
set
K111
(
(
'not'
(
'not'
t
)
)
,
(
'not'
(
A2
'xor'
s2
)
)
) is
set
'not'
(
(
'not'
(
'not'
t
)
)
'&'
(
'not'
(
A2
'xor'
s2
)
)
)
is
boolean
set
K221
(
(
A2
'xor'
s2
)
,
t
)
'&'
K221
(
t
,
(
A2
'xor'
s2
)
) is
set
'not'
K222
(
(
A2
'xor'
s2
)
,
t
) is
boolean
set
A2
'&'
s2
is
boolean
Element
of
BOOLEAN
K111
(
A2
,
s2
) is
set
s2
'&'
t
is
boolean
Element
of
BOOLEAN
K111
(
s2
,
t
) is
set
(
A2
'&'
s2
)
'or'
(
s2
'&'
t
)
is
boolean
Element
of
BOOLEAN
'not'
(
A2
'&'
s2
)
is
boolean
set
K114
(1,
(
A2
'&'
s2
)
) is
set
'not'
(
s2
'&'
t
)
is
boolean
set
K114
(1,
(
s2
'&'
t
)
) is
set
(
'not'
(
A2
'&'
s2
)
)
'&'
(
'not'
(
s2
'&'
t
)
)
is
set
K111
(
(
'not'
(
A2
'&'
s2
)
)
,
(
'not'
(
s2
'&'
t
)
)
) is
set
'not'
(
(
'not'
(
A2
'&'
s2
)
)
'&'
(
'not'
(
s2
'&'
t
)
)
)
is
boolean
set
t
'&'
A2
is
boolean
Element
of
BOOLEAN
K111
(
t
,
A2
) is
set
(
(
A2
'&'
s2
)
'or'
(
s2
'&'
t
)
)
'or'
(
t
'&'
A2
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
A2
'&'
s2
)
'or'
(
s2
'&'
t
)
)
is
boolean
set
K114
(1,
(
(
A2
'&'
s2
)
'or'
(
s2
'&'
t
)
)
) is
set
'not'
(
t
'&'
A2
)
is
boolean
set
K114
(1,
(
t
'&'
A2
)
) is
set
(
'not'
(
(
A2
'&'
s2
)
'or'
(
s2
'&'
t
)
)
)
'&'
(
'not'
(
t
'&'
A2
)
)
is
set
K111
(
(
'not'
(
(
A2
'&'
s2
)
'or'
(
s2
'&'
t
)
)
)
,
(
'not'
(
t
'&'
A2
)
)
) is
set
'not'
(
(
'not'
(
(
A2
'&'
s2
)
'or'
(
s2
'&'
t
)
)
)
'&'
(
'not'
(
t
'&'
A2
)
)
)
is
boolean
set
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s1
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
S
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
S
is
set
S
.
z
is
set
S
.
y
is
set
the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is
Relation-like
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
-defined
Function-like
V23
( the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
set
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is non
empty
set
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
) is
functional
V49
()
V50
()
set
a
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
Following
(
a
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
a
,2)
)
.
(
x
,
y
,
z
) is
set
Following
(
S
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
S
,2)
)
.
(
x
,
y
,
z
) is
boolean
Element
of
BOOLEAN
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s1
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s2
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
s2
is
set
S
.
x
is
set
(
Following
(
a
,2)
)
.
(
x
,
y
,
z
) is
set
Following
(
s2
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
s2
,2)
)
.
(
x
,
y
,
z
) is
boolean
Element
of
BOOLEAN
s2
.
z
is
set
s2
.
y
is
set
s2
.
x
is
set
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
xor2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
xor2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
xor2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
2GatesCircuit
(
x
,
y
,
z
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
1GateCircuit
(
x
,
y
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
1GateCircuit
(
<*
x
,
y
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
1GateCircuit
(
[
<*
x
,
y
*>
,
xor2
]
,
z
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
(
1GateCircuit
(
x
,
y
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,
xor2
]
,
z
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
1GateCircuit
(
x
,
y
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
1GateCircuit
(
<*
x
,
y
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
1GateCircuit
(
y
,
z
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
1GateCircuit
(
<*
y
,
z
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
(
1GateCircuit
(
x
,
y
,
and2
)
)
+*
(
1GateCircuit
(
y
,
z
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
1GateCircuit
(
z
,
x
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
1GateCircuit
(
<*
z
,
x
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
(
(
1GateCircuit
(
x
,
y
,
and2
)
)
+*
(
1GateCircuit
(
y
,
z
,
and2
)
)
)
+*
(
1GateCircuit
(
z
,
x
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
1GateCircuit
(
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
(
x
,
y
,
z
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2
]
,
[
<*
y
,
z
*>
,
and2
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
Following
(
s1
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
2
+
1 is
V9
()
V10
()
V11
()
V15
() non
pair
Element
of
NAT
Following
(
s1
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s2
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s2
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
Following
(
s2
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s2
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is
Relation-like
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
-defined
Function-like
V23
( the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
set
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is non
empty
set
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
) is
functional
V49
()
V50
()
set
Following
(
s
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
(
Following
(
s
,3)
)
is
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
t
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
Following
(
t
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
t
,2)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
Following
(
s1
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
t
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
t
,3)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
(
Following
(
t
,2)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
Following
(
s2
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
t
,3)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
the
carrier
of (
x
,
y
,
z
)
\/
the
carrier
of (
x
,
y
,
z
) is
set
proj1
(
Following
(
s1
,2)
)
is
set
proj1
(
Following
(
s2
,2)
)
is
set
a
is
set
(
Following
(
s
,2)
)
.
a
is
set
(
Following
(
s1
,2)
)
.
a
is
set
(
Following
(
s
,3)
)
.
a
is
set
(
Following
(
s1
,3)
)
.
a
is
set
(
Following
(
s2
,2)
)
.
a
is
set
(
Following
(
s2
,3)
)
.
a
is
set
Following
(
Following
(
s
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
Following
(
s
,2)
)
)
.
a
is
set
Following
(
s
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
(
Following
(
s
,2)
)
is
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircuit
(
f1
,
f2
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
<*
f1
,
f2
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
f2
,
f3
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2a
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
1GateCircuit
(
f3
,
f1
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
(
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2a
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
<*
f1
,
f2
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
f2
,
f3
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2a
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
1GateCircuit
(
f3
,
f1
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
(
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2a
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Function-like
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
set
the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
))
the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
InnerVertices
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
set
the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
))
the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
, the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
(
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
(
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
(
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Function-like
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is
set
{
f2
,
f3
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
set
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
set
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
)
is
set
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
Function-like
set
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Function-like
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
)
is
set
{
f1
,
f2
}
is
set
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Element
of
K18
(
{
f1
,
f2
}
)
K18
(
{
f1
,
f2
}
) is
set
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
is
set
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
)
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
)
is
set
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
is
Element
of
K18
(
{
f2
,
f3
}
)
K18
(
{
f2
,
f3
}
) is
set
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
is
set
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
)
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
)
is
set
{
f3
,
f1
}
is
set
{
f3
,
f1
}
\
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
is
Element
of
K18
(
{
f3
,
f1
}
)
K18
(
{
f3
,
f1
}
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
{
f3
,
f1
}
\
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
)
is
set
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Element
of
K18
(
{
f3
,
f1
}
)
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
)
is
set
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
is
set
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
)
K18
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
) is
set
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,()
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
)
is
set
{
f1
,
f2
}
\/
{
f2
,
f3
}
is
set
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
)
K18
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
) is
set
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
)
is
set
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f2
,
f3
}
is
set
{
f1
,
f2
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f2
,
f3
}
) is
set
(
{
f1
,
f2
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
f3
,
f1
}
is
set
{
f2
,
f2
,
f1
,
f3
}
is
set
{
f2
,
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
{
f2
,
f2
,
f1
,
f3
}
)
K18
(
{
f2
,
f2
,
f1
,
f3
}
) is
set
(
{
f2
,
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
f3
,
f1
}
is
set
{
f2
,
f1
,
f3
}
is
set
{
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
{
f2
,
f1
,
f3
}
)
K18
(
{
f2
,
f1
,
f3
}
) is
set
(
{
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f3
}
) is
set
(
{
f1
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
}
is
set
{
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
}
\/
{
f1
}
is
set
{
f3
,
f3
,
f1
,
f2
}
is
set
{
f3
,
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
}
is
set
{
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
,
f1
}
is
set
{
f1
,
f1
,
f2
,
f3
}
is
set
f1
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is
set
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
proj2
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
{
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
}
is
Relation-like
Function-like
set
{
f1
,
f2
,
f3
}
\
{
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f3
}
) is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Element
of
K18
(
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
)
K18
(
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
) is
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
f1
,
f2
,
f3
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
(
(
InputVertices
(
f1
,
f2
,
f3
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Relation-like
Element
of
K18
(
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
)
{
f1
,
f2
,
f3
}
\/
(
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
{
f1
,
f2
,
f3
}
\/
{}
is
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
S
is non
empty
pair
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
Function-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
(
InputVertices
(
f1
,
f2
,
f3
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
set
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
proj2
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
set
{
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
}
is
Relation-like
Function-like
set
(
proj2
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
)
\/
{
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
}
is
set
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
,(
f1
,
f2
,
f3
)
}
is
set
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
and2a
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2a
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
and2a
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,()
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,()
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,()
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
{
f0
,
x
,
y
}
is
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
{
f1
,
f2
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
{
f2
,
f3
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
{
f3
,
f1
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
Function-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2a
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
f1
,
f2
,
f3
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
is
set
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
is
set
{
f1
,
f2
,
f2
,
f3
}
is
set
{
f1
,
f2
,
f2
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f2
,
f2
,
f1
,
f3
}
is
set
{
f2
,
f2
,
f1
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f2
,
f1
,
f3
}
is non
with_pair
set
{
f2
,
f1
,
f3
}
\/
{
f3
,
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f3
,
f1
}
is non
with_pair
set
{
f3
}
is non
with_pair
set
{
f1
}
is non
with_pair
set
{
f3
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
(
{
f3
}
\/
{
f1
}
)
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f3
}
is non
with_pair
set
(
{
f1
,
f2
,
f3
}
\/
{
f3
}
)
\/
{
f1
}
is non
with_pair
set
{
f3
,
f1
,
f2
}
is non
with_pair
set
{
f3
,
f1
,
f2
}
\/
{
f3
}
is non
with_pair
set
(
{
f3
,
f1
,
f2
}
\/
{
f3
}
)
\/
{
f1
}
is non
with_pair
set
{
f3
,
f3
,
f1
,
f2
}
is
set
{
f3
,
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f1
,
f2
,
f3
}
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
<*
f1
,
f2
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
f2
,
f3
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2a
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
1GateCircuit
(
f3
,
f1
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
(
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2a
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
the
Sorts
of (
f1
,
f2
,
f3
) is
Relation-like
the
carrier
of (
f1
,
f2
,
f3
)
-defined
Function-like
V23
( the
carrier
of (
f1
,
f2
,
f3
))
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K230
( the
Sorts
of (
f1
,
f2
,
f3
)) is
functional
V49
()
V50
()
set
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
z
.
f1
is
set
z
.
f2
is
set
z
.
f3
is
set
Following
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
(
Following
z
)
.
[
<*
f1
,
f2
*>
,()
]
is
set
(
Following
z
)
.
[
<*
f2
,
f3
*>
,
and2a
]
is
set
(
Following
z
)
.
[
<*
f3
,
f1
*>
,
and2
]
is
set
S1
is
boolean
Element
of
BOOLEAN
A1
is
boolean
Element
of
BOOLEAN
s1
is
boolean
Element
of
BOOLEAN
'not'
A1
is
boolean
Element
of
BOOLEAN
K114
(1,
A1
) is
set
S1
'&'
(
'not'
A1
)
is
boolean
Element
of
BOOLEAN
K111
(
S1
,
(
'not'
A1
)
) is
set
(
'not'
A1
)
'&'
s1
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
A1
)
,
s1
) is
set
s1
'&'
S1
is
boolean
Element
of
BOOLEAN
K111
(
s1
,
S1
) is
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
proj1
z
is
set
<*
f1
,
f2
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
()
.
(
<*
f1
,
f2
*>
*
z
)
is
boolean
set
<*
S1
,
A1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
S1
,
A1
*>
is
boolean
set
<*
f2
,
f3
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
and2a
.
(
<*
f2
,
f3
*>
*
z
)
is
boolean
set
<*
A1
,
s1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2a
.
<*
A1
,
s1
*>
is
boolean
set
<*
f3
,
f1
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
and2
.
(
<*
f3
,
f1
*>
*
z
)
is
boolean
set
<*
s1
,
S1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2
.
<*
s1
,
S1
*>
is
boolean
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
<*
f1
,
f2
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
f2
,
f3
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2a
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
1GateCircuit
(
f3
,
f1
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
(
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2a
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
the
Sorts
of (
f1
,
f2
,
f3
) is
Relation-like
the
carrier
of (
f1
,
f2
,
f3
)
-defined
Function-like
V23
( the
carrier
of (
f1
,
f2
,
f3
))
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K230
( the
Sorts
of (
f1
,
f2
,
f3
)) is
functional
V49
()
V50
()
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
A
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
A
.
[
<*
f1
,
f2
*>
,()
]
is
set
A
.
[
<*
f2
,
f3
*>
,
and2a
]
is
set
A
.
[
<*
f3
,
f1
*>
,
and2
]
is
set
Following
A
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
(
Following
A
)
.
(
f1
,
f2
,
f3
) is
boolean
Element
of
BOOLEAN
A1
is
boolean
Element
of
BOOLEAN
s1
is
boolean
Element
of
BOOLEAN
A2
is
boolean
Element
of
BOOLEAN
A1
'or'
s1
is
boolean
Element
of
BOOLEAN
'not'
A1
is
boolean
set
K114
(1,
A1
) is
set
'not'
s1
is
boolean
set
K114
(1,
s1
) is
set
(
'not'
A1
)
'&'
(
'not'
s1
)
is
set
K111
(
(
'not'
A1
)
,
(
'not'
s1
)
) is
set
'not'
(
(
'not'
A1
)
'&'
(
'not'
s1
)
)
is
boolean
set
(
A1
'or'
s1
)
'or'
A2
is
boolean
Element
of
BOOLEAN
'not'
(
A1
'or'
s1
)
is
boolean
set
K114
(1,
(
A1
'or'
s1
)
) is
set
'not'
A2
is
boolean
set
K114
(1,
A2
) is
set
(
'not'
(
A1
'or'
s1
)
)
'&'
(
'not'
A2
)
is
set
K111
(
(
'not'
(
A1
'or'
s1
)
)
,
(
'not'
A2
)
) is
set
'not'
(
(
'not'
(
A1
'or'
s1
)
)
'&'
(
'not'
A2
)
)
is
boolean
set
proj1
A
is
set
t
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
S
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
a
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
<*
t
,
S
,
a
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
<*
t
,
S
,
a
*>
*
A
is
Relation-like
NAT
-defined
Function-like
set
or3
.
(
<*
t
,
S
,
a
*>
*
A
)
is
boolean
set
<*
A1
,
s1
,
A2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
or3
.
<*
A1
,
s1
,
A2
*>
is
boolean
set
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
and2a
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2a
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
and2a
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,()
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,()
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,()
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
1GateCircuit
(
f0
,
x
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f0
,
x
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,())
1GateCircuit
(
<*
f0
,
x
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,())
1GateCircuit
(
x
,
y
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
1GateCircuit
(
<*
x
,
y
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
(
1GateCircuit
(
f0
,
x
,())
)
+*
(
1GateCircuit
(
x
,
y
,
and2a
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
1GateCircuit
(
y
,
f0
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
1GateCircuit
(
<*
y
,
f0
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
(
(
1GateCircuit
(
f0
,
x
,())
)
+*
(
1GateCircuit
(
x
,
y
,
and2a
)
)
)
+*
(
1GateCircuit
(
y
,
f0
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
1GateCircuit
(
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
(
f0
,
x
,
y
)
+*
(
1GateCircuit
(
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
the
Sorts
of (
f0
,
x
,
y
) is
Relation-like
the
carrier
of (
f0
,
x
,
y
)
-defined
Function-like
V23
( the
carrier
of (
f0
,
x
,
y
))
set
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K230
( the
Sorts
of (
f0
,
x
,
y
)) is
functional
V49
()
V50
()
set
(
f0
,
x
,
y
) is
Element
of
InnerVertices
(
f0
,
x
,
y
)
InnerVertices
(
f0
,
x
,
y
) is non
empty
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
[
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
}
}
is
set
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
S1
.
f0
is
set
S1
.
x
is
set
S1
.
y
is
set
Following
(
S1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
(
Following
(
S1
,2)
)
.
(
f0
,
x
,
y
) is
boolean
Element
of
BOOLEAN
(
Following
(
S1
,2)
)
.
[
<*
f0
,
x
*>
,()
]
is
set
(
Following
(
S1
,2)
)
.
[
<*
x
,
y
*>
,
and2a
]
is
set
(
Following
(
S1
,2)
)
.
[
<*
y
,
f0
*>
,
and2
]
is
set
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
Following
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
s
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
s
is
boolean
Element
of
BOOLEAN
S2
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
S2
is
boolean
Element
of
BOOLEAN
Following
(
Following
S1
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
s2
is
boolean
Element
of
BOOLEAN
t
is
boolean
Element
of
BOOLEAN
S
is
boolean
Element
of
BOOLEAN
'not'
t
is
boolean
Element
of
BOOLEAN
K114
(1,
t
) is
set
s2
'&'
(
'not'
t
)
is
boolean
Element
of
BOOLEAN
K111
(
s2
,
(
'not'
t
)
) is
set
(
'not'
t
)
'&'
S
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
t
)
,
S
) is
set
(
s2
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
S
)
is
boolean
Element
of
BOOLEAN
'not'
(
s2
'&'
(
'not'
t
)
)
is
boolean
set
K114
(1,
(
s2
'&'
(
'not'
t
)
)
) is
set
'not'
(
(
'not'
t
)
'&'
S
)
is
boolean
set
K114
(1,
(
(
'not'
t
)
'&'
S
)
) is
set
(
'not'
(
s2
'&'
(
'not'
t
)
)
)
'&'
(
'not'
(
(
'not'
t
)
'&'
S
)
)
is
set
K111
(
(
'not'
(
s2
'&'
(
'not'
t
)
)
)
,
(
'not'
(
(
'not'
t
)
'&'
S
)
)
) is
set
'not'
(
(
'not'
(
s2
'&'
(
'not'
t
)
)
)
'&'
(
'not'
(
(
'not'
t
)
'&'
S
)
)
)
is
boolean
set
S
'&'
s2
is
boolean
Element
of
BOOLEAN
K111
(
S
,
s2
) is
set
(
(
s2
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
S
)
)
'or'
(
S
'&'
s2
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
s2
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
S
)
)
is
boolean
set
K114
(1,
(
(
s2
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
S
)
)
) is
set
'not'
(
S
'&'
s2
)
is
boolean
set
K114
(1,
(
S
'&'
s2
)
) is
set
(
'not'
(
(
s2
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
S
)
)
)
'&'
(
'not'
(
S
'&'
s2
)
)
is
set
K111
(
(
'not'
(
(
s2
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
S
)
)
)
,
(
'not'
(
S
'&'
s2
)
)
) is
set
'not'
(
(
'not'
(
(
s2
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
S
)
)
)
'&'
(
'not'
(
S
'&'
s2
)
)
)
is
boolean
set
(
Following
S1
)
.
[
<*
y
,
f0
*>
,
and2
]
is
set
(
Following
S1
)
.
[
<*
f0
,
x
*>
,()
]
is
set
(
Following
S1
)
.
[
<*
x
,
y
*>
,
and2a
]
is
set
A
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
A
is
boolean
Element
of
BOOLEAN
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
and2a
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2a
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
and2a
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,()
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,()
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,()
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
1GateCircuit
(
f0
,
x
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f0
,
x
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,())
1GateCircuit
(
<*
f0
,
x
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,())
1GateCircuit
(
x
,
y
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
1GateCircuit
(
<*
x
,
y
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
(
1GateCircuit
(
f0
,
x
,())
)
+*
(
1GateCircuit
(
x
,
y
,
and2a
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
1GateCircuit
(
y
,
f0
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
1GateCircuit
(
<*
y
,
f0
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
(
(
1GateCircuit
(
f0
,
x
,())
)
+*
(
1GateCircuit
(
x
,
y
,
and2a
)
)
)
+*
(
1GateCircuit
(
y
,
f0
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2
)
)
1GateCircuit
(
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
(
f0
,
x
,
y
)
+*
(
1GateCircuit
(
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
)
)
the
Sorts
of (
f0
,
x
,
y
) is
Relation-like
the
carrier
of (
f0
,
x
,
y
)
-defined
Function-like
V23
( the
carrier
of (
f0
,
x
,
y
))
set
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K230
( the
Sorts
of (
f0
,
x
,
y
)) is
functional
V49
()
V50
()
set
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
(
S1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
A
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
A
is
boolean
Element
of
BOOLEAN
s
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
s
is
boolean
Element
of
BOOLEAN
S2
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
S2
is
boolean
Element
of
BOOLEAN
Following
(
Following
(
S1
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
(
Following
S1
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
(
Following
S1
)
.
y
is
set
(
Following
(
S1
,2)
)
.
y
is
set
(
Following
S1
)
.
x
is
set
(
Following
(
S1
,2)
)
.
x
is
set
(
Following
S1
)
.
f0
is
set
(
Following
(
S1
,2)
)
.
f0
is
set
S1
.
y
is
set
(
Following
(
S1
,2)
)
.
[
<*
f0
,
x
*>
,()
]
is
set
'not'
(
S1
.
s
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
S1
.
s
)
) is
set
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
is
boolean
Element
of
BOOLEAN
K111
(
(
S1
.
A
)
,
(
'not'
(
S1
.
s
)
)
) is
set
S1
.
x
is
set
(
Following
(
S1
,2)
)
.
[
<*
y
,
f0
*>
,
and2
]
is
set
(
S1
.
A
)
'&'
(
S1
.
S2
)
is
boolean
Element
of
BOOLEAN
K111
(
(
S1
.
A
)
,
(
S1
.
S2
)
) is
set
S1
.
f0
is
set
(
Following
(
S1
,2)
)
.
[
<*
x
,
y
*>
,
and2a
]
is
set
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
(
S1
.
s
)
)
,
(
S1
.
S2
)
) is
set
(
f0
,
x
,
y
) is
Element
of
InnerVertices
(
f0
,
x
,
y
)
InnerVertices
(
f0
,
x
,
y
) is non
empty
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
[
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
*>
}
}
is
set
(
Following
(
S1
,2)
)
.
(
f0
,
x
,
y
) is
boolean
Element
of
BOOLEAN
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
is
boolean
set
K114
(1,
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
) is
set
'not'
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
is
boolean
set
K114
(1,
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
) is
set
(
'not'
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
)
'&'
(
'not'
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
)
is
set
K111
(
(
'not'
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
)
,
(
'not'
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
)
) is
set
'not'
(
(
'not'
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
)
'&'
(
'not'
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
)
)
is
boolean
set
(
S1
.
S2
)
'&'
(
S1
.
A
)
is
boolean
Element
of
BOOLEAN
K111
(
(
S1
.
S2
)
,
(
S1
.
A
)
) is
set
(
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
)
'or'
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
)
is
boolean
set
K114
(1,
(
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
)
) is
set
'not'
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
is
boolean
set
K114
(1,
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
) is
set
(
'not'
(
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
)
)
'&'
(
'not'
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
)
is
set
K111
(
(
'not'
(
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
)
)
,
(
'not'
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
)
) is
set
'not'
(
(
'not'
(
(
(
S1
.
A
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
S1
.
S2
)
)
)
)
'&'
(
'not'
(
(
S1
.
S2
)
'&'
(
S1
.
A
)
)
)
)
is
boolean
set
a
is
set
v
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
InputVertices
(
f0
,
x
,
y
)
)
\/
(
InnerVertices
(
f0
,
x
,
y
)
)
is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
(
Following
(
S1
,2)
)
.
a
is
set
(
Following
(
Following
(
S1
,2)
)
)
.
a
is
set
{
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
}
is
Relation-like
set
{
(
f0
,
x
,
y
)
}
is
set
{
[
<*
f0
,
x
*>
,()
]
,
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
f0
*>
,
and2
]
}
\/
{
(
f0
,
x
,
y
)
}
is
set
proj1
(
Following
(
Following
(
S1
,2)
)
)
is
set
proj1
(
Following
(
S1
,2)
)
is
set
f1
is
set
f2
is
set
f3
is
set
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
2GatesCircuit
(
f1
,
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f1
,
f2
,
f3
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f1
,
f2
,
f3
,())
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircuit
(
f1
,
f2
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
<*
f1
,
f2
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
f3
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
)
}
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
x
is
set
f0
is
set
y
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f0
,
x
,
y
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f0
,
x
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f0
,
x
*>
,()
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,()
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,()
}
,
{
<*
f0
,
x
*>
}
}
is
set
<*
[
<*
f0
,
x
*>
,()
]
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
y
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
s
is
set
z
is
set
A
is
set
(
z
,
A
,
s
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
z
,
A
,
s
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
z
,
A
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
z
,
A
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
z
,
A
*>
,()
]
is non
empty
pair
set
{
<*
z
,
A
*>
,()
}
is
functional
set
{
<*
z
,
A
*>
}
is
functional
V49
()
set
{
{
<*
z
,
A
*>
,()
}
,
{
<*
z
,
A
*>
}
}
is
set
<*
[
<*
z
,
A
*>
,()
]
,
s
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
z
,
A
*>
,()
]
,
s
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
z
,
A
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
z
,
A
*>
,()
]
,
s
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
z
,
A
,
s
) is non
empty
set
S2
is
set
S1
is
set
<*
S2
,
S1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
S2
,
S1
*>
,()
]
is non
empty
pair
set
{
<*
S2
,
S1
*>
,()
}
is
functional
set
{
<*
S2
,
S1
*>
}
is
functional
V49
()
set
{
{
<*
S2
,
S1
*>
,()
}
,
{
<*
S2
,
S1
*>
}
}
is
set
A1
is
set
(
S2
,
S1
,
A1
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
S2
,
S1
,
A1
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
S2
,
S1
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
S2
,
S1
*>
,()
]
,
A1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
S2
,
S1
*>
,()
]
,
A1
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
S2
,
S1
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
S2
,
S1
*>
,()
]
,
A1
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
S2
,
S1
,
A1
) is non
empty
set
s1
is
set
A2
is
set
<*
s1
,
A2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
s1
,
A2
*>
,()
]
is non
empty
pair
set
{
<*
s1
,
A2
*>
,()
}
is
functional
set
{
<*
s1
,
A2
*>
}
is
functional
V49
()
set
{
{
<*
s1
,
A2
*>
,()
}
,
{
<*
s1
,
A2
*>
}
}
is
set
s2
is
set
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
,()
}
is
functional
set
{
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
,()
}
,
{
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
}
}
is
set
(
s1
,
A2
,
s2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
s1
,
A2
,
s2
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
s1
,
A2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
s1
,
A2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
s1
,
A2
,
s2
) is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
)
}
is
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f2
,
f3
,
f0
) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
the
carrier
of (
f2
,
f3
,
f0
)
\
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
{
f2
,
f3
,
f0
}
is
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,())
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
(
1GateCircuit
(
f2
,
f3
,())
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
z
.
f2
is
set
z
.
f3
is
set
z
.
f0
is
set
Following
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
z
)
.
[
<*
f2
,
f3
*>
,()
]
is
set
(
Following
z
)
.
f2
is
set
(
Following
z
)
.
f3
is
set
(
Following
z
)
.
f0
is
set
A
is
boolean
Element
of
BOOLEAN
s
is
boolean
Element
of
BOOLEAN
S2
is
boolean
Element
of
BOOLEAN
'not'
s
is
boolean
Element
of
BOOLEAN
K114
(1,
s
) is
set
A
'xor'
(
'not'
s
)
is
boolean
Element
of
BOOLEAN
K222
(
A
,
(
'not'
s
)
) is
set
K221
(
A
,
(
'not'
s
)
) is
set
'not'
A
is
boolean
set
K114
(1,
A
) is
set
K220
(
(
'not'
A
)
,
(
'not'
s
)
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
'not'
(
'not'
s
)
is
boolean
set
K114
(1,
(
'not'
s
)
) is
set
(
'not'
(
'not'
A
)
)
'&'
(
'not'
(
'not'
s
)
)
is
set
K111
(
(
'not'
(
'not'
A
)
)
,
(
'not'
(
'not'
s
)
)
) is
set
'not'
(
(
'not'
(
'not'
A
)
)
'&'
(
'not'
(
'not'
s
)
)
)
is
boolean
set
K221
(
(
'not'
s
)
,
A
) is
set
K220
(
(
'not'
(
'not'
s
)
)
,
A
) is
set
'not'
(
'not'
(
'not'
s
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
s
)
)
) is
set
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
A
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
s
)
)
)
,
(
'not'
A
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
A
)
)
is
boolean
set
K221
(
A
,
(
'not'
s
)
)
'&'
K221
(
(
'not'
s
)
,
A
) is
set
'not'
K222
(
A
,
(
'not'
s
)
) is
boolean
set
<*
A
,
s
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
A
,
s
*>
is
boolean
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,())
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
(
1GateCircuit
(
f2
,
f3
,())
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
2GatesCircOutput
(
f2
,
f3
,
f0
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
[
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
,
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
}
is
set
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
z
.
[
<*
f2
,
f3
*>
,()
]
is
set
z
.
f0
is
set
Following
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
z
)
.
(
f2
,
f3
,
f0
) is
boolean
Element
of
BOOLEAN
A
is
boolean
Element
of
BOOLEAN
S1
is
boolean
Element
of
BOOLEAN
'not'
S1
is
boolean
Element
of
BOOLEAN
K114
(1,
S1
) is
set
A
'xor'
(
'not'
S1
)
is
boolean
Element
of
BOOLEAN
K222
(
A
,
(
'not'
S1
)
) is
set
K221
(
A
,
(
'not'
S1
)
) is
set
'not'
A
is
boolean
set
K114
(1,
A
) is
set
K220
(
(
'not'
A
)
,
(
'not'
S1
)
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
'not'
(
'not'
S1
)
is
boolean
set
K114
(1,
(
'not'
S1
)
) is
set
(
'not'
(
'not'
A
)
)
'&'
(
'not'
(
'not'
S1
)
)
is
set
K111
(
(
'not'
(
'not'
A
)
)
,
(
'not'
(
'not'
S1
)
)
) is
set
'not'
(
(
'not'
(
'not'
A
)
)
'&'
(
'not'
(
'not'
S1
)
)
)
is
boolean
set
K221
(
(
'not'
S1
)
,
A
) is
set
K220
(
(
'not'
(
'not'
S1
)
)
,
A
) is
set
'not'
(
'not'
(
'not'
S1
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
S1
)
)
) is
set
(
'not'
(
'not'
(
'not'
S1
)
)
)
'&'
(
'not'
A
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
S1
)
)
)
,
(
'not'
A
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
S1
)
)
)
'&'
(
'not'
A
)
)
is
boolean
set
K221
(
A
,
(
'not'
S1
)
)
'&'
K221
(
(
'not'
S1
)
,
A
) is
set
'not'
K222
(
A
,
(
'not'
S1
)
) is
boolean
set
<*
(
z
.
[
<*
f2
,
f3
*>
,()
]
)
,
(
z
.
f0
)
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
z
.
[
<*
f2
,
f3
*>
,()
]
)
,
(
z
.
f0
)
*>
is
boolean
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,())
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
(
1GateCircuit
(
f2
,
f3
,())
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
2GatesCircOutput
(
f2
,
f3
,
f0
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
[
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
,
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
}
is
set
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
z
.
f2
is
set
z
.
f3
is
set
z
.
f0
is
set
Following
(
z
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
(
z
,2)
)
.
(
f2
,
f3
,
f0
) is
boolean
Element
of
BOOLEAN
(
Following
(
z
,2)
)
.
[
<*
f2
,
f3
*>
,()
]
is
set
(
Following
(
z
,2)
)
.
f2
is
set
(
Following
(
z
,2)
)
.
f3
is
set
(
Following
(
z
,2)
)
.
f0
is
set
A
is
boolean
Element
of
BOOLEAN
s
is
boolean
Element
of
BOOLEAN
S2
is
boolean
Element
of
BOOLEAN
'not'
s
is
boolean
Element
of
BOOLEAN
K114
(1,
s
) is
set
A
'xor'
(
'not'
s
)
is
boolean
Element
of
BOOLEAN
K222
(
A
,
(
'not'
s
)
) is
set
K221
(
A
,
(
'not'
s
)
) is
set
'not'
A
is
boolean
set
K114
(1,
A
) is
set
K220
(
(
'not'
A
)
,
(
'not'
s
)
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
'not'
(
'not'
s
)
is
boolean
set
K114
(1,
(
'not'
s
)
) is
set
(
'not'
(
'not'
A
)
)
'&'
(
'not'
(
'not'
s
)
)
is
set
K111
(
(
'not'
(
'not'
A
)
)
,
(
'not'
(
'not'
s
)
)
) is
set
'not'
(
(
'not'
(
'not'
A
)
)
'&'
(
'not'
(
'not'
s
)
)
)
is
boolean
set
K221
(
(
'not'
s
)
,
A
) is
set
K220
(
(
'not'
(
'not'
s
)
)
,
A
) is
set
'not'
(
'not'
(
'not'
s
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
s
)
)
) is
set
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
A
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
s
)
)
)
,
(
'not'
A
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
A
)
)
is
boolean
set
K221
(
A
,
(
'not'
s
)
)
'&'
K221
(
(
'not'
s
)
,
A
) is
set
'not'
K222
(
A
,
(
'not'
s
)
) is
boolean
set
'not'
S2
is
boolean
Element
of
BOOLEAN
K114
(1,
S2
) is
set
(
A
'xor'
(
'not'
s
)
)
'xor'
(
'not'
S2
)
is
boolean
Element
of
BOOLEAN
K222
(
(
A
'xor'
(
'not'
s
)
)
,
(
'not'
S2
)
) is
set
K221
(
(
A
'xor'
(
'not'
s
)
)
,
(
'not'
S2
)
) is
set
'not'
(
A
'xor'
(
'not'
s
)
)
is
boolean
set
K114
(1,
(
A
'xor'
(
'not'
s
)
)
) is
set
K220
(
(
'not'
(
A
'xor'
(
'not'
s
)
)
)
,
(
'not'
S2
)
) is
set
'not'
(
'not'
(
A
'xor'
(
'not'
s
)
)
)
is
boolean
set
K114
(1,
(
'not'
(
A
'xor'
(
'not'
s
)
)
)
) is
set
'not'
(
'not'
S2
)
is
boolean
set
K114
(1,
(
'not'
S2
)
) is
set
(
'not'
(
'not'
(
A
'xor'
(
'not'
s
)
)
)
)
'&'
(
'not'
(
'not'
S2
)
)
is
set
K111
(
(
'not'
(
'not'
(
A
'xor'
(
'not'
s
)
)
)
)
,
(
'not'
(
'not'
S2
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
A
'xor'
(
'not'
s
)
)
)
)
'&'
(
'not'
(
'not'
S2
)
)
)
is
boolean
set
K221
(
(
'not'
S2
)
,
(
A
'xor'
(
'not'
s
)
)
) is
set
K220
(
(
'not'
(
'not'
S2
)
)
,
(
A
'xor'
(
'not'
s
)
)
) is
set
'not'
(
'not'
(
'not'
S2
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
S2
)
)
) is
set
(
'not'
(
'not'
(
'not'
S2
)
)
)
'&'
(
'not'
(
A
'xor'
(
'not'
s
)
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
S2
)
)
)
,
(
'not'
(
A
'xor'
(
'not'
s
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
S2
)
)
)
'&'
(
'not'
(
A
'xor'
(
'not'
s
)
)
)
)
is
boolean
set
K221
(
(
A
'xor'
(
'not'
s
)
)
,
(
'not'
S2
)
)
'&'
K221
(
(
'not'
S2
)
,
(
A
'xor'
(
'not'
s
)
)
) is
set
'not'
K222
(
(
A
'xor'
(
'not'
s
)
)
,
(
'not'
S2
)
) is
boolean
set
<*
A
,
s
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
A
,
s
*>
is
boolean
set
<*
(
()
.
<*
A
,
s
*>
)
,
S2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
()
.
<*
A
,
s
*>
)
,
S2
*>
is
boolean
set
<*
(
A
'xor'
(
'not'
s
)
)
,
S2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
(
A
'xor'
(
'not'
s
)
)
,
S2
*>
is
boolean
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,())
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
(
1GateCircuit
(
f2
,
f3
,())
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
2GatesCircOutput
(
f2
,
f3
,
f0
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
[
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
,
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
}
is
set
y
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
y
.
f2
is
set
y
.
f3
is
set
y
.
f0
is
set
Following
(
y
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
(
y
,2)
)
.
(
f2
,
f3
,
f0
) is
boolean
Element
of
BOOLEAN
z
is
boolean
Element
of
BOOLEAN
A
is
boolean
Element
of
BOOLEAN
s
is
boolean
Element
of
BOOLEAN
'not'
A
is
boolean
Element
of
BOOLEAN
K114
(1,
A
) is
set
z
'xor'
(
'not'
A
)
is
boolean
Element
of
BOOLEAN
K222
(
z
,
(
'not'
A
)
) is
set
K221
(
z
,
(
'not'
A
)
) is
set
'not'
z
is
boolean
set
K114
(1,
z
) is
set
K220
(
(
'not'
z
)
,
(
'not'
A
)
) is
set
'not'
(
'not'
z
)
is
boolean
set
K114
(1,
(
'not'
z
)
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
(
'not'
(
'not'
z
)
)
'&'
(
'not'
(
'not'
A
)
)
is
set
K111
(
(
'not'
(
'not'
z
)
)
,
(
'not'
(
'not'
A
)
)
) is
set
'not'
(
(
'not'
(
'not'
z
)
)
'&'
(
'not'
(
'not'
A
)
)
)
is
boolean
set
K221
(
(
'not'
A
)
,
z
) is
set
K220
(
(
'not'
(
'not'
A
)
)
,
z
) is
set
'not'
(
'not'
(
'not'
A
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
A
)
)
) is
set
(
'not'
(
'not'
(
'not'
A
)
)
)
'&'
(
'not'
z
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
A
)
)
)
,
(
'not'
z
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
A
)
)
)
'&'
(
'not'
z
)
)
is
boolean
set
K221
(
z
,
(
'not'
A
)
)
'&'
K221
(
(
'not'
A
)
,
z
) is
set
'not'
K222
(
z
,
(
'not'
A
)
) is
boolean
set
(
z
'xor'
(
'not'
A
)
)
'xor'
s
is
boolean
Element
of
BOOLEAN
K222
(
(
z
'xor'
(
'not'
A
)
)
,
s
) is
set
K221
(
(
z
'xor'
(
'not'
A
)
)
,
s
) is
set
'not'
(
z
'xor'
(
'not'
A
)
)
is
boolean
set
K114
(1,
(
z
'xor'
(
'not'
A
)
)
) is
set
K220
(
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
,
s
) is
set
'not'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
is
boolean
set
K114
(1,
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
) is
set
'not'
s
is
boolean
set
K114
(1,
s
) is
set
(
'not'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
'&'
(
'not'
s
)
is
set
K111
(
(
'not'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
,
(
'not'
s
)
) is
set
'not'
(
(
'not'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
'&'
(
'not'
s
)
)
is
boolean
set
K221
(
s
,
(
z
'xor'
(
'not'
A
)
)
) is
set
K220
(
(
'not'
s
)
,
(
z
'xor'
(
'not'
A
)
)
) is
set
'not'
(
'not'
s
)
is
boolean
set
K114
(1,
(
'not'
s
)
) is
set
(
'not'
(
'not'
s
)
)
'&'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
is
set
K111
(
(
'not'
(
'not'
s
)
)
,
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
s
)
)
'&'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
is
boolean
set
K221
(
(
z
'xor'
(
'not'
A
)
)
,
s
)
'&'
K221
(
s
,
(
z
'xor'
(
'not'
A
)
)
) is
set
'not'
K222
(
(
z
'xor'
(
'not'
A
)
)
,
s
) is
boolean
set
'not'
(
(
z
'xor'
(
'not'
A
)
)
'xor'
s
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
z
'xor'
(
'not'
A
)
)
'xor'
s
)
) is
set
'not'
s
is
boolean
Element
of
BOOLEAN
(
z
'xor'
(
'not'
A
)
)
'xor'
(
'not'
s
)
is
boolean
Element
of
BOOLEAN
K222
(
(
z
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
) is
set
K221
(
(
z
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
) is
set
K220
(
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
,
(
'not'
s
)
) is
set
'not'
(
'not'
s
)
is
boolean
set
K114
(1,
(
'not'
s
)
) is
set
(
'not'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
'&'
(
'not'
(
'not'
s
)
)
is
set
K111
(
(
'not'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
,
(
'not'
(
'not'
s
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
'&'
(
'not'
(
'not'
s
)
)
)
is
boolean
set
K221
(
(
'not'
s
)
,
(
z
'xor'
(
'not'
A
)
)
) is
set
K220
(
(
'not'
(
'not'
s
)
)
,
(
z
'xor'
(
'not'
A
)
)
) is
set
'not'
(
'not'
(
'not'
s
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
s
)
)
) is
set
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
s
)
)
)
,
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
is
boolean
set
K221
(
(
z
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
)
'&'
K221
(
(
'not'
s
)
,
(
z
'xor'
(
'not'
A
)
)
) is
set
'not'
K222
(
(
z
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
) is
boolean
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
2GatesCircuit
(
f1
,
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f1
,
f2
,
f3
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f1
,
f2
,
f3
,())
1GateCircuit
(
f1
,
f2
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
<*
f1
,
f2
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
f3
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
<*
f1
,
f2
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
f2
,
f3
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2a
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
1GateCircuit
(
f3
,
f1
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
(
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2a
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
(
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
InnerVertices
(
f1
,
f2
,
f3
)
)
\/
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
(
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2a
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2a
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2a
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
\/
{
f1
,
f2
,
f3
}
is non
with_pair
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
(
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
)
}
\/
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
set
(
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
)
}
\/
{
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
,(
f1
,
f2
,
f3
)
}
is
set
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2a
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2a
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2a
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2a
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2a
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2a
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
[
<*
f2
,
f3
*>
,
and2a
]
,
[
<*
f3
,
f1
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2a
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2a
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2a
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
2GatesCircuit
(
x
,
y
,
z
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
x
,
y
,
z
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
x
,
y
,
z
,())
1GateCircuit
(
x
,
y
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
<*
x
,
y
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
z
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
1GateCircuit
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
(
1GateCircuit
(
x
,
y
,())
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
z
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
1GateCircuit
(
x
,
y
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
<*
x
,
y
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
y
,
z
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
1GateCircuit
(
<*
y
,
z
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
(
1GateCircuit
(
x
,
y
,())
)
+*
(
1GateCircuit
(
y
,
z
,
and2a
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
1GateCircuit
(
z
,
x
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
1GateCircuit
(
<*
z
,
x
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
(
(
1GateCircuit
(
x
,
y
,())
)
+*
(
1GateCircuit
(
y
,
z
,
and2a
)
)
)
+*
(
1GateCircuit
(
z
,
x
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
(
x
,
y
,
z
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
(
x
,
y
,
z
) is
Element
of
InnerVertices
(
x
,
y
,
z
)
the
carrier
of (
x
,
y
,
z
) is non
empty
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
2GatesCircOutput
(
x
,
y
,
z
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
x
,
y
,
z
,())
)
the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
x
,
y
,
z
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
)
[
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()
}
is
functional
set
{
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()
}
,
{
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
}
}
is
set
(
x
,
y
,
z
) is
Element
of
InnerVertices
(
x
,
y
,
z
)
the
carrier
of (
x
,
y
,
z
) is non
empty
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
[
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
]
is non
empty
pair
set
{
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
}
is
functional
set
{
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
}
,
{
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
}
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
s1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
s1
.
x
is
set
s1
.
y
is
set
s1
.
z
is
set
Following
(
s1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
s1
,2)
)
.
(
x
,
y
,
z
) is
set
(
Following
(
s1
,2)
)
.
(
x
,
y
,
z
) is
set
A2
is
boolean
Element
of
BOOLEAN
s2
is
boolean
Element
of
BOOLEAN
t
is
boolean
Element
of
BOOLEAN
'not'
s2
is
boolean
Element
of
BOOLEAN
K114
(1,
s2
) is
set
A2
'xor'
(
'not'
s2
)
is
boolean
Element
of
BOOLEAN
K222
(
A2
,
(
'not'
s2
)
) is
set
K221
(
A2
,
(
'not'
s2
)
) is
set
'not'
A2
is
boolean
set
K114
(1,
A2
) is
set
K220
(
(
'not'
A2
)
,
(
'not'
s2
)
) is
set
'not'
(
'not'
A2
)
is
boolean
set
K114
(1,
(
'not'
A2
)
) is
set
'not'
(
'not'
s2
)
is
boolean
set
K114
(1,
(
'not'
s2
)
) is
set
(
'not'
(
'not'
A2
)
)
'&'
(
'not'
(
'not'
s2
)
)
is
set
K111
(
(
'not'
(
'not'
A2
)
)
,
(
'not'
(
'not'
s2
)
)
) is
set
'not'
(
(
'not'
(
'not'
A2
)
)
'&'
(
'not'
(
'not'
s2
)
)
)
is
boolean
set
K221
(
(
'not'
s2
)
,
A2
) is
set
K220
(
(
'not'
(
'not'
s2
)
)
,
A2
) is
set
'not'
(
'not'
(
'not'
s2
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
s2
)
)
) is
set
(
'not'
(
'not'
(
'not'
s2
)
)
)
'&'
(
'not'
A2
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
s2
)
)
)
,
(
'not'
A2
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
s2
)
)
)
'&'
(
'not'
A2
)
)
is
boolean
set
K221
(
A2
,
(
'not'
s2
)
)
'&'
K221
(
(
'not'
s2
)
,
A2
) is
set
'not'
K222
(
A2
,
(
'not'
s2
)
) is
boolean
set
(
A2
'xor'
(
'not'
s2
)
)
'xor'
t
is
boolean
Element
of
BOOLEAN
K222
(
(
A2
'xor'
(
'not'
s2
)
)
,
t
) is
set
K221
(
(
A2
'xor'
(
'not'
s2
)
)
,
t
) is
set
'not'
(
A2
'xor'
(
'not'
s2
)
)
is
boolean
set
K114
(1,
(
A2
'xor'
(
'not'
s2
)
)
) is
set
K220
(
(
'not'
(
A2
'xor'
(
'not'
s2
)
)
)
,
t
) is
set
'not'
(
'not'
(
A2
'xor'
(
'not'
s2
)
)
)
is
boolean
set
K114
(1,
(
'not'
(
A2
'xor'
(
'not'
s2
)
)
)
) is
set
'not'
t
is
boolean
set
K114
(1,
t
) is
set
(
'not'
(
'not'
(
A2
'xor'
(
'not'
s2
)
)
)
)
'&'
(
'not'
t
)
is
set
K111
(
(
'not'
(
'not'
(
A2
'xor'
(
'not'
s2
)
)
)
)
,
(
'not'
t
)
) is
set
'not'
(
(
'not'
(
'not'
(
A2
'xor'
(
'not'
s2
)
)
)
)
'&'
(
'not'
t
)
)
is
boolean
set
K221
(
t
,
(
A2
'xor'
(
'not'
s2
)
)
) is
set
K220
(
(
'not'
t
)
,
(
A2
'xor'
(
'not'
s2
)
)
) is
set
'not'
(
'not'
t
)
is
boolean
set
K114
(1,
(
'not'
t
)
) is
set
(
'not'
(
'not'
t
)
)
'&'
(
'not'
(
A2
'xor'
(
'not'
s2
)
)
)
is
set
K111
(
(
'not'
(
'not'
t
)
)
,
(
'not'
(
A2
'xor'
(
'not'
s2
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
t
)
)
'&'
(
'not'
(
A2
'xor'
(
'not'
s2
)
)
)
)
is
boolean
set
K221
(
(
A2
'xor'
(
'not'
s2
)
)
,
t
)
'&'
K221
(
t
,
(
A2
'xor'
(
'not'
s2
)
)
) is
set
'not'
K222
(
(
A2
'xor'
(
'not'
s2
)
)
,
t
) is
boolean
set
'not'
(
(
A2
'xor'
(
'not'
s2
)
)
'xor'
t
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
A2
'xor'
(
'not'
s2
)
)
'xor'
t
)
) is
set
A2
'&'
(
'not'
s2
)
is
boolean
Element
of
BOOLEAN
K111
(
A2
,
(
'not'
s2
)
) is
set
(
'not'
s2
)
'&'
t
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
s2
)
,
t
) is
set
(
A2
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
t
)
is
boolean
Element
of
BOOLEAN
'not'
(
A2
'&'
(
'not'
s2
)
)
is
boolean
set
K114
(1,
(
A2
'&'
(
'not'
s2
)
)
) is
set
'not'
(
(
'not'
s2
)
'&'
t
)
is
boolean
set
K114
(1,
(
(
'not'
s2
)
'&'
t
)
) is
set
(
'not'
(
A2
'&'
(
'not'
s2
)
)
)
'&'
(
'not'
(
(
'not'
s2
)
'&'
t
)
)
is
set
K111
(
(
'not'
(
A2
'&'
(
'not'
s2
)
)
)
,
(
'not'
(
(
'not'
s2
)
'&'
t
)
)
) is
set
'not'
(
(
'not'
(
A2
'&'
(
'not'
s2
)
)
)
'&'
(
'not'
(
(
'not'
s2
)
'&'
t
)
)
)
is
boolean
set
t
'&'
A2
is
boolean
Element
of
BOOLEAN
K111
(
t
,
A2
) is
set
(
(
A2
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
t
)
)
'or'
(
t
'&'
A2
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
A2
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
t
)
)
is
boolean
set
K114
(1,
(
(
A2
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
t
)
)
) is
set
'not'
(
t
'&'
A2
)
is
boolean
set
K114
(1,
(
t
'&'
A2
)
) is
set
(
'not'
(
(
A2
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
t
)
)
)
'&'
(
'not'
(
t
'&'
A2
)
)
is
set
K111
(
(
'not'
(
(
A2
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
t
)
)
)
,
(
'not'
(
t
'&'
A2
)
)
) is
set
'not'
(
(
'not'
(
(
A2
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
t
)
)
)
'&'
(
'not'
(
t
'&'
A2
)
)
)
is
boolean
set
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s1
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
S
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
S
is
set
S
.
z
is
set
S
.
y
is
set
the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is
Relation-like
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
-defined
Function-like
V23
( the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
set
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is non
empty
set
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
) is
functional
V49
()
V50
()
set
a
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
Following
(
a
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
a
,2)
)
.
(
x
,
y
,
z
) is
set
Following
(
S
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
S
,2)
)
.
(
x
,
y
,
z
) is
boolean
Element
of
BOOLEAN
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s1
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s2
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
s2
is
set
S
.
x
is
set
(
Following
(
a
,2)
)
.
(
x
,
y
,
z
) is
set
Following
(
s2
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
s2
,2)
)
.
(
x
,
y
,
z
) is
boolean
Element
of
BOOLEAN
s2
.
z
is
set
s2
.
y
is
set
s2
.
x
is
set
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2a
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2a
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2a
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
2GatesCircuit
(
x
,
y
,
z
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
x
,
y
,
z
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
x
,
y
,
z
,())
1GateCircuit
(
x
,
y
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
<*
x
,
y
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
z
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
1GateCircuit
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
(
1GateCircuit
(
x
,
y
,())
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
z
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
1GateCircuit
(
x
,
y
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
<*
x
,
y
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
y
,
z
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
1GateCircuit
(
<*
y
,
z
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
(
1GateCircuit
(
x
,
y
,())
)
+*
(
1GateCircuit
(
y
,
z
,
and2a
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
1GateCircuit
(
z
,
x
,
and2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
1GateCircuit
(
<*
z
,
x
*>
,
and2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
(
(
1GateCircuit
(
x
,
y
,())
)
+*
(
1GateCircuit
(
y
,
z
,
and2a
)
)
)
+*
(
1GateCircuit
(
z
,
x
,
and2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2a
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2
)
)
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
,
or3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
(
x
,
y
,
z
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
,
or3
)
)
is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
z
*>
,
and2a
]
,
[
<*
z
,
x
*>
,
and2
]
*>
,
or3
)
)
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
Following
(
s1
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
2
+
1 is
V9
()
V10
()
V11
()
V15
() non
pair
Element
of
NAT
Following
(
s1
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s2
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s2
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
Following
(
s2
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s2
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is
Relation-like
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
-defined
Function-like
V23
( the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
set
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is non
empty
set
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
) is
functional
V49
()
V50
()
set
Following
(
s
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
(
Following
(
s
,3)
)
is
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
t
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
Following
(
t
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
t
,2)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
Following
(
s1
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
t
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
t
,3)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
(
Following
(
t
,2)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
Following
(
s2
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
t
,3)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
the
carrier
of (
x
,
y
,
z
)
\/
the
carrier
of (
x
,
y
,
z
) is
set
proj1
(
Following
(
s1
,2)
)
is
set
proj1
(
Following
(
s2
,2)
)
is
set
a
is
set
(
Following
(
s
,2)
)
.
a
is
set
(
Following
(
s1
,2)
)
.
a
is
set
(
Following
(
s
,3)
)
.
a
is
set
(
Following
(
s1
,3)
)
.
a
is
set
(
Following
(
s2
,2)
)
.
a
is
set
(
Following
(
s2
,3)
)
.
a
is
set
Following
(
Following
(
s
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
Following
(
s
,2)
)
)
.
a
is
set
Following
(
s
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
(
Following
(
s
,2)
)
is
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircuit
(
f1
,
f2
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
(
1GateCircuit
(
f1
,
f2
,
and2a
)
)
+*
(
1GateCircuit
(
f2
,
f3
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
1GateCircuit
(
f3
,
f1
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
(
(
1GateCircuit
(
f1
,
f2
,
and2a
)
)
+*
(
1GateCircuit
(
f2
,
f3
,())
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
(
1GateCircuit
(
f1
,
f2
,
and2a
)
)
+*
(
1GateCircuit
(
f2
,
f3
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
1GateCircuit
(
f3
,
f1
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
(
(
1GateCircuit
(
f1
,
f2
,
and2a
)
)
+*
(
1GateCircuit
(
f2
,
f3
,())
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Function-like
set
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\/
(
InnerVertices
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
set
the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
))
the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
InnerVertices
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
set
the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
))
the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
(
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
(
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
(
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Function-like
set
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is
set
{
f2
,
f3
}
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
set
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
set
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
)
is
set
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
Function-like
set
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
}
is
Relation-like
Function-like
set
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Function-like
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
)
is
set
{
f1
,
f2
}
is
set
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
is
Element
of
K18
(
{
f1
,
f2
}
)
K18
(
{
f1
,
f2
}
) is
set
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
is
set
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
)
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
)
is
set
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
is
Element
of
K18
(
{
f2
,
f3
}
)
K18
(
{
f2
,
f3
}
) is
set
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
is
set
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
)
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
)
is
set
{
f3
,
f1
}
is
set
{
f3
,
f1
}
\
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
is
Element
of
K18
(
{
f3
,
f1
}
)
K18
(
{
f3
,
f1
}
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
{
f3
,
f1
}
\
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
)
is
set
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
is
Element
of
K18
(
{
f3
,
f1
}
)
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
)
is
set
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
is
set
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
)
K18
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
) is
set
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
)
is
set
{
f1
,
f2
}
\/
{
f2
,
f3
}
is
set
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
)
K18
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
) is
set
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
)
is
set
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f2
,
f3
}
is
set
{
f1
,
f2
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f2
,
f3
}
) is
set
(
{
f1
,
f2
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
f3
,
f1
}
is
set
{
f2
,
f2
,
f1
,
f3
}
is
set
{
f2
,
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
{
f2
,
f2
,
f1
,
f3
}
)
K18
(
{
f2
,
f2
,
f1
,
f3
}
) is
set
(
{
f2
,
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
f3
,
f1
}
is
set
{
f2
,
f1
,
f3
}
is
set
{
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
{
f2
,
f1
,
f3
}
)
K18
(
{
f2
,
f1
,
f3
}
) is
set
(
{
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f3
}
) is
set
(
{
f1
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
}
is
set
{
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
}
\/
{
f1
}
is
set
{
f3
,
f3
,
f1
,
f2
}
is
set
{
f3
,
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
}
is
set
{
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
,
f1
}
is
set
{
f1
,
f1
,
f2
,
f3
}
is
set
f1
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is
set
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
proj2
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
{
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
}
is
Relation-like
Function-like
set
{
f1
,
f2
,
f3
}
\
{
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f3
}
) is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Element
of
K18
(
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
)
K18
(
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
) is
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
f1
,
f2
,
f3
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
(
(
InputVertices
(
f1
,
f2
,
f3
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Relation-like
Element
of
K18
(
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
)
{
f1
,
f2
,
f3
}
\/
(
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
{
f1
,
f2
,
f3
}
\/
{}
is
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
S
is non
empty
pair
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
{
[
<*
f1
,
f2
*>
,
and2a
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
{
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
Function-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
(
InputVertices
(
f1
,
f2
,
f3
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
set
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
proj2
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
set
{
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
}
is
Relation-like
Function-like
set
(
proj2
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
)
\/
{
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
}
is
set
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,(
f1
,
f2
,
f3
)
}
is
set
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2b
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2b
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2b
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,
and2a
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
and2a
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
and2a
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
{
f0
,
x
,
y
}
is
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
{
f1
,
f2
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
{
f2
,
f3
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
{
f3
,
f1
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
{
[
<*
f1
,
f2
*>
,
and2a
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
{
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Function-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
{
[
<*
f1
,
f2
*>
,
and2a
]
}
\/
{
[
<*
f2
,
f3
*>
,()
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
f1
,
f2
,
f3
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
is
set
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
{
f1
,
f2
,
f2
,
f3
}
is
set
{
f1
,
f2
,
f2
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f2
,
f2
,
f1
,
f3
}
is
set
{
f2
,
f2
,
f1
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f2
,
f1
,
f3
}
is non
with_pair
set
{
f2
,
f1
,
f3
}
\/
{
f3
,
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f3
,
f1
}
is non
with_pair
set
{
f3
}
is non
with_pair
set
{
f1
}
is non
with_pair
set
{
f3
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
(
{
f3
}
\/
{
f1
}
)
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f3
}
is non
with_pair
set
(
{
f1
,
f2
,
f3
}
\/
{
f3
}
)
\/
{
f1
}
is non
with_pair
set
{
f3
,
f1
,
f2
}
is non
with_pair
set
{
f3
,
f1
,
f2
}
\/
{
f3
}
is non
with_pair
set
(
{
f3
,
f1
,
f2
}
\/
{
f3
}
)
\/
{
f1
}
is non
with_pair
set
{
f3
,
f3
,
f1
,
f2
}
is
set
{
f3
,
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f1
,
f2
,
f3
}
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
(
1GateCircuit
(
f1
,
f2
,
and2a
)
)
+*
(
1GateCircuit
(
f2
,
f3
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
1GateCircuit
(
f3
,
f1
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
(
(
1GateCircuit
(
f1
,
f2
,
and2a
)
)
+*
(
1GateCircuit
(
f2
,
f3
,())
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
the
Sorts
of (
f1
,
f2
,
f3
) is
Relation-like
the
carrier
of (
f1
,
f2
,
f3
)
-defined
Function-like
V23
( the
carrier
of (
f1
,
f2
,
f3
))
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K230
( the
Sorts
of (
f1
,
f2
,
f3
)) is
functional
V49
()
V50
()
set
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
z
.
f1
is
set
z
.
f2
is
set
z
.
f3
is
set
Following
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
(
Following
z
)
.
[
<*
f1
,
f2
*>
,
and2a
]
is
set
(
Following
z
)
.
[
<*
f2
,
f3
*>
,()
]
is
set
(
Following
z
)
.
[
<*
f3
,
f1
*>
,
and2b
]
is
set
S1
is
boolean
Element
of
BOOLEAN
A1
is
boolean
Element
of
BOOLEAN
s1
is
boolean
Element
of
BOOLEAN
'not'
S1
is
boolean
Element
of
BOOLEAN
K114
(1,
S1
) is
set
(
'not'
S1
)
'&'
A1
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
S1
)
,
A1
) is
set
'not'
s1
is
boolean
Element
of
BOOLEAN
K114
(1,
s1
) is
set
A1
'&'
(
'not'
s1
)
is
boolean
Element
of
BOOLEAN
K111
(
A1
,
(
'not'
s1
)
) is
set
(
'not'
s1
)
'&'
(
'not'
S1
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
s1
)
,
(
'not'
S1
)
) is
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
proj1
z
is
set
<*
f1
,
f2
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
and2a
.
(
<*
f1
,
f2
*>
*
z
)
is
boolean
set
<*
S1
,
A1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2a
.
<*
S1
,
A1
*>
is
boolean
set
<*
f2
,
f3
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
()
.
(
<*
f2
,
f3
*>
*
z
)
is
boolean
set
<*
A1
,
s1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
()
.
<*
A1
,
s1
*>
is
boolean
set
<*
f3
,
f1
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
and2b
.
(
<*
f3
,
f1
*>
*
z
)
is
boolean
set
<*
s1
,
S1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2b
.
<*
s1
,
S1
*>
is
boolean
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
(
1GateCircuit
(
f1
,
f2
,
and2a
)
)
+*
(
1GateCircuit
(
f2
,
f3
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
1GateCircuit
(
f3
,
f1
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
(
(
1GateCircuit
(
f1
,
f2
,
and2a
)
)
+*
(
1GateCircuit
(
f2
,
f3
,())
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
the
Sorts
of (
f1
,
f2
,
f3
) is
Relation-like
the
carrier
of (
f1
,
f2
,
f3
)
-defined
Function-like
V23
( the
carrier
of (
f1
,
f2
,
f3
))
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K230
( the
Sorts
of (
f1
,
f2
,
f3
)) is
functional
V49
()
V50
()
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
A
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
A
.
[
<*
f1
,
f2
*>
,
and2a
]
is
set
A
.
[
<*
f2
,
f3
*>
,()
]
is
set
A
.
[
<*
f3
,
f1
*>
,
and2b
]
is
set
Following
A
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
(
Following
A
)
.
(
f1
,
f2
,
f3
) is
boolean
Element
of
BOOLEAN
A1
is
boolean
Element
of
BOOLEAN
s1
is
boolean
Element
of
BOOLEAN
A2
is
boolean
Element
of
BOOLEAN
A1
'or'
s1
is
boolean
Element
of
BOOLEAN
'not'
A1
is
boolean
set
K114
(1,
A1
) is
set
'not'
s1
is
boolean
set
K114
(1,
s1
) is
set
(
'not'
A1
)
'&'
(
'not'
s1
)
is
set
K111
(
(
'not'
A1
)
,
(
'not'
s1
)
) is
set
'not'
(
(
'not'
A1
)
'&'
(
'not'
s1
)
)
is
boolean
set
(
A1
'or'
s1
)
'or'
A2
is
boolean
Element
of
BOOLEAN
'not'
(
A1
'or'
s1
)
is
boolean
set
K114
(1,
(
A1
'or'
s1
)
) is
set
'not'
A2
is
boolean
set
K114
(1,
A2
) is
set
(
'not'
(
A1
'or'
s1
)
)
'&'
(
'not'
A2
)
is
set
K111
(
(
'not'
(
A1
'or'
s1
)
)
,
(
'not'
A2
)
) is
set
'not'
(
(
'not'
(
A1
'or'
s1
)
)
'&'
(
'not'
A2
)
)
is
boolean
set
'not'
(
(
A1
'or'
s1
)
'or'
A2
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
A1
'or'
s1
)
'or'
A2
)
) is
set
proj1
A
is
set
t
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
S
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
a
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
<*
t
,
S
,
a
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
<*
t
,
S
,
a
*>
*
A
is
Relation-like
NAT
-defined
Function-like
set
nor3
.
(
<*
t
,
S
,
a
*>
*
A
)
is
boolean
set
<*
A1
,
s1
,
A2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
nor3
.
<*
A1
,
s1
,
A2
*>
is
boolean
set
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2b
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2b
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2b
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,
and2a
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
and2a
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
and2a
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
1GateCircuit
(
f0
,
x
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
1GateCircuit
(
<*
f0
,
x
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
1GateCircuit
(
x
,
y
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
<*
x
,
y
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
(
1GateCircuit
(
f0
,
x
,
and2a
)
)
+*
(
1GateCircuit
(
x
,
y
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
1GateCircuit
(
y
,
f0
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
1GateCircuit
(
<*
y
,
f0
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
(
(
1GateCircuit
(
f0
,
x
,
and2a
)
)
+*
(
1GateCircuit
(
x
,
y
,())
)
)
+*
(
1GateCircuit
(
y
,
f0
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
(
f0
,
x
,
y
)
+*
(
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
the
Sorts
of (
f0
,
x
,
y
) is
Relation-like
the
carrier
of (
f0
,
x
,
y
)
-defined
Function-like
V23
( the
carrier
of (
f0
,
x
,
y
))
set
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K230
( the
Sorts
of (
f0
,
x
,
y
)) is
functional
V49
()
V50
()
set
(
f0
,
x
,
y
) is
Element
of
InnerVertices
(
f0
,
x
,
y
)
InnerVertices
(
f0
,
x
,
y
) is non
empty
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
[
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
}
}
is
set
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
S1
.
f0
is
set
S1
.
x
is
set
S1
.
y
is
set
Following
(
S1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
(
Following
(
S1
,2)
)
.
(
f0
,
x
,
y
) is
boolean
Element
of
BOOLEAN
(
Following
(
S1
,2)
)
.
[
<*
f0
,
x
*>
,
and2a
]
is
set
(
Following
(
S1
,2)
)
.
[
<*
x
,
y
*>
,()
]
is
set
(
Following
(
S1
,2)
)
.
[
<*
y
,
f0
*>
,
and2b
]
is
set
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
Following
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
s
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
s
is
boolean
Element
of
BOOLEAN
S2
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
S2
is
boolean
Element
of
BOOLEAN
Following
(
Following
S1
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
s2
is
boolean
Element
of
BOOLEAN
t
is
boolean
Element
of
BOOLEAN
S
is
boolean
Element
of
BOOLEAN
'not'
s2
is
boolean
Element
of
BOOLEAN
K114
(1,
s2
) is
set
(
'not'
s2
)
'&'
t
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
s2
)
,
t
) is
set
'not'
S
is
boolean
Element
of
BOOLEAN
K114
(1,
S
) is
set
t
'&'
(
'not'
S
)
is
boolean
Element
of
BOOLEAN
K111
(
t
,
(
'not'
S
)
) is
set
(
(
'not'
s2
)
'&'
t
)
'or'
(
t
'&'
(
'not'
S
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
'not'
s2
)
'&'
t
)
is
boolean
set
K114
(1,
(
(
'not'
s2
)
'&'
t
)
) is
set
'not'
(
t
'&'
(
'not'
S
)
)
is
boolean
set
K114
(1,
(
t
'&'
(
'not'
S
)
)
) is
set
(
'not'
(
(
'not'
s2
)
'&'
t
)
)
'&'
(
'not'
(
t
'&'
(
'not'
S
)
)
)
is
set
K111
(
(
'not'
(
(
'not'
s2
)
'&'
t
)
)
,
(
'not'
(
t
'&'
(
'not'
S
)
)
)
) is
set
'not'
(
(
'not'
(
(
'not'
s2
)
'&'
t
)
)
'&'
(
'not'
(
t
'&'
(
'not'
S
)
)
)
)
is
boolean
set
(
'not'
S
)
'&'
(
'not'
s2
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
S
)
,
(
'not'
s2
)
) is
set
(
(
(
'not'
s2
)
'&'
t
)
'or'
(
t
'&'
(
'not'
S
)
)
)
'or'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
(
'not'
s2
)
'&'
t
)
'or'
(
t
'&'
(
'not'
S
)
)
)
is
boolean
set
K114
(1,
(
(
(
'not'
s2
)
'&'
t
)
'or'
(
t
'&'
(
'not'
S
)
)
)
) is
set
'not'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
is
boolean
set
K114
(1,
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
) is
set
(
'not'
(
(
(
'not'
s2
)
'&'
t
)
'or'
(
t
'&'
(
'not'
S
)
)
)
)
'&'
(
'not'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
)
is
set
K111
(
(
'not'
(
(
(
'not'
s2
)
'&'
t
)
'or'
(
t
'&'
(
'not'
S
)
)
)
)
,
(
'not'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
)
) is
set
'not'
(
(
'not'
(
(
(
'not'
s2
)
'&'
t
)
'or'
(
t
'&'
(
'not'
S
)
)
)
)
'&'
(
'not'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
)
)
is
boolean
set
'not'
(
(
(
(
'not'
s2
)
'&'
t
)
'or'
(
t
'&'
(
'not'
S
)
)
)
'or'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
(
(
'not'
s2
)
'&'
t
)
'or'
(
t
'&'
(
'not'
S
)
)
)
'or'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
)
) is
set
(
Following
S1
)
.
[
<*
y
,
f0
*>
,
and2b
]
is
set
(
Following
S1
)
.
[
<*
f0
,
x
*>
,
and2a
]
is
set
(
Following
S1
)
.
[
<*
x
,
y
*>
,()
]
is
set
A
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
A
is
boolean
Element
of
BOOLEAN
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2b
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2b
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2b
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,
and2a
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
and2a
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
and2a
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
1GateCircuit
(
f0
,
x
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
1GateCircuit
(
<*
f0
,
x
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
1GateCircuit
(
x
,
y
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
<*
x
,
y
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
(
1GateCircuit
(
f0
,
x
,
and2a
)
)
+*
(
1GateCircuit
(
x
,
y
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
1GateCircuit
(
y
,
f0
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
1GateCircuit
(
<*
y
,
f0
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
(
(
1GateCircuit
(
f0
,
x
,
and2a
)
)
+*
(
1GateCircuit
(
x
,
y
,())
)
)
+*
(
1GateCircuit
(
y
,
f0
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
(
f0
,
x
,
y
)
+*
(
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
the
Sorts
of (
f0
,
x
,
y
) is
Relation-like
the
carrier
of (
f0
,
x
,
y
)
-defined
Function-like
V23
( the
carrier
of (
f0
,
x
,
y
))
set
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K230
( the
Sorts
of (
f0
,
x
,
y
)) is
functional
V49
()
V50
()
set
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
(
S1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
A
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
A
is
boolean
Element
of
BOOLEAN
s
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
s
is
boolean
Element
of
BOOLEAN
S2
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
S2
is
boolean
Element
of
BOOLEAN
Following
(
Following
(
S1
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
(
Following
S1
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
(
Following
S1
)
.
y
is
set
(
Following
(
S1
,2)
)
.
y
is
set
(
Following
S1
)
.
x
is
set
(
Following
(
S1
,2)
)
.
x
is
set
(
Following
S1
)
.
f0
is
set
(
Following
(
S1
,2)
)
.
f0
is
set
S1
.
y
is
set
(
Following
(
S1
,2)
)
.
[
<*
f0
,
x
*>
,
and2a
]
is
set
'not'
(
S1
.
A
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
S1
.
A
)
) is
set
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
(
S1
.
A
)
)
,
(
S1
.
s
)
) is
set
S1
.
x
is
set
(
Following
(
S1
,2)
)
.
[
<*
y
,
f0
*>
,
and2b
]
is
set
'not'
(
S1
.
S2
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
S1
.
S2
)
) is
set
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
S2
)
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
(
S1
.
A
)
)
,
(
'not'
(
S1
.
S2
)
)
) is
set
S1
.
f0
is
set
(
Following
(
S1
,2)
)
.
[
<*
x
,
y
*>
,()
]
is
set
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
is
boolean
Element
of
BOOLEAN
K111
(
(
S1
.
s
)
,
(
'not'
(
S1
.
S2
)
)
) is
set
(
f0
,
x
,
y
) is
Element
of
InnerVertices
(
f0
,
x
,
y
)
InnerVertices
(
f0
,
x
,
y
) is non
empty
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
[
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
}
}
is
set
(
Following
(
S1
,2)
)
.
(
f0
,
x
,
y
) is
boolean
Element
of
BOOLEAN
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
is
boolean
set
K114
(1,
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
) is
set
'not'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
is
boolean
set
K114
(1,
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
) is
set
(
'not'
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
)
'&'
(
'not'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
is
set
K111
(
(
'not'
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
)
,
(
'not'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
) is
set
'not'
(
(
'not'
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
)
'&'
(
'not'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
)
is
boolean
set
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
(
S1
.
S2
)
)
,
(
'not'
(
S1
.
A
)
)
) is
set
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
'or'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
is
boolean
set
K114
(1,
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
) is
set
'not'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
is
boolean
set
K114
(1,
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
) is
set
(
'not'
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
)
'&'
(
'not'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
)
is
set
K111
(
(
'not'
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
)
,
(
'not'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
)
) is
set
'not'
(
(
'not'
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
)
'&'
(
'not'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
)
)
is
boolean
set
'not'
(
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
'or'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
S1
.
s
)
)
'or'
(
(
S1
.
s
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
'or'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
)
) is
set
a
is
set
v
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
InputVertices
(
f0
,
x
,
y
)
)
\/
(
InnerVertices
(
f0
,
x
,
y
)
)
is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
(
Following
(
S1
,2)
)
.
a
is
set
(
Following
(
Following
(
S1
,2)
)
)
.
a
is
set
{
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
}
is
Relation-like
set
{
(
f0
,
x
,
y
)
}
is
set
{
[
<*
f0
,
x
*>
,
and2a
]
,
[
<*
x
,
y
*>
,()
]
,
[
<*
y
,
f0
*>
,
and2b
]
}
\/
{
(
f0
,
x
,
y
)
}
is
set
proj1
(
Following
(
Following
(
S1
,2)
)
)
is
set
proj1
(
Following
(
S1
,2)
)
is
set
f1
is
set
f2
is
set
f3
is
set
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
2GatesCircuit
(
f1
,
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f1
,
f2
,
f3
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f1
,
f2
,
f3
,())
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircuit
(
f1
,
f2
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
<*
f1
,
f2
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
f3
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
x
is
set
f0
is
set
y
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f0
,
x
,
y
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f0
,
x
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f0
,
x
*>
,()
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,()
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,()
}
,
{
<*
f0
,
x
*>
}
}
is
set
<*
[
<*
f0
,
x
*>
,()
]
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,()
]
,
y
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
s
is
set
z
is
set
A
is
set
(
z
,
A
,
s
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
z
,
A
,
s
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
z
,
A
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
z
,
A
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
z
,
A
*>
,()
]
is non
empty
pair
set
{
<*
z
,
A
*>
,()
}
is
functional
set
{
<*
z
,
A
*>
}
is
functional
V49
()
set
{
{
<*
z
,
A
*>
,()
}
,
{
<*
z
,
A
*>
}
}
is
set
<*
[
<*
z
,
A
*>
,()
]
,
s
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
z
,
A
*>
,()
]
,
s
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
z
,
A
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
z
,
A
*>
,()
]
,
s
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
z
,
A
,
s
) is non
empty
set
S2
is
set
S1
is
set
<*
S2
,
S1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
S2
,
S1
*>
,()
]
is non
empty
pair
set
{
<*
S2
,
S1
*>
,()
}
is
functional
set
{
<*
S2
,
S1
*>
}
is
functional
V49
()
set
{
{
<*
S2
,
S1
*>
,()
}
,
{
<*
S2
,
S1
*>
}
}
is
set
A1
is
set
(
S2
,
S1
,
A1
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
S2
,
S1
,
A1
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
S2
,
S1
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
S2
,
S1
*>
,()
]
,
A1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
S2
,
S1
*>
,()
]
,
A1
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
S2
,
S1
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
S2
,
S1
*>
,()
]
,
A1
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
S2
,
S1
,
A1
) is non
empty
set
s1
is
set
A2
is
set
<*
s1
,
A2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
s1
,
A2
*>
,()
]
is non
empty
pair
set
{
<*
s1
,
A2
*>
,()
}
is
functional
set
{
<*
s1
,
A2
*>
}
is
functional
V49
()
set
{
{
<*
s1
,
A2
*>
,()
}
,
{
<*
s1
,
A2
*>
}
}
is
set
s2
is
set
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
,()
}
is
functional
set
{
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
,()
}
,
{
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
}
}
is
set
(
s1
,
A2
,
s2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
s1
,
A2
,
s2
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
s1
,
A2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
s1
,
A2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
s1
,
A2
*>
,()
]
,
s2
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
s1
,
A2
,
s2
) is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f2
,
f3
,
f0
) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
the
carrier
of (
f2
,
f3
,
f0
)
\
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,())
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
(
1GateCircuit
(
f2
,
f3
,())
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
z
is
boolean
Element
of
BOOLEAN
y
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
y
.
f2
is
set
A
is
boolean
Element
of
BOOLEAN
y
.
f3
is
set
s
is
boolean
Element
of
BOOLEAN
y
.
f0
is
set
Following
y
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
y
)
.
[
<*
f2
,
f3
*>
,()
]
is
set
'not'
A
is
boolean
Element
of
BOOLEAN
K114
(1,
A
) is
set
z
'xor'
(
'not'
A
)
is
boolean
Element
of
BOOLEAN
K222
(
z
,
(
'not'
A
)
) is
set
K221
(
z
,
(
'not'
A
)
) is
set
'not'
z
is
boolean
set
K114
(1,
z
) is
set
K220
(
(
'not'
z
)
,
(
'not'
A
)
) is
set
'not'
(
'not'
z
)
is
boolean
set
K114
(1,
(
'not'
z
)
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
(
'not'
(
'not'
z
)
)
'&'
(
'not'
(
'not'
A
)
)
is
set
K111
(
(
'not'
(
'not'
z
)
)
,
(
'not'
(
'not'
A
)
)
) is
set
'not'
(
(
'not'
(
'not'
z
)
)
'&'
(
'not'
(
'not'
A
)
)
)
is
boolean
set
K221
(
(
'not'
A
)
,
z
) is
set
K220
(
(
'not'
(
'not'
A
)
)
,
z
) is
set
'not'
(
'not'
(
'not'
A
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
A
)
)
) is
set
(
'not'
(
'not'
(
'not'
A
)
)
)
'&'
(
'not'
z
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
A
)
)
)
,
(
'not'
z
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
A
)
)
)
'&'
(
'not'
z
)
)
is
boolean
set
K221
(
z
,
(
'not'
A
)
)
'&'
K221
(
(
'not'
A
)
,
z
) is
set
'not'
K222
(
z
,
(
'not'
A
)
) is
boolean
set
(
Following
y
)
.
f2
is
set
(
Following
y
)
.
f3
is
set
(
Following
y
)
.
f0
is
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,())
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
(
1GateCircuit
(
f2
,
f3
,())
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
2GatesCircOutput
(
f2
,
f3
,
f0
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
[
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
,
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
}
is
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
S2
is
boolean
Element
of
BOOLEAN
s
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
s
.
[
<*
f2
,
f3
*>
,()
]
is
set
S1
is
boolean
Element
of
BOOLEAN
s
.
f2
is
set
A1
is
boolean
Element
of
BOOLEAN
s
.
f3
is
set
s1
is
boolean
Element
of
BOOLEAN
s
.
f0
is
set
Following
s
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
s
)
.
(
f2
,
f3
,
f0
) is
boolean
Element
of
BOOLEAN
'not'
s1
is
boolean
Element
of
BOOLEAN
K114
(1,
s1
) is
set
S2
'xor'
(
'not'
s1
)
is
boolean
Element
of
BOOLEAN
K222
(
S2
,
(
'not'
s1
)
) is
set
K221
(
S2
,
(
'not'
s1
)
) is
set
'not'
S2
is
boolean
set
K114
(1,
S2
) is
set
K220
(
(
'not'
S2
)
,
(
'not'
s1
)
) is
set
'not'
(
'not'
S2
)
is
boolean
set
K114
(1,
(
'not'
S2
)
) is
set
'not'
(
'not'
s1
)
is
boolean
set
K114
(1,
(
'not'
s1
)
) is
set
(
'not'
(
'not'
S2
)
)
'&'
(
'not'
(
'not'
s1
)
)
is
set
K111
(
(
'not'
(
'not'
S2
)
)
,
(
'not'
(
'not'
s1
)
)
) is
set
'not'
(
(
'not'
(
'not'
S2
)
)
'&'
(
'not'
(
'not'
s1
)
)
)
is
boolean
set
K221
(
(
'not'
s1
)
,
S2
) is
set
K220
(
(
'not'
(
'not'
s1
)
)
,
S2
) is
set
'not'
(
'not'
(
'not'
s1
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
s1
)
)
) is
set
(
'not'
(
'not'
(
'not'
s1
)
)
)
'&'
(
'not'
S2
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
s1
)
)
)
,
(
'not'
S2
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
s1
)
)
)
'&'
(
'not'
S2
)
)
is
boolean
set
K221
(
S2
,
(
'not'
s1
)
)
'&'
K221
(
(
'not'
s1
)
,
S2
) is
set
'not'
K222
(
S2
,
(
'not'
s1
)
) is
boolean
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,())
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
(
1GateCircuit
(
f2
,
f3
,())
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
2GatesCircOutput
(
f2
,
f3
,
f0
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
[
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
,
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
}
is
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
S2
is
boolean
Element
of
BOOLEAN
s
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
s
.
f2
is
set
S1
is
boolean
Element
of
BOOLEAN
s
.
f3
is
set
A1
is
boolean
Element
of
BOOLEAN
s
.
f0
is
set
Following
(
s
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
(
s
,2)
)
.
(
f2
,
f3
,
f0
) is
boolean
Element
of
BOOLEAN
'not'
S1
is
boolean
Element
of
BOOLEAN
K114
(1,
S1
) is
set
S2
'xor'
(
'not'
S1
)
is
boolean
Element
of
BOOLEAN
K222
(
S2
,
(
'not'
S1
)
) is
set
K221
(
S2
,
(
'not'
S1
)
) is
set
'not'
S2
is
boolean
set
K114
(1,
S2
) is
set
K220
(
(
'not'
S2
)
,
(
'not'
S1
)
) is
set
'not'
(
'not'
S2
)
is
boolean
set
K114
(1,
(
'not'
S2
)
) is
set
'not'
(
'not'
S1
)
is
boolean
set
K114
(1,
(
'not'
S1
)
) is
set
(
'not'
(
'not'
S2
)
)
'&'
(
'not'
(
'not'
S1
)
)
is
set
K111
(
(
'not'
(
'not'
S2
)
)
,
(
'not'
(
'not'
S1
)
)
) is
set
'not'
(
(
'not'
(
'not'
S2
)
)
'&'
(
'not'
(
'not'
S1
)
)
)
is
boolean
set
K221
(
(
'not'
S1
)
,
S2
) is
set
K220
(
(
'not'
(
'not'
S1
)
)
,
S2
) is
set
'not'
(
'not'
(
'not'
S1
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
S1
)
)
) is
set
(
'not'
(
'not'
(
'not'
S1
)
)
)
'&'
(
'not'
S2
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
S1
)
)
)
,
(
'not'
S2
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
S1
)
)
)
'&'
(
'not'
S2
)
)
is
boolean
set
K221
(
S2
,
(
'not'
S1
)
)
'&'
K221
(
(
'not'
S1
)
,
S2
) is
set
'not'
K222
(
S2
,
(
'not'
S1
)
) is
boolean
set
'not'
A1
is
boolean
Element
of
BOOLEAN
K114
(1,
A1
) is
set
(
S2
'xor'
(
'not'
S1
)
)
'xor'
(
'not'
A1
)
is
boolean
Element
of
BOOLEAN
K222
(
(
S2
'xor'
(
'not'
S1
)
)
,
(
'not'
A1
)
) is
set
K221
(
(
S2
'xor'
(
'not'
S1
)
)
,
(
'not'
A1
)
) is
set
'not'
(
S2
'xor'
(
'not'
S1
)
)
is
boolean
set
K114
(1,
(
S2
'xor'
(
'not'
S1
)
)
) is
set
K220
(
(
'not'
(
S2
'xor'
(
'not'
S1
)
)
)
,
(
'not'
A1
)
) is
set
'not'
(
'not'
(
S2
'xor'
(
'not'
S1
)
)
)
is
boolean
set
K114
(1,
(
'not'
(
S2
'xor'
(
'not'
S1
)
)
)
) is
set
'not'
(
'not'
A1
)
is
boolean
set
K114
(1,
(
'not'
A1
)
) is
set
(
'not'
(
'not'
(
S2
'xor'
(
'not'
S1
)
)
)
)
'&'
(
'not'
(
'not'
A1
)
)
is
set
K111
(
(
'not'
(
'not'
(
S2
'xor'
(
'not'
S1
)
)
)
)
,
(
'not'
(
'not'
A1
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
S2
'xor'
(
'not'
S1
)
)
)
)
'&'
(
'not'
(
'not'
A1
)
)
)
is
boolean
set
K221
(
(
'not'
A1
)
,
(
S2
'xor'
(
'not'
S1
)
)
) is
set
K220
(
(
'not'
(
'not'
A1
)
)
,
(
S2
'xor'
(
'not'
S1
)
)
) is
set
'not'
(
'not'
(
'not'
A1
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
A1
)
)
) is
set
(
'not'
(
'not'
(
'not'
A1
)
)
)
'&'
(
'not'
(
S2
'xor'
(
'not'
S1
)
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
A1
)
)
)
,
(
'not'
(
S2
'xor'
(
'not'
S1
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
A1
)
)
)
'&'
(
'not'
(
S2
'xor'
(
'not'
S1
)
)
)
)
is
boolean
set
K221
(
(
S2
'xor'
(
'not'
S1
)
)
,
(
'not'
A1
)
)
'&'
K221
(
(
'not'
A1
)
,
(
S2
'xor'
(
'not'
S1
)
)
) is
set
'not'
K222
(
(
S2
'xor'
(
'not'
S1
)
)
,
(
'not'
A1
)
) is
boolean
set
(
Following
(
s
,2)
)
.
[
<*
f2
,
f3
*>
,()
]
is
set
(
Following
(
s
,2)
)
.
f2
is
set
(
Following
(
s
,2)
)
.
f3
is
set
(
Following
(
s
,2)
)
.
f0
is
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,())
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
(
1GateCircuit
(
f2
,
f3
,())
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,()
]
,
f0
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,())
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
2GatesCircOutput
(
f2
,
f3
,
f0
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,())
)
)
[
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
,()
}
,
{
<*
[
<*
f2
,
f3
*>
,()
]
,
f0
*>
}
}
is
set
y
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
y
.
f2
is
set
y
.
f3
is
set
y
.
f0
is
set
Following
(
y
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
(
y
,2)
)
.
(
f2
,
f3
,
f0
) is
boolean
Element
of
BOOLEAN
z
is
boolean
Element
of
BOOLEAN
A
is
boolean
Element
of
BOOLEAN
s
is
boolean
Element
of
BOOLEAN
'not'
z
is
boolean
Element
of
BOOLEAN
K114
(1,
z
) is
set
(
'not'
z
)
'xor'
A
is
boolean
Element
of
BOOLEAN
K222
(
(
'not'
z
)
,
A
) is
set
K221
(
(
'not'
z
)
,
A
) is
set
'not'
(
'not'
z
)
is
boolean
set
K114
(1,
(
'not'
z
)
) is
set
K220
(
(
'not'
(
'not'
z
)
)
,
A
) is
set
'not'
(
'not'
(
'not'
z
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
z
)
)
) is
set
'not'
A
is
boolean
set
K114
(1,
A
) is
set
(
'not'
(
'not'
(
'not'
z
)
)
)
'&'
(
'not'
A
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
z
)
)
)
,
(
'not'
A
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
z
)
)
)
'&'
(
'not'
A
)
)
is
boolean
set
K221
(
A
,
(
'not'
z
)
) is
set
K220
(
(
'not'
A
)
,
(
'not'
z
)
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
(
'not'
(
'not'
A
)
)
'&'
(
'not'
(
'not'
z
)
)
is
set
K111
(
(
'not'
(
'not'
A
)
)
,
(
'not'
(
'not'
z
)
)
) is
set
'not'
(
(
'not'
(
'not'
A
)
)
'&'
(
'not'
(
'not'
z
)
)
)
is
boolean
set
K221
(
(
'not'
z
)
,
A
)
'&'
K221
(
A
,
(
'not'
z
)
) is
set
'not'
K222
(
(
'not'
z
)
,
A
) is
boolean
set
'not'
s
is
boolean
Element
of
BOOLEAN
K114
(1,
s
) is
set
(
(
'not'
z
)
'xor'
A
)
'xor'
(
'not'
s
)
is
boolean
Element
of
BOOLEAN
K222
(
(
(
'not'
z
)
'xor'
A
)
,
(
'not'
s
)
) is
set
K221
(
(
(
'not'
z
)
'xor'
A
)
,
(
'not'
s
)
) is
set
'not'
(
(
'not'
z
)
'xor'
A
)
is
boolean
set
K114
(1,
(
(
'not'
z
)
'xor'
A
)
) is
set
K220
(
(
'not'
(
(
'not'
z
)
'xor'
A
)
)
,
(
'not'
s
)
) is
set
'not'
(
'not'
(
(
'not'
z
)
'xor'
A
)
)
is
boolean
set
K114
(1,
(
'not'
(
(
'not'
z
)
'xor'
A
)
)
) is
set
'not'
(
'not'
s
)
is
boolean
set
K114
(1,
(
'not'
s
)
) is
set
(
'not'
(
'not'
(
(
'not'
z
)
'xor'
A
)
)
)
'&'
(
'not'
(
'not'
s
)
)
is
set
K111
(
(
'not'
(
'not'
(
(
'not'
z
)
'xor'
A
)
)
)
,
(
'not'
(
'not'
s
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
(
'not'
z
)
'xor'
A
)
)
)
'&'
(
'not'
(
'not'
s
)
)
)
is
boolean
set
K221
(
(
'not'
s
)
,
(
(
'not'
z
)
'xor'
A
)
) is
set
K220
(
(
'not'
(
'not'
s
)
)
,
(
(
'not'
z
)
'xor'
A
)
) is
set
'not'
(
'not'
(
'not'
s
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
s
)
)
) is
set
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
(
(
'not'
z
)
'xor'
A
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
s
)
)
)
,
(
'not'
(
(
'not'
z
)
'xor'
A
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
(
(
'not'
z
)
'xor'
A
)
)
)
is
boolean
set
K221
(
(
(
'not'
z
)
'xor'
A
)
,
(
'not'
s
)
)
'&'
K221
(
(
'not'
s
)
,
(
(
'not'
z
)
'xor'
A
)
) is
set
'not'
K222
(
(
(
'not'
z
)
'xor'
A
)
,
(
'not'
s
)
) is
boolean
set
'not'
A
is
boolean
Element
of
BOOLEAN
z
'xor'
(
'not'
A
)
is
boolean
Element
of
BOOLEAN
K222
(
z
,
(
'not'
A
)
) is
set
K221
(
z
,
(
'not'
A
)
) is
set
'not'
z
is
boolean
set
K220
(
(
'not'
z
)
,
(
'not'
A
)
) is
set
'not'
(
'not'
z
)
is
boolean
set
K114
(1,
(
'not'
z
)
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
(
'not'
(
'not'
z
)
)
'&'
(
'not'
(
'not'
A
)
)
is
set
K111
(
(
'not'
(
'not'
z
)
)
,
(
'not'
(
'not'
A
)
)
) is
set
'not'
(
(
'not'
(
'not'
z
)
)
'&'
(
'not'
(
'not'
A
)
)
)
is
boolean
set
K221
(
(
'not'
A
)
,
z
) is
set
K220
(
(
'not'
(
'not'
A
)
)
,
z
) is
set
'not'
(
'not'
(
'not'
A
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
A
)
)
) is
set
(
'not'
(
'not'
(
'not'
A
)
)
)
'&'
(
'not'
z
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
A
)
)
)
,
(
'not'
z
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
A
)
)
)
'&'
(
'not'
z
)
)
is
boolean
set
K221
(
z
,
(
'not'
A
)
)
'&'
K221
(
(
'not'
A
)
,
z
) is
set
'not'
K222
(
z
,
(
'not'
A
)
) is
boolean
set
(
z
'xor'
(
'not'
A
)
)
'xor'
(
'not'
s
)
is
boolean
Element
of
BOOLEAN
K222
(
(
z
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
) is
set
K221
(
(
z
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
) is
set
'not'
(
z
'xor'
(
'not'
A
)
)
is
boolean
set
K114
(1,
(
z
'xor'
(
'not'
A
)
)
) is
set
K220
(
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
,
(
'not'
s
)
) is
set
'not'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
is
boolean
set
K114
(1,
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
) is
set
(
'not'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
'&'
(
'not'
(
'not'
s
)
)
is
set
K111
(
(
'not'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
,
(
'not'
(
'not'
s
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
'&'
(
'not'
(
'not'
s
)
)
)
is
boolean
set
K221
(
(
'not'
s
)
,
(
z
'xor'
(
'not'
A
)
)
) is
set
K220
(
(
'not'
(
'not'
s
)
)
,
(
z
'xor'
(
'not'
A
)
)
) is
set
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
s
)
)
)
,
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
(
z
'xor'
(
'not'
A
)
)
)
)
is
boolean
set
K221
(
(
z
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
)
'&'
K221
(
(
'not'
s
)
,
(
z
'xor'
(
'not'
A
)
)
) is
set
'not'
K222
(
(
z
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
) is
boolean
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
2GatesCircuit
(
f1
,
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f1
,
f2
,
f3
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f1
,
f2
,
f3
,())
1GateCircuit
(
f1
,
f2
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
<*
f1
,
f2
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,())
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
(
1GateCircuit
(
f1
,
f2
,())
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,()
]
,
f3
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
1GateCircuit
(
f2
,
f3
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
1GateCircuit
(
<*
f2
,
f3
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,())
(
1GateCircuit
(
f1
,
f2
,
and2a
)
)
+*
(
1GateCircuit
(
f2
,
f3
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
1GateCircuit
(
f3
,
f1
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
(
(
1GateCircuit
(
f1
,
f2
,
and2a
)
)
+*
(
1GateCircuit
(
f2
,
f3
,())
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
(
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
InnerVertices
(
f1
,
f2
,
f3
)
)
\/
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
(
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,()
]
is non
empty
pair
set
{
<*
y
,
z
*>
,()
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,()
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2b
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2b
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2b
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2a
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2a
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2a
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
\/
{
f1
,
f2
,
f3
}
is non
with_pair
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
is
Relation-like
Function-like
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
(
(
{
[
<*
f1
,
f2
*>
,()
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
)
}
\/
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
set
(
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
)
}
\/
{
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,()
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,(
f1
,
f2
,
f3
)
}
is
set
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,()
]
is non
empty
pair
set
{
<*
y
,
z
*>
,()
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,()
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2b
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2b
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2b
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2a
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2a
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2a
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
2GatesCircOutput
(
f1
,
f2
,
f3
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
2GatesCircStr
(
f1
,
f2
,
f3
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,()
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,()
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,()
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,())
)
)
[
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
,()
}
,
{
<*
[
<*
f1
,
f2
*>
,()
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,())
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2a
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2a
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2a
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,()
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,()
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,()
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2a
]
,
[
<*
f2
,
f3
*>
,()
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,()
]
is non
empty
pair
set
{
<*
y
,
z
*>
,()
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,()
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2b
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2b
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2b
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2a
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2a
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2a
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
2GatesCircuit
(
x
,
y
,
z
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
x
,
y
,
z
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
x
,
y
,
z
,())
1GateCircuit
(
x
,
y
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
<*
x
,
y
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
z
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
1GateCircuit
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
(
1GateCircuit
(
x
,
y
,())
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
z
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
1GateCircuit
(
x
,
y
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
1GateCircuit
(
<*
x
,
y
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
1GateCircuit
(
y
,
z
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
z
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,())
1GateCircuit
(
<*
y
,
z
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,())
(
1GateCircuit
(
x
,
y
,
and2a
)
)
+*
(
1GateCircuit
(
y
,
z
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
1GateCircuit
(
z
,
x
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
1GateCircuit
(
<*
z
,
x
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
(
(
1GateCircuit
(
x
,
y
,
and2a
)
)
+*
(
1GateCircuit
(
y
,
z
,())
)
)
+*
(
1GateCircuit
(
z
,
x
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
1GateCircuit
(
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
(
x
,
y
,
z
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
(
x
,
y
,
z
) is
Element
of
InnerVertices
(
x
,
y
,
z
)
the
carrier
of (
x
,
y
,
z
) is non
empty
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
2GatesCircOutput
(
x
,
y
,
z
,()) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
x
,
y
,
z
,())
)
the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
x
,
y
,
z
,())
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
))
the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
, the
ResultSort
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,())
)
)
[
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()
]
is non
empty
pair
set
{
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()
}
is
functional
set
{
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()
}
,
{
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
}
}
is
set
(
x
,
y
,
z
) is
Element
of
InnerVertices
(
x
,
y
,
z
)
the
carrier
of (
x
,
y
,
z
) is non
empty
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
[
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
}
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
s1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
s1
.
x
is
set
s1
.
y
is
set
s1
.
z
is
set
Following
(
s1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
s1
,2)
)
.
(
x
,
y
,
z
) is
set
(
Following
(
s1
,2)
)
.
(
x
,
y
,
z
) is
set
A2
is
boolean
Element
of
BOOLEAN
s2
is
boolean
Element
of
BOOLEAN
t
is
boolean
Element
of
BOOLEAN
'not'
A2
is
boolean
Element
of
BOOLEAN
K114
(1,
A2
) is
set
(
'not'
A2
)
'xor'
s2
is
boolean
Element
of
BOOLEAN
K222
(
(
'not'
A2
)
,
s2
) is
set
K221
(
(
'not'
A2
)
,
s2
) is
set
'not'
(
'not'
A2
)
is
boolean
set
K114
(1,
(
'not'
A2
)
) is
set
K220
(
(
'not'
(
'not'
A2
)
)
,
s2
) is
set
'not'
(
'not'
(
'not'
A2
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
A2
)
)
) is
set
'not'
s2
is
boolean
set
K114
(1,
s2
) is
set
(
'not'
(
'not'
(
'not'
A2
)
)
)
'&'
(
'not'
s2
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
A2
)
)
)
,
(
'not'
s2
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
A2
)
)
)
'&'
(
'not'
s2
)
)
is
boolean
set
K221
(
s2
,
(
'not'
A2
)
) is
set
K220
(
(
'not'
s2
)
,
(
'not'
A2
)
) is
set
'not'
(
'not'
s2
)
is
boolean
set
K114
(1,
(
'not'
s2
)
) is
set
(
'not'
(
'not'
s2
)
)
'&'
(
'not'
(
'not'
A2
)
)
is
set
K111
(
(
'not'
(
'not'
s2
)
)
,
(
'not'
(
'not'
A2
)
)
) is
set
'not'
(
(
'not'
(
'not'
s2
)
)
'&'
(
'not'
(
'not'
A2
)
)
)
is
boolean
set
K221
(
(
'not'
A2
)
,
s2
)
'&'
K221
(
s2
,
(
'not'
A2
)
) is
set
'not'
K222
(
(
'not'
A2
)
,
s2
) is
boolean
set
'not'
t
is
boolean
Element
of
BOOLEAN
K114
(1,
t
) is
set
(
(
'not'
A2
)
'xor'
s2
)
'xor'
(
'not'
t
)
is
boolean
Element
of
BOOLEAN
K222
(
(
(
'not'
A2
)
'xor'
s2
)
,
(
'not'
t
)
) is
set
K221
(
(
(
'not'
A2
)
'xor'
s2
)
,
(
'not'
t
)
) is
set
'not'
(
(
'not'
A2
)
'xor'
s2
)
is
boolean
set
K114
(1,
(
(
'not'
A2
)
'xor'
s2
)
) is
set
K220
(
(
'not'
(
(
'not'
A2
)
'xor'
s2
)
)
,
(
'not'
t
)
) is
set
'not'
(
'not'
(
(
'not'
A2
)
'xor'
s2
)
)
is
boolean
set
K114
(1,
(
'not'
(
(
'not'
A2
)
'xor'
s2
)
)
) is
set
'not'
(
'not'
t
)
is
boolean
set
K114
(1,
(
'not'
t
)
) is
set
(
'not'
(
'not'
(
(
'not'
A2
)
'xor'
s2
)
)
)
'&'
(
'not'
(
'not'
t
)
)
is
set
K111
(
(
'not'
(
'not'
(
(
'not'
A2
)
'xor'
s2
)
)
)
,
(
'not'
(
'not'
t
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
(
'not'
A2
)
'xor'
s2
)
)
)
'&'
(
'not'
(
'not'
t
)
)
)
is
boolean
set
K221
(
(
'not'
t
)
,
(
(
'not'
A2
)
'xor'
s2
)
) is
set
K220
(
(
'not'
(
'not'
t
)
)
,
(
(
'not'
A2
)
'xor'
s2
)
) is
set
'not'
(
'not'
(
'not'
t
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
t
)
)
) is
set
(
'not'
(
'not'
(
'not'
t
)
)
)
'&'
(
'not'
(
(
'not'
A2
)
'xor'
s2
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
t
)
)
)
,
(
'not'
(
(
'not'
A2
)
'xor'
s2
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
t
)
)
)
'&'
(
'not'
(
(
'not'
A2
)
'xor'
s2
)
)
)
is
boolean
set
K221
(
(
(
'not'
A2
)
'xor'
s2
)
,
(
'not'
t
)
)
'&'
K221
(
(
'not'
t
)
,
(
(
'not'
A2
)
'xor'
s2
)
) is
set
'not'
K222
(
(
(
'not'
A2
)
'xor'
s2
)
,
(
'not'
t
)
) is
boolean
set
(
'not'
A2
)
'&'
s2
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
A2
)
,
s2
) is
set
s2
'&'
(
'not'
t
)
is
boolean
Element
of
BOOLEAN
K111
(
s2
,
(
'not'
t
)
) is
set
(
(
'not'
A2
)
'&'
s2
)
'or'
(
s2
'&'
(
'not'
t
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
'not'
A2
)
'&'
s2
)
is
boolean
set
K114
(1,
(
(
'not'
A2
)
'&'
s2
)
) is
set
'not'
(
s2
'&'
(
'not'
t
)
)
is
boolean
set
K114
(1,
(
s2
'&'
(
'not'
t
)
)
) is
set
(
'not'
(
(
'not'
A2
)
'&'
s2
)
)
'&'
(
'not'
(
s2
'&'
(
'not'
t
)
)
)
is
set
K111
(
(
'not'
(
(
'not'
A2
)
'&'
s2
)
)
,
(
'not'
(
s2
'&'
(
'not'
t
)
)
)
) is
set
'not'
(
(
'not'
(
(
'not'
A2
)
'&'
s2
)
)
'&'
(
'not'
(
s2
'&'
(
'not'
t
)
)
)
)
is
boolean
set
(
'not'
t
)
'&'
(
'not'
A2
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
t
)
,
(
'not'
A2
)
) is
set
(
(
(
'not'
A2
)
'&'
s2
)
'or'
(
s2
'&'
(
'not'
t
)
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
(
'not'
A2
)
'&'
s2
)
'or'
(
s2
'&'
(
'not'
t
)
)
)
is
boolean
set
K114
(1,
(
(
(
'not'
A2
)
'&'
s2
)
'or'
(
s2
'&'
(
'not'
t
)
)
)
) is
set
'not'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
is
boolean
set
K114
(1,
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
) is
set
(
'not'
(
(
(
'not'
A2
)
'&'
s2
)
'or'
(
s2
'&'
(
'not'
t
)
)
)
)
'&'
(
'not'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
)
is
set
K111
(
(
'not'
(
(
(
'not'
A2
)
'&'
s2
)
'or'
(
s2
'&'
(
'not'
t
)
)
)
)
,
(
'not'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
)
) is
set
'not'
(
(
'not'
(
(
(
'not'
A2
)
'&'
s2
)
'or'
(
s2
'&'
(
'not'
t
)
)
)
)
'&'
(
'not'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
)
)
is
boolean
set
'not'
(
(
(
(
'not'
A2
)
'&'
s2
)
'or'
(
s2
'&'
(
'not'
t
)
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
(
(
'not'
A2
)
'&'
s2
)
'or'
(
s2
'&'
(
'not'
t
)
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
)
) is
set
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s1
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
S
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
S
is
set
S
.
z
is
set
S
.
y
is
set
the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is
Relation-like
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
-defined
Function-like
V23
( the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
set
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is non
empty
set
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
) is
functional
V49
()
V50
()
set
a
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
Following
(
a
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
a
,2)
)
.
(
x
,
y
,
z
) is
set
Following
(
S
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
S
,2)
)
.
(
x
,
y
,
z
) is
boolean
Element
of
BOOLEAN
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s1
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s2
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
s2
is
set
S
.
x
is
set
(
Following
(
a
,2)
)
.
(
x
,
y
,
z
) is
set
Following
(
s2
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
s2
,2)
)
.
(
x
,
y
,
z
) is
boolean
Element
of
BOOLEAN
s2
.
z
is
set
s2
.
y
is
set
s2
.
x
is
set
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,()
]
is non
empty
pair
set
{
<*
x
,
y
*>
,()
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,()
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,()
]
is non
empty
pair
set
{
<*
y
,
z
*>
,()
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,()
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2b
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2b
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2b
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2a
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2a
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2a
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2a
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,()) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
2GatesCircuit
(
x
,
y
,
z
,()) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
x
,
y
,
z
,()))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
x
,
y
,
z
,())
1GateCircuit
(
x
,
y
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
<*
x
,
y
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,())
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
z
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
1GateCircuit
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
(
1GateCircuit
(
x
,
y
,())
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,()
]
,
z
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,())
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,()
]
,
z
*>
,())
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
1GateCircuit
(
x
,
y
,
and2a
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
1GateCircuit
(
<*
x
,
y
*>
,
and2a
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
1GateCircuit
(
y
,
z
,()) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
z
*>
,()))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,())
1GateCircuit
(
<*
y
,
z
*>
,()) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,())
(
1GateCircuit
(
x
,
y
,
and2a
)
)
+*
(
1GateCircuit
(
y
,
z
,())
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
1GateCircuit
(
z
,
x
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
1GateCircuit
(
<*
z
,
x
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
(
(
1GateCircuit
(
x
,
y
,
and2a
)
)
+*
(
1GateCircuit
(
y
,
z
,())
)
)
+*
(
1GateCircuit
(
z
,
x
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2a
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,())
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
1GateCircuit
(
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
(
x
,
y
,
z
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2a
]
,
[
<*
y
,
z
*>
,()
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
Following
(
s1
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
2
+
1 is
V9
()
V10
()
V11
()
V15
() non
pair
Element
of
NAT
Following
(
s1
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s2
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s2
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
Following
(
s2
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s2
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is
Relation-like
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
-defined
Function-like
V23
( the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
set
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is non
empty
set
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
) is
functional
V49
()
V50
()
set
Following
(
s
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
(
Following
(
s
,3)
)
is
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
t
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
Following
(
t
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
t
,2)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
Following
(
s1
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
t
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
t
,3)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
(
Following
(
t
,2)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
Following
(
s2
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
t
,3)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
the
carrier
of (
x
,
y
,
z
)
\/
the
carrier
of (
x
,
y
,
z
) is
set
proj1
(
Following
(
s1
,2)
)
is
set
proj1
(
Following
(
s2
,2)
)
is
set
a
is
set
(
Following
(
s
,2)
)
.
a
is
set
(
Following
(
s1
,2)
)
.
a
is
set
(
Following
(
s
,3)
)
.
a
is
set
(
Following
(
s1
,3)
)
.
a
is
set
(
Following
(
s2
,2)
)
.
a
is
set
(
Following
(
s2
,3)
)
.
a
is
set
Following
(
Following
(
s
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
Following
(
s
,2)
)
)
.
a
is
set
Following
(
s
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
(
Following
(
s
,2)
)
is
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircuit
(
f1
,
f2
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
1GateCircuit
(
f2
,
f3
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
(
1GateCircuit
(
f1
,
f2
,
and2b
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
1GateCircuit
(
f3
,
f1
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
(
(
1GateCircuit
(
f1
,
f2
,
and2b
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2b
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
1GateCircuit
(
f2
,
f3
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
(
1GateCircuit
(
f1
,
f2
,
and2b
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
1GateCircuit
(
f3
,
f1
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
(
(
1GateCircuit
(
f1
,
f2
,
and2b
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2b
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Function-like
set
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
set
the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
))
the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
InnerVertices
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
set
the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
))
the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)) is
set
K538
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
, the
ResultSort
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
+*
(
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
is
set
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
(
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
(
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
Function-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
(
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Function-like
set
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is
set
{
f2
,
f3
}
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
set
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
set
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
)
is
set
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
)
is
set
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
)
is
set
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
Function-like
set
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
}
is
Relation-like
Function-like
set
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
is
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
)
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
) is
set
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
)
is
set
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Function-like
set
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
(
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
(
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
set
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
(
(
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
)
is
set
{
f1
,
f2
}
is
set
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Element
of
K18
(
{
f1
,
f2
}
)
K18
(
{
f1
,
f2
}
) is
set
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
is
set
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
)
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
)
is
set
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
is
Element
of
K18
(
{
f2
,
f3
}
)
K18
(
{
f2
,
f3
}
) is
set
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
is
set
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
)
K18
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
\
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
)
is
set
{
f3
,
f1
}
is
set
{
f3
,
f1
}
\
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
is
Element
of
K18
(
{
f3
,
f1
}
)
K18
(
{
f3
,
f1
}
) is
set
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
{
f3
,
f1
}
\
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
)
is
set
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Element
of
K18
(
{
f3
,
f1
}
)
(
(
(
{
f1
,
f2
}
\
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
)
is
set
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
is
set
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
)
K18
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
) is
set
(
(
{
f1
,
f2
}
\/
(
{
f2
,
f3
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
}
)
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
)
is
set
{
f1
,
f2
}
\/
{
f2
,
f3
}
is
set
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
)
K18
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
) is
set
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
(
{
f3
,
f1
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
)
is
set
(
(
{
f1
,
f2
}
\/
{
f2
,
f3
}
)
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f2
,
f3
}
is
set
{
f1
,
f2
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f2
,
f3
}
) is
set
(
{
f1
,
f2
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
f3
,
f1
}
is
set
{
f2
,
f2
,
f1
,
f3
}
is
set
{
f2
,
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
{
f2
,
f2
,
f1
,
f3
}
)
K18
(
{
f2
,
f2
,
f1
,
f3
}
) is
set
(
{
f2
,
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
f3
,
f1
}
is
set
{
f2
,
f1
,
f3
}
is
set
{
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
{
f2
,
f1
,
f3
}
)
K18
(
{
f2
,
f1
,
f3
}
) is
set
(
{
f2
,
f1
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f3
}
) is
set
(
{
f1
,
f2
,
f3
}
\
{
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
,
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
}
is
set
{
f1
}
is
set
{
f1
,
f2
,
f3
,
f3
}
\/
{
f1
}
is
set
{
f3
,
f3
,
f1
,
f2
}
is
set
{
f3
,
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
}
is
set
{
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
,
f1
}
is
set
{
f1
,
f1
,
f2
,
f3
}
is
set
f1
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is
set
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
proj2
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
{
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
}
is
Relation-like
Function-like
set
{
f1
,
f2
,
f3
}
\
{
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
}
is
Element
of
K18
(
{
f1
,
f2
,
f3
}
)
K18
(
{
f1
,
f2
,
f3
}
) is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Element
of
K18
(
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
)
K18
(
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
) is
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
f1
,
f2
,
f3
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
(
(
InputVertices
(
f1
,
f2
,
f3
)
)
\
(
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Relation-like
Element
of
K18
(
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
)
{
f1
,
f2
,
f3
}
\/
(
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
{
f1
,
f2
,
f3
}
\/
{}
is
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
S
is non
empty
pair
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
{
[
<*
f1
,
f2
*>
,
and2b
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
Function-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
(
InputVertices
(
f1
,
f2
,
f3
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
set
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
proj2
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
set
{
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
}
is
Relation-like
Function-like
set
(
proj2
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
)
\/
{
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
}
is
set
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,(
f1
,
f2
,
f3
)
}
is
set
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
and2b
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2b
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
and2b
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2b
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2b
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2b
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,
and2b
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
and2b
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
and2b
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
{
f0
,
x
,
y
}
is
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
{
f1
,
f2
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
{
f2
,
f3
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
{
f3
,
f1
}
is non
with_pair
set
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
set
the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
))
the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
set
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)) is
set
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
\
K538
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
, the
ResultSort
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
) is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
InnerVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
InnerVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
{
[
<*
f1
,
f2
*>
,
and2b
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
Function-like
set
InnerVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
Function-like
set
InnerVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
set
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
set
the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
))
the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is non
empty
set
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)) is
set
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
{
[
<*
f1
,
f2
*>
,
and2b
]
}
\/
{
[
<*
f2
,
f3
*>
,
and2b
]
}
)
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
is
Relation-like
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
}
\/
{
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
Element
of
K18
( the
carrier
of
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
\
K538
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
, the
ResultSort
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
) is
Element
of
K18
( the
carrier
of
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
InputVertices
(
f1
,
f2
,
f3
)
)
\/
(
(
InputVertices
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
\
(
InnerVertices
(
f1
,
f2
,
f3
)
)
)
is
set
(
InputVertices
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
is
set
(
(
InputVertices
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
)
\/
(
InputVertices
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
is
set
{
f1
,
f2
,
f2
,
f3
}
is
set
{
f1
,
f2
,
f2
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f2
,
f2
,
f1
,
f3
}
is
set
{
f2
,
f2
,
f1
,
f3
}
\/
{
f3
,
f1
}
is
set
{
f2
,
f1
,
f3
}
is non
with_pair
set
{
f2
,
f1
,
f3
}
\/
{
f3
,
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f3
,
f1
}
is non
with_pair
set
{
f3
}
is non
with_pair
set
{
f1
}
is non
with_pair
set
{
f3
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
(
{
f3
}
\/
{
f1
}
)
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f3
}
is non
with_pair
set
(
{
f1
,
f2
,
f3
}
\/
{
f3
}
)
\/
{
f1
}
is non
with_pair
set
{
f3
,
f1
,
f2
}
is non
with_pair
set
{
f3
,
f1
,
f2
}
\/
{
f3
}
is non
with_pair
set
(
{
f3
,
f1
,
f2
}
\/
{
f3
}
)
\/
{
f1
}
is non
with_pair
set
{
f3
,
f3
,
f1
,
f2
}
is
set
{
f3
,
f3
,
f1
,
f2
}
\/
{
f1
}
is
set
{
f3
,
f1
,
f2
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f2
,
f3
}
\/
{
f1
}
is non
with_pair
set
{
f1
,
f1
,
f2
,
f3
}
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
1GateCircuit
(
f2
,
f3
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
(
1GateCircuit
(
f1
,
f2
,
and2b
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
1GateCircuit
(
f3
,
f1
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
(
(
1GateCircuit
(
f1
,
f2
,
and2b
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2b
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
the
Sorts
of (
f1
,
f2
,
f3
) is
Relation-like
the
carrier
of (
f1
,
f2
,
f3
)
-defined
Function-like
V23
( the
carrier
of (
f1
,
f2
,
f3
))
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K230
( the
Sorts
of (
f1
,
f2
,
f3
)) is
functional
V49
()
V50
()
set
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
z
.
f1
is
set
z
.
f2
is
set
z
.
f3
is
set
Following
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
(
Following
z
)
.
[
<*
f1
,
f2
*>
,
and2b
]
is
set
(
Following
z
)
.
[
<*
f2
,
f3
*>
,
and2b
]
is
set
(
Following
z
)
.
[
<*
f3
,
f1
*>
,
and2b
]
is
set
S1
is
boolean
Element
of
BOOLEAN
A1
is
boolean
Element
of
BOOLEAN
s1
is
boolean
Element
of
BOOLEAN
'not'
S1
is
boolean
Element
of
BOOLEAN
K114
(1,
S1
) is
set
'not'
A1
is
boolean
Element
of
BOOLEAN
K114
(1,
A1
) is
set
(
'not'
S1
)
'&'
(
'not'
A1
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
S1
)
,
(
'not'
A1
)
) is
set
'not'
s1
is
boolean
Element
of
BOOLEAN
K114
(1,
s1
) is
set
(
'not'
A1
)
'&'
(
'not'
s1
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
A1
)
,
(
'not'
s1
)
) is
set
(
'not'
s1
)
'&'
(
'not'
S1
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
s1
)
,
(
'not'
S1
)
) is
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
proj1
z
is
set
<*
f1
,
f2
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
and2b
.
(
<*
f1
,
f2
*>
*
z
)
is
boolean
set
<*
S1
,
A1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2b
.
<*
S1
,
A1
*>
is
boolean
set
<*
f2
,
f3
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
and2b
.
(
<*
f2
,
f3
*>
*
z
)
is
boolean
set
<*
A1
,
s1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2b
.
<*
A1
,
s1
*>
is
boolean
set
<*
f3
,
f1
*>
*
z
is
Relation-like
NAT
-defined
Function-like
set
and2b
.
(
<*
f3
,
f1
*>
*
z
)
is
boolean
set
<*
s1
,
S1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
and2b
.
<*
s1
,
S1
*>
is
boolean
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
1GateCircuit
(
f2
,
f3
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
(
1GateCircuit
(
f1
,
f2
,
and2b
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
1GateCircuit
(
f3
,
f1
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
(
(
1GateCircuit
(
f1
,
f2
,
and2b
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2b
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
the
Sorts
of (
f1
,
f2
,
f3
) is
Relation-like
the
carrier
of (
f1
,
f2
,
f3
)
-defined
Function-like
V23
( the
carrier
of (
f1
,
f2
,
f3
))
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K230
( the
Sorts
of (
f1
,
f2
,
f3
)) is
functional
V49
()
V50
()
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
A
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
A
.
[
<*
f1
,
f2
*>
,
and2b
]
is
set
A
.
[
<*
f2
,
f3
*>
,
and2b
]
is
set
A
.
[
<*
f3
,
f1
*>
,
and2b
]
is
set
Following
A
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f1
,
f2
,
f3
))
(
Following
A
)
.
(
f1
,
f2
,
f3
) is
boolean
Element
of
BOOLEAN
A1
is
boolean
Element
of
BOOLEAN
s1
is
boolean
Element
of
BOOLEAN
A2
is
boolean
Element
of
BOOLEAN
A1
'or'
s1
is
boolean
Element
of
BOOLEAN
'not'
A1
is
boolean
set
K114
(1,
A1
) is
set
'not'
s1
is
boolean
set
K114
(1,
s1
) is
set
(
'not'
A1
)
'&'
(
'not'
s1
)
is
set
K111
(
(
'not'
A1
)
,
(
'not'
s1
)
) is
set
'not'
(
(
'not'
A1
)
'&'
(
'not'
s1
)
)
is
boolean
set
(
A1
'or'
s1
)
'or'
A2
is
boolean
Element
of
BOOLEAN
'not'
(
A1
'or'
s1
)
is
boolean
set
K114
(1,
(
A1
'or'
s1
)
) is
set
'not'
A2
is
boolean
set
K114
(1,
A2
) is
set
(
'not'
(
A1
'or'
s1
)
)
'&'
(
'not'
A2
)
is
set
K111
(
(
'not'
(
A1
'or'
s1
)
)
,
(
'not'
A2
)
) is
set
'not'
(
(
'not'
(
A1
'or'
s1
)
)
'&'
(
'not'
A2
)
)
is
boolean
set
'not'
(
(
A1
'or'
s1
)
'or'
A2
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
A1
'or'
s1
)
'or'
A2
)
) is
set
proj1
A
is
set
t
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
S
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
a
is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
<*
t
,
S
,
a
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
<*
t
,
S
,
a
*>
*
A
is
Relation-like
NAT
-defined
Function-like
set
nor3
.
(
<*
t
,
S
,
a
*>
*
A
)
is
boolean
set
<*
A1
,
s1
,
A2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
nor3
.
<*
A1
,
s1
,
A2
*>
is
boolean
set
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
and2b
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2b
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
and2b
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2b
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2b
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2b
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,
and2b
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
and2b
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
and2b
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
1GateCircuit
(
f0
,
x
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
1GateCircuit
(
<*
f0
,
x
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
1GateCircuit
(
x
,
y
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
1GateCircuit
(
<*
x
,
y
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
(
1GateCircuit
(
f0
,
x
,
and2b
)
)
+*
(
1GateCircuit
(
x
,
y
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
1GateCircuit
(
y
,
f0
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
1GateCircuit
(
<*
y
,
f0
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
(
(
1GateCircuit
(
f0
,
x
,
and2b
)
)
+*
(
1GateCircuit
(
x
,
y
,
and2b
)
)
)
+*
(
1GateCircuit
(
y
,
f0
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
(
f0
,
x
,
y
)
+*
(
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
the
Sorts
of (
f0
,
x
,
y
) is
Relation-like
the
carrier
of (
f0
,
x
,
y
)
-defined
Function-like
V23
( the
carrier
of (
f0
,
x
,
y
))
set
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K230
( the
Sorts
of (
f0
,
x
,
y
)) is
functional
V49
()
V50
()
set
(
f0
,
x
,
y
) is
Element
of
InnerVertices
(
f0
,
x
,
y
)
InnerVertices
(
f0
,
x
,
y
) is non
empty
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
[
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
}
}
is
set
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
S1
.
f0
is
set
S1
.
x
is
set
S1
.
y
is
set
Following
(
S1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
(
Following
(
S1
,2)
)
.
(
f0
,
x
,
y
) is
boolean
Element
of
BOOLEAN
(
Following
(
S1
,2)
)
.
[
<*
f0
,
x
*>
,
and2b
]
is
set
(
Following
(
S1
,2)
)
.
[
<*
x
,
y
*>
,
and2b
]
is
set
(
Following
(
S1
,2)
)
.
[
<*
y
,
f0
*>
,
and2b
]
is
set
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
Following
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
s
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
s
is
boolean
Element
of
BOOLEAN
S2
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
S2
is
boolean
Element
of
BOOLEAN
Following
(
Following
S1
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
s2
is
boolean
Element
of
BOOLEAN
t
is
boolean
Element
of
BOOLEAN
S
is
boolean
Element
of
BOOLEAN
'not'
s2
is
boolean
Element
of
BOOLEAN
K114
(1,
s2
) is
set
'not'
t
is
boolean
Element
of
BOOLEAN
K114
(1,
t
) is
set
(
'not'
s2
)
'&'
(
'not'
t
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
s2
)
,
(
'not'
t
)
) is
set
'not'
S
is
boolean
Element
of
BOOLEAN
K114
(1,
S
) is
set
(
'not'
t
)
'&'
(
'not'
S
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
t
)
,
(
'not'
S
)
) is
set
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
is
boolean
set
K114
(1,
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
) is
set
'not'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
is
boolean
set
K114
(1,
(
(
'not'
t
)
'&'
(
'not'
S
)
)
) is
set
(
'not'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
'&'
(
'not'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
)
is
set
K111
(
(
'not'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
,
(
'not'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
)
) is
set
'not'
(
(
'not'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
'&'
(
'not'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
)
)
is
boolean
set
(
'not'
S
)
'&'
(
'not'
s2
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
S
)
,
(
'not'
s2
)
) is
set
(
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
)
'or'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
)
is
boolean
set
K114
(1,
(
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
)
) is
set
'not'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
is
boolean
set
K114
(1,
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
) is
set
(
'not'
(
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
)
)
'&'
(
'not'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
)
is
set
K111
(
(
'not'
(
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
)
)
,
(
'not'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
)
) is
set
'not'
(
(
'not'
(
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
)
)
'&'
(
'not'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
)
)
is
boolean
set
'not'
(
(
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
)
'or'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
S
)
)
)
'or'
(
(
'not'
S
)
'&'
(
'not'
s2
)
)
)
) is
set
(
Following
S1
)
.
[
<*
y
,
f0
*>
,
and2b
]
is
set
(
Following
S1
)
.
[
<*
f0
,
x
*>
,
and2b
]
is
set
(
Following
S1
)
.
[
<*
x
,
y
*>
,
and2b
]
is
set
A
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
Following
S1
)
.
A
is
boolean
Element
of
BOOLEAN
f0
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
and2b
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2b
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
and2b
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
f0
*>
,
and2b
]
is non
empty
pair
set
{
<*
y
,
f0
*>
,
and2b
}
is
functional
set
{
<*
y
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
y
,
f0
*>
,
and2b
}
,
{
<*
y
,
f0
*>
}
}
is
set
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f0
,
x
*>
,
and2b
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
and2b
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
and2b
}
,
{
<*
f0
,
x
*>
}
}
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
(
f0
,
x
,
y
) is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
))
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
1GateCircuit
(
f0
,
x
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
1GateCircuit
(
<*
f0
,
x
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
1GateCircuit
(
x
,
y
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
1GateCircuit
(
<*
x
,
y
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
(
1GateCircuit
(
f0
,
x
,
and2b
)
)
+*
(
1GateCircuit
(
x
,
y
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
1GateCircuit
(
y
,
f0
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
1GateCircuit
(
<*
y
,
f0
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
(
(
1GateCircuit
(
f0
,
x
,
and2b
)
)
+*
(
1GateCircuit
(
x
,
y
,
and2b
)
)
)
+*
(
1GateCircuit
(
y
,
f0
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f0
,
x
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
y
,
f0
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
(
f0
,
x
,
y
)
+*
(
1GateCircuit
(
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f0
,
x
,
y
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
)
)
the
Sorts
of (
f0
,
x
,
y
) is
Relation-like
the
carrier
of (
f0
,
x
,
y
)
-defined
Function-like
V23
( the
carrier
of (
f0
,
x
,
y
))
set
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
K230
( the
Sorts
of (
f0
,
x
,
y
)) is
functional
V49
()
V50
()
set
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
(
S1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
A
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
A
is
boolean
Element
of
BOOLEAN
s
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
s
is
boolean
Element
of
BOOLEAN
S2
is
Element
of the
carrier
of (
f0
,
x
,
y
)
S1
.
S2
is
boolean
Element
of
BOOLEAN
Following
(
Following
(
S1
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
S1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
Following
(
Following
S1
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f0
,
x
,
y
))
InputVertices
(
f0
,
x
,
y
) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
K18
( the
carrier
of (
f0
,
x
,
y
)) is
set
the
ResultSort
of (
f0
,
x
,
y
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))
Element
of
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)))
the
carrier'
of (
f0
,
x
,
y
) is non
empty
set
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f0
,
x
,
y
), the
carrier
of (
f0
,
x
,
y
))) is
set
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
the
carrier
of (
f0
,
x
,
y
)
\
K538
( the
carrier
of (
f0
,
x
,
y
), the
ResultSort
of (
f0
,
x
,
y
)) is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
(
Following
S1
)
.
y
is
set
(
Following
(
S1
,2)
)
.
y
is
set
(
Following
S1
)
.
x
is
set
(
Following
(
S1
,2)
)
.
x
is
set
(
Following
S1
)
.
f0
is
set
(
Following
(
S1
,2)
)
.
f0
is
set
S1
.
y
is
set
(
Following
(
S1
,2)
)
.
[
<*
f0
,
x
*>
,
and2b
]
is
set
'not'
(
S1
.
A
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
S1
.
A
)
) is
set
'not'
(
S1
.
s
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
S1
.
s
)
) is
set
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
(
S1
.
A
)
)
,
(
'not'
(
S1
.
s
)
)
) is
set
S1
.
x
is
set
(
Following
(
S1
,2)
)
.
[
<*
y
,
f0
*>
,
and2b
]
is
set
'not'
(
S1
.
S2
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
S1
.
S2
)
) is
set
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
S2
)
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
(
S1
.
A
)
)
,
(
'not'
(
S1
.
S2
)
)
) is
set
S1
.
f0
is
set
(
Following
(
S1
,2)
)
.
[
<*
x
,
y
*>
,
and2b
]
is
set
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
(
S1
.
s
)
)
,
(
'not'
(
S1
.
S2
)
)
) is
set
(
f0
,
x
,
y
) is
Element
of
InnerVertices
(
f0
,
x
,
y
)
InnerVertices
(
f0
,
x
,
y
) is non
empty
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
[
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
*>
}
}
is
set
(
Following
(
S1
,2)
)
.
(
f0
,
x
,
y
) is
boolean
Element
of
BOOLEAN
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
is
boolean
set
K114
(1,
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
) is
set
'not'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
is
boolean
set
K114
(1,
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
) is
set
(
'not'
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
)
'&'
(
'not'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
is
set
K111
(
(
'not'
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
)
,
(
'not'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
) is
set
'not'
(
(
'not'
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
)
'&'
(
'not'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
)
is
boolean
set
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
(
S1
.
S2
)
)
,
(
'not'
(
S1
.
A
)
)
) is
set
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
'or'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
is
boolean
set
K114
(1,
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
) is
set
'not'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
is
boolean
set
K114
(1,
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
) is
set
(
'not'
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
)
'&'
(
'not'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
)
is
set
K111
(
(
'not'
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
)
,
(
'not'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
)
) is
set
'not'
(
(
'not'
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
)
'&'
(
'not'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
)
)
is
boolean
set
'not'
(
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
'or'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
(
(
'not'
(
S1
.
A
)
)
'&'
(
'not'
(
S1
.
s
)
)
)
'or'
(
(
'not'
(
S1
.
s
)
)
'&'
(
'not'
(
S1
.
S2
)
)
)
)
'or'
(
(
'not'
(
S1
.
S2
)
)
'&'
(
'not'
(
S1
.
A
)
)
)
)
) is
set
a
is
set
v
is
Element
of the
carrier
of (
f0
,
x
,
y
)
(
InputVertices
(
f0
,
x
,
y
)
)
\/
(
InnerVertices
(
f0
,
x
,
y
)
)
is
Element
of
K18
( the
carrier
of (
f0
,
x
,
y
))
(
Following
(
S1
,2)
)
.
a
is
set
(
Following
(
Following
(
S1
,2)
)
)
.
a
is
set
{
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
}
is
Relation-like
set
{
(
f0
,
x
,
y
)
}
is
set
{
[
<*
f0
,
x
*>
,
and2b
]
,
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
f0
*>
,
and2b
]
}
\/
{
(
f0
,
x
,
y
)
}
is
set
proj1
(
Following
(
Following
(
S1
,2)
)
)
is
set
proj1
(
Following
(
S1
,2)
)
is
set
f1
is
set
f2
is
set
f3
is
set
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
2GatesCircuit
(
f1
,
f2
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircuit
(
f1
,
f2
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
1GateCircuit
(
<*
f1
,
f2
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
(
1GateCircuit
(
f1
,
f2
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,
xor2
]
}
is
Relation-like
Function-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
x
is
set
f0
is
set
y
is
set
(
f0
,
x
,
y
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f0
,
x
,
y
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f0
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f0
,
x
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f0
,
x
*>
,
xor2
]
is non
empty
pair
set
{
<*
f0
,
x
*>
,
xor2
}
is
functional
set
{
<*
f0
,
x
*>
}
is
functional
V49
()
set
{
{
<*
f0
,
x
*>
,
xor2
}
,
{
<*
f0
,
x
*>
}
}
is
set
<*
[
<*
f0
,
x
*>
,
xor2
]
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
xor2
]
,
y
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f0
,
x
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f0
,
x
*>
,
xor2
]
,
y
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f0
,
x
,
y
) is non
empty
set
s
is
set
z
is
set
A
is
set
(
z
,
A
,
s
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
z
,
A
,
s
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
z
,
A
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
z
,
A
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
z
,
A
*>
,
xor2
]
is non
empty
pair
set
{
<*
z
,
A
*>
,
xor2
}
is
functional
set
{
<*
z
,
A
*>
}
is
functional
V49
()
set
{
{
<*
z
,
A
*>
,
xor2
}
,
{
<*
z
,
A
*>
}
}
is
set
<*
[
<*
z
,
A
*>
,
xor2
]
,
s
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
z
,
A
*>
,
xor2
]
,
s
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
z
,
A
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
z
,
A
*>
,
xor2
]
,
s
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
z
,
A
,
s
) is non
empty
set
S2
is
set
S1
is
set
<*
S2
,
S1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
S2
,
S1
*>
,
xor2
]
is non
empty
pair
set
{
<*
S2
,
S1
*>
,
xor2
}
is
functional
set
{
<*
S2
,
S1
*>
}
is
functional
V49
()
set
{
{
<*
S2
,
S1
*>
,
xor2
}
,
{
<*
S2
,
S1
*>
}
}
is
set
A1
is
set
(
S2
,
S1
,
A1
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
S2
,
S1
,
A1
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
S2
,
S1
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
S2
,
S1
*>
,
xor2
]
,
A1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
S2
,
S1
*>
,
xor2
]
,
A1
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
S2
,
S1
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
S2
,
S1
*>
,
xor2
]
,
A1
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
S2
,
S1
,
A1
) is non
empty
set
s1
is
set
A2
is
set
<*
s1
,
A2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
s1
,
A2
*>
,
xor2
]
is non
empty
pair
set
{
<*
s1
,
A2
*>
,
xor2
}
is
functional
set
{
<*
s1
,
A2
*>
}
is
functional
V49
()
set
{
{
<*
s1
,
A2
*>
,
xor2
}
,
{
<*
s1
,
A2
*>
}
}
is
set
s2
is
set
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
,
xor2
}
is
functional
set
{
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
,
xor2
}
,
{
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
}
}
is
set
(
s1
,
A2
,
s2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
s1
,
A2
,
s2
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
s1
,
A2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
s1
,
A2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
s1
,
A2
*>
,
xor2
]
,
s2
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
s1
,
A2
,
s2
) is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f3
is
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
xor2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
xor2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
1GateCircuit
(
f2
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
(
1GateCircuit
(
f2
,
f3
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
A
is
boolean
Element
of
BOOLEAN
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
z
.
f2
is
set
s
is
boolean
Element
of
BOOLEAN
z
.
f3
is
set
S2
is
boolean
Element
of
BOOLEAN
z
.
f0
is
set
Following
z
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
z
)
.
[
<*
f2
,
f3
*>
,
xor2
]
is
set
A
'xor'
s
is
boolean
Element
of
BOOLEAN
K222
(
A
,
s
) is
set
K221
(
A
,
s
) is
set
'not'
A
is
boolean
set
K114
(1,
A
) is
set
K220
(
(
'not'
A
)
,
s
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
'not'
s
is
boolean
set
K114
(1,
s
) is
set
(
'not'
(
'not'
A
)
)
'&'
(
'not'
s
)
is
set
K111
(
(
'not'
(
'not'
A
)
)
,
(
'not'
s
)
) is
set
'not'
(
(
'not'
(
'not'
A
)
)
'&'
(
'not'
s
)
)
is
boolean
set
K221
(
s
,
A
) is
set
K220
(
(
'not'
s
)
,
A
) is
set
'not'
(
'not'
s
)
is
boolean
set
K114
(1,
(
'not'
s
)
) is
set
(
'not'
(
'not'
s
)
)
'&'
(
'not'
A
)
is
set
K111
(
(
'not'
(
'not'
s
)
)
,
(
'not'
A
)
) is
set
'not'
(
(
'not'
(
'not'
s
)
)
'&'
(
'not'
A
)
)
is
boolean
set
K221
(
A
,
s
)
'&'
K221
(
s
,
A
) is
set
'not'
K222
(
A
,
s
) is
boolean
set
(
Following
z
)
.
f2
is
set
(
Following
z
)
.
f3
is
set
(
Following
z
)
.
f0
is
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
xor2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
xor2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
1GateCircuit
(
f2
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
(
1GateCircuit
(
f2
,
f3
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
2GatesCircOutput
(
f2
,
f3
,
f0
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
[
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
}
,
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
}
}
is
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
S2
is
boolean
Element
of
BOOLEAN
s
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
s
.
[
<*
f2
,
f3
*>
,
xor2
]
is
set
S1
is
boolean
Element
of
BOOLEAN
s
.
f2
is
set
A1
is
boolean
Element
of
BOOLEAN
s
.
f3
is
set
s1
is
boolean
Element
of
BOOLEAN
s
.
f0
is
set
Following
s
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
s
)
.
(
f2
,
f3
,
f0
) is
boolean
Element
of
BOOLEAN
S2
'xor'
s1
is
boolean
Element
of
BOOLEAN
K222
(
S2
,
s1
) is
set
K221
(
S2
,
s1
) is
set
'not'
S2
is
boolean
set
K114
(1,
S2
) is
set
K220
(
(
'not'
S2
)
,
s1
) is
set
'not'
(
'not'
S2
)
is
boolean
set
K114
(1,
(
'not'
S2
)
) is
set
'not'
s1
is
boolean
set
K114
(1,
s1
) is
set
(
'not'
(
'not'
S2
)
)
'&'
(
'not'
s1
)
is
set
K111
(
(
'not'
(
'not'
S2
)
)
,
(
'not'
s1
)
) is
set
'not'
(
(
'not'
(
'not'
S2
)
)
'&'
(
'not'
s1
)
)
is
boolean
set
K221
(
s1
,
S2
) is
set
K220
(
(
'not'
s1
)
,
S2
) is
set
'not'
(
'not'
s1
)
is
boolean
set
K114
(1,
(
'not'
s1
)
) is
set
(
'not'
(
'not'
s1
)
)
'&'
(
'not'
S2
)
is
set
K111
(
(
'not'
(
'not'
s1
)
)
,
(
'not'
S2
)
) is
set
'not'
(
(
'not'
(
'not'
s1
)
)
'&'
(
'not'
S2
)
)
is
boolean
set
K221
(
S2
,
s1
)
'&'
K221
(
s1
,
S2
) is
set
'not'
K222
(
S2
,
s1
) is
boolean
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
xor2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
xor2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
1GateCircuit
(
f2
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
(
1GateCircuit
(
f2
,
f3
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
2GatesCircOutput
(
f2
,
f3
,
f0
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
[
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
}
,
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
}
}
is
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
S2
is
boolean
Element
of
BOOLEAN
s
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
s
.
f2
is
set
S1
is
boolean
Element
of
BOOLEAN
s
.
f3
is
set
A1
is
boolean
Element
of
BOOLEAN
s
.
f0
is
set
Following
(
s
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
(
s
,2)
)
.
(
f2
,
f3
,
f0
) is
boolean
Element
of
BOOLEAN
S2
'xor'
S1
is
boolean
Element
of
BOOLEAN
K222
(
S2
,
S1
) is
set
K221
(
S2
,
S1
) is
set
'not'
S2
is
boolean
set
K114
(1,
S2
) is
set
K220
(
(
'not'
S2
)
,
S1
) is
set
'not'
(
'not'
S2
)
is
boolean
set
K114
(1,
(
'not'
S2
)
) is
set
'not'
S1
is
boolean
set
K114
(1,
S1
) is
set
(
'not'
(
'not'
S2
)
)
'&'
(
'not'
S1
)
is
set
K111
(
(
'not'
(
'not'
S2
)
)
,
(
'not'
S1
)
) is
set
'not'
(
(
'not'
(
'not'
S2
)
)
'&'
(
'not'
S1
)
)
is
boolean
set
K221
(
S1
,
S2
) is
set
K220
(
(
'not'
S1
)
,
S2
) is
set
'not'
(
'not'
S1
)
is
boolean
set
K114
(1,
(
'not'
S1
)
) is
set
(
'not'
(
'not'
S1
)
)
'&'
(
'not'
S2
)
is
set
K111
(
(
'not'
(
'not'
S1
)
)
,
(
'not'
S2
)
) is
set
'not'
(
(
'not'
(
'not'
S1
)
)
'&'
(
'not'
S2
)
)
is
boolean
set
K221
(
S2
,
S1
)
'&'
K221
(
S1
,
S2
) is
set
'not'
K222
(
S2
,
S1
) is
boolean
set
(
S2
'xor'
S1
)
'xor'
A1
is
boolean
Element
of
BOOLEAN
K222
(
(
S2
'xor'
S1
)
,
A1
) is
set
K221
(
(
S2
'xor'
S1
)
,
A1
) is
set
'not'
(
S2
'xor'
S1
)
is
boolean
set
K114
(1,
(
S2
'xor'
S1
)
) is
set
K220
(
(
'not'
(
S2
'xor'
S1
)
)
,
A1
) is
set
'not'
(
'not'
(
S2
'xor'
S1
)
)
is
boolean
set
K114
(1,
(
'not'
(
S2
'xor'
S1
)
)
) is
set
'not'
A1
is
boolean
set
K114
(1,
A1
) is
set
(
'not'
(
'not'
(
S2
'xor'
S1
)
)
)
'&'
(
'not'
A1
)
is
set
K111
(
(
'not'
(
'not'
(
S2
'xor'
S1
)
)
)
,
(
'not'
A1
)
) is
set
'not'
(
(
'not'
(
'not'
(
S2
'xor'
S1
)
)
)
'&'
(
'not'
A1
)
)
is
boolean
set
K221
(
A1
,
(
S2
'xor'
S1
)
) is
set
K220
(
(
'not'
A1
)
,
(
S2
'xor'
S1
)
) is
set
'not'
(
'not'
A1
)
is
boolean
set
K114
(1,
(
'not'
A1
)
) is
set
(
'not'
(
'not'
A1
)
)
'&'
(
'not'
(
S2
'xor'
S1
)
)
is
set
K111
(
(
'not'
(
'not'
A1
)
)
,
(
'not'
(
S2
'xor'
S1
)
)
) is
set
'not'
(
(
'not'
(
'not'
A1
)
)
'&'
(
'not'
(
S2
'xor'
S1
)
)
)
is
boolean
set
K221
(
(
S2
'xor'
S1
)
,
A1
)
'&'
K221
(
A1
,
(
S2
'xor'
S1
)
) is
set
'not'
K222
(
(
S2
'xor'
S1
)
,
A1
) is
boolean
set
(
Following
(
s
,2)
)
.
[
<*
f2
,
f3
*>
,
xor2
]
is
set
(
Following
(
s
,2)
)
.
f2
is
set
(
Following
(
s
,2)
)
.
f3
is
set
(
Following
(
s
,2)
)
.
f0
is
set
f0
is
set
f2
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
xor2
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
xor2
}
,
{
<*
f2
,
f3
*>
}
}
is
set
(
f2
,
f3
,
f0
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f2
,
f3
,
f0
) is
strict
non-empty
finitely-generated
V107
((
f2
,
f3
,
f0
))
gate`2=den
Boolean
MSAlgebra
over (
f2
,
f3
,
f0
)
2GatesCircuit
(
f2
,
f3
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
1GateCircuit
(
f2
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
<*
f2
,
f3
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
(
1GateCircuit
(
f2
,
f3
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f2
,
f3
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
)
)
the
Sorts
of (
f2
,
f3
,
f0
) is
Relation-like
the
carrier
of (
f2
,
f3
,
f0
)
-defined
Function-like
V23
( the
carrier
of (
f2
,
f3
,
f0
))
set
the
carrier
of (
f2
,
f3
,
f0
) is non
empty
set
K230
( the
Sorts
of (
f2
,
f3
,
f0
)) is
functional
V49
()
V50
()
set
(
f2
,
f3
,
f0
) is
Element
of
InnerVertices
(
f2
,
f3
,
f0
)
InnerVertices
(
f2
,
f3
,
f0
) is non
empty
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
K18
( the
carrier
of (
f2
,
f3
,
f0
)) is
set
the
ResultSort
of (
f2
,
f3
,
f0
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))
Element
of
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)))
the
carrier'
of (
f2
,
f3
,
f0
) is non
empty
set
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f2
,
f3
,
f0
), the
carrier
of (
f2
,
f3
,
f0
))) is
set
K538
( the
carrier
of (
f2
,
f3
,
f0
), the
ResultSort
of (
f2
,
f3
,
f0
)) is
Element
of
K18
( the
carrier
of (
f2
,
f3
,
f0
))
2GatesCircOutput
(
f2
,
f3
,
f0
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f2
,
f3
,
f0
,
xor2
)
)
)
[
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
,
xor2
}
,
{
<*
[
<*
f2
,
f3
*>
,
xor2
]
,
f0
*>
}
}
is
set
y
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
y
.
f2
is
set
y
.
f3
is
set
y
.
f0
is
set
Following
(
y
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
f2
,
f3
,
f0
))
(
Following
(
y
,2)
)
.
(
f2
,
f3
,
f0
) is
boolean
Element
of
BOOLEAN
z
is
boolean
Element
of
BOOLEAN
A
is
boolean
Element
of
BOOLEAN
s
is
boolean
Element
of
BOOLEAN
'not'
z
is
boolean
Element
of
BOOLEAN
K114
(1,
z
) is
set
'not'
A
is
boolean
Element
of
BOOLEAN
K114
(1,
A
) is
set
(
'not'
z
)
'xor'
(
'not'
A
)
is
boolean
Element
of
BOOLEAN
K222
(
(
'not'
z
)
,
(
'not'
A
)
) is
set
K221
(
(
'not'
z
)
,
(
'not'
A
)
) is
set
'not'
(
'not'
z
)
is
boolean
set
K114
(1,
(
'not'
z
)
) is
set
K220
(
(
'not'
(
'not'
z
)
)
,
(
'not'
A
)
) is
set
'not'
(
'not'
(
'not'
z
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
z
)
)
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
(
'not'
(
'not'
(
'not'
z
)
)
)
'&'
(
'not'
(
'not'
A
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
z
)
)
)
,
(
'not'
(
'not'
A
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
z
)
)
)
'&'
(
'not'
(
'not'
A
)
)
)
is
boolean
set
K221
(
(
'not'
A
)
,
(
'not'
z
)
) is
set
K220
(
(
'not'
(
'not'
A
)
)
,
(
'not'
z
)
) is
set
'not'
(
'not'
(
'not'
A
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
A
)
)
) is
set
(
'not'
(
'not'
(
'not'
A
)
)
)
'&'
(
'not'
(
'not'
z
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
A
)
)
)
,
(
'not'
(
'not'
z
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
A
)
)
)
'&'
(
'not'
(
'not'
z
)
)
)
is
boolean
set
K221
(
(
'not'
z
)
,
(
'not'
A
)
)
'&'
K221
(
(
'not'
A
)
,
(
'not'
z
)
) is
set
'not'
K222
(
(
'not'
z
)
,
(
'not'
A
)
) is
boolean
set
'not'
s
is
boolean
Element
of
BOOLEAN
K114
(1,
s
) is
set
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
'xor'
(
'not'
s
)
is
boolean
Element
of
BOOLEAN
K222
(
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
) is
set
K221
(
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
) is
set
'not'
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
is
boolean
set
K114
(1,
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
) is
set
K220
(
(
'not'
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
)
,
(
'not'
s
)
) is
set
'not'
(
'not'
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
)
is
boolean
set
K114
(1,
(
'not'
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
)
) is
set
'not'
(
'not'
s
)
is
boolean
set
K114
(1,
(
'not'
s
)
) is
set
(
'not'
(
'not'
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
)
)
'&'
(
'not'
(
'not'
s
)
)
is
set
K111
(
(
'not'
(
'not'
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
)
)
,
(
'not'
(
'not'
s
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
)
)
'&'
(
'not'
(
'not'
s
)
)
)
is
boolean
set
K221
(
(
'not'
s
)
,
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
) is
set
K220
(
(
'not'
(
'not'
s
)
)
,
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
) is
set
'not'
(
'not'
(
'not'
s
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
s
)
)
) is
set
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
s
)
)
)
,
(
'not'
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
s
)
)
)
'&'
(
'not'
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
)
)
is
boolean
set
K221
(
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
)
'&'
K221
(
(
'not'
s
)
,
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
) is
set
'not'
K222
(
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
,
(
'not'
s
)
) is
boolean
set
'not'
(
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
'xor'
(
'not'
s
)
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
(
'not'
z
)
'xor'
(
'not'
A
)
)
'xor'
(
'not'
s
)
)
) is
set
z
'xor'
A
is
boolean
Element
of
BOOLEAN
K222
(
z
,
A
) is
set
K221
(
z
,
A
) is
set
'not'
z
is
boolean
set
K220
(
(
'not'
z
)
,
A
) is
set
'not'
(
'not'
z
)
is
boolean
set
K114
(1,
(
'not'
z
)
) is
set
'not'
A
is
boolean
set
(
'not'
(
'not'
z
)
)
'&'
(
'not'
A
)
is
set
K111
(
(
'not'
(
'not'
z
)
)
,
(
'not'
A
)
) is
set
'not'
(
(
'not'
(
'not'
z
)
)
'&'
(
'not'
A
)
)
is
boolean
set
K221
(
A
,
z
) is
set
K220
(
(
'not'
A
)
,
z
) is
set
'not'
(
'not'
A
)
is
boolean
set
K114
(1,
(
'not'
A
)
) is
set
(
'not'
(
'not'
A
)
)
'&'
(
'not'
z
)
is
set
K111
(
(
'not'
(
'not'
A
)
)
,
(
'not'
z
)
) is
set
'not'
(
(
'not'
(
'not'
A
)
)
'&'
(
'not'
z
)
)
is
boolean
set
K221
(
z
,
A
)
'&'
K221
(
A
,
z
) is
set
'not'
K222
(
z
,
A
) is
boolean
set
(
z
'xor'
A
)
'xor'
s
is
boolean
Element
of
BOOLEAN
K222
(
(
z
'xor'
A
)
,
s
) is
set
K221
(
(
z
'xor'
A
)
,
s
) is
set
'not'
(
z
'xor'
A
)
is
boolean
set
K114
(1,
(
z
'xor'
A
)
) is
set
K220
(
(
'not'
(
z
'xor'
A
)
)
,
s
) is
set
'not'
(
'not'
(
z
'xor'
A
)
)
is
boolean
set
K114
(1,
(
'not'
(
z
'xor'
A
)
)
) is
set
'not'
s
is
boolean
set
(
'not'
(
'not'
(
z
'xor'
A
)
)
)
'&'
(
'not'
s
)
is
set
K111
(
(
'not'
(
'not'
(
z
'xor'
A
)
)
)
,
(
'not'
s
)
) is
set
'not'
(
(
'not'
(
'not'
(
z
'xor'
A
)
)
)
'&'
(
'not'
s
)
)
is
boolean
set
K221
(
s
,
(
z
'xor'
A
)
) is
set
K220
(
(
'not'
s
)
,
(
z
'xor'
A
)
) is
set
'not'
(
'not'
s
)
is
boolean
set
K114
(1,
(
'not'
s
)
) is
set
(
'not'
(
'not'
s
)
)
'&'
(
'not'
(
z
'xor'
A
)
)
is
set
K111
(
(
'not'
(
'not'
s
)
)
,
(
'not'
(
z
'xor'
A
)
)
) is
set
'not'
(
(
'not'
(
'not'
s
)
)
'&'
(
'not'
(
z
'xor'
A
)
)
)
is
boolean
set
K221
(
(
z
'xor'
A
)
,
s
)
'&'
K221
(
s
,
(
z
'xor'
A
)
) is
set
'not'
K222
(
(
z
'xor'
A
)
,
s
) is
boolean
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
2GatesCircuit
(
f1
,
f2
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
1GateCircuit
(
f1
,
f2
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
1GateCircuit
(
<*
f1
,
f2
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
(
1GateCircuit
(
f1
,
f2
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
1GateCircuit
(
f1
,
f2
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
1GateCircuit
(
<*
f1
,
f2
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
1GateCircuit
(
f2
,
f3
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
1GateCircuit
(
<*
f2
,
f3
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
(
1GateCircuit
(
f1
,
f2
,
and2b
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
1GateCircuit
(
f3
,
f1
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
1GateCircuit
(
<*
f3
,
f1
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
(
(
1GateCircuit
(
f1
,
f2
,
and2b
)
)
+*
(
1GateCircuit
(
f2
,
f3
,
and2b
)
)
)
+*
(
1GateCircuit
(
f3
,
f1
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
(
f1
,
f2
,
f3
)
+*
(
1GateCircuit
(
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is
strict
non-empty
finitely-generated
V107
((
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
))
gate`2=den
Boolean
MSAlgebra
over (
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
)
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
[
<*
f1
,
f2
*>
,
xor2
]
}
is
Relation-like
Function-like
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
(
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
InnerVertices
(
f1
,
f2
,
f3
)
)
\/
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
set
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
(
InnerVertices
(
f1
,
f2
,
f3
)
)
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
(
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
is
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
xor2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
xor2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
xor2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2b
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2b
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2b
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2b
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2b
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2b
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2b
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2b
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2b
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
\/
{
f1
,
f2
,
f3
}
is non
with_pair
set
f1
is non
pair
set
f2
is non
pair
set
f3
is non
pair
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
nonpair-yielding
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
f1
,
f2
,
f3
) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
)
\
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
{
f1
,
f2
,
f3
}
is non
with_pair
set
f1
is
set
f2
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
}
is
Relation-like
Function-like
set
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
Relation-like
set
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
set
{
(
f1
,
f2
,
f3
)
}
is
set
(
(
{
[
<*
f1
,
f2
*>
,
xor2
]
}
\/
{
(
f1
,
f2
,
f3
)
}
)
\/
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
)
}
\/
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
set
(
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
)
}
\/
{
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
)
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
}
\/
{
(
f1
,
f2
,
f3
)
}
is
set
{
[
<*
f1
,
f2
*>
,
xor2
]
,(
f1
,
f2
,
f3
),
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
,(
f1
,
f2
,
f3
)
}
is
set
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
xor2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
xor2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
xor2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2b
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2b
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2b
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2b
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2b
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2b
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2b
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2b
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2b
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
f1
is
set
f2
is
set
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
f3
is
set
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
f1
is
set
f2
is
set
f3
is
set
2GatesCircOutput
(
f1
,
f2
,
f3
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f1
,
f2
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
xor2
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
xor2
}
is
functional
set
{
<*
f1
,
f2
*>
}
is
functional
V49
()
set
{
{
<*
f1
,
f2
*>
,
xor2
}
,
{
<*
f1
,
f2
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
f1
,
f2
,
f3
,
xor2
)
)
)
[
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
is
functional
set
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
,
xor2
}
,
{
<*
[
<*
f1
,
f2
*>
,
xor2
]
,
f3
*>
}
}
is
set
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f2
,
f3
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
f3
,
f1
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
f1
,
f2
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
f2
,
f3
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
f3
,
f1
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
[
<*
f1
,
f2
*>
,
and2b
]
is non
empty
pair
set
{
<*
f1
,
f2
*>
,
and2b
}
is
functional
set
{
{
<*
f1
,
f2
*>
,
and2b
}
,
{
<*
f1
,
f2
*>
}
}
is
set
[
<*
f2
,
f3
*>
,
and2b
]
is non
empty
pair
set
{
<*
f2
,
f3
*>
,
and2b
}
is
functional
set
{
<*
f2
,
f3
*>
}
is
functional
V49
()
set
{
{
<*
f2
,
f3
*>
,
and2b
}
,
{
<*
f2
,
f3
*>
}
}
is
set
[
<*
f3
,
f1
*>
,
and2b
]
is non
empty
pair
set
{
<*
f3
,
f1
*>
,
and2b
}
is
functional
set
{
<*
f3
,
f1
*>
}
is
functional
V49
()
set
{
{
<*
f3
,
f1
*>
,
and2b
}
,
{
<*
f3
,
f1
*>
}
}
is
set
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
1GateCircStr
(
<*
[
<*
f1
,
f2
*>
,
and2b
]
,
[
<*
f2
,
f3
*>
,
and2b
]
,
[
<*
f3
,
f1
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
f1
,
f2
,
f3
)
+*
(
f1
,
f2
,
f3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
(
f1
,
f2
,
f3
) is
Element
of
InnerVertices
(
f1
,
f2
,
f3
)
the
carrier
of (
f1
,
f2
,
f3
) is non
empty
set
InnerVertices
(
f1
,
f2
,
f3
) is non
empty
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
K18
( the
carrier
of (
f1
,
f2
,
f3
)) is
set
the
ResultSort
of (
f1
,
f2
,
f3
) is
Relation-like
Function-like
V27
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))
Element
of
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)))
the
carrier'
of (
f1
,
f2
,
f3
) is non
empty
set
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
f1
,
f2
,
f3
), the
carrier
of (
f1
,
f2
,
f3
))) is
set
K538
( the
carrier
of (
f1
,
f2
,
f3
), the
ResultSort
of (
f1
,
f2
,
f3
)) is
Element
of
K18
( the
carrier
of (
f1
,
f2
,
f3
))
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
xor2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
xor2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
xor2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2b
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2b
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2b
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2b
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2b
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2b
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2b
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2b
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2b
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
2GatesCircuit
(
x
,
y
,
z
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
1GateCircuit
(
x
,
y
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
1GateCircuit
(
<*
x
,
y
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
1GateCircuit
(
[
<*
x
,
y
*>
,
xor2
]
,
z
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
(
1GateCircuit
(
x
,
y
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,
xor2
]
,
z
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
1GateCircuit
(
x
,
y
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
1GateCircuit
(
<*
x
,
y
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
1GateCircuit
(
y
,
z
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
1GateCircuit
(
<*
y
,
z
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
(
1GateCircuit
(
x
,
y
,
and2b
)
)
+*
(
1GateCircuit
(
y
,
z
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
1GateCircuit
(
z
,
x
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
1GateCircuit
(
<*
z
,
x
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
(
(
1GateCircuit
(
x
,
y
,
and2b
)
)
+*
(
1GateCircuit
(
y
,
z
,
and2b
)
)
)
+*
(
1GateCircuit
(
z
,
x
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
1GateCircuit
(
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
(
x
,
y
,
z
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
(
x
,
y
,
z
) is
Element
of
InnerVertices
(
x
,
y
,
z
)
the
carrier
of (
x
,
y
,
z
) is non
empty
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
2GatesCircOutput
(
x
,
y
,
z
,
xor2
) is non
empty
pair
Element
of
InnerVertices
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
is non
empty
set
InnerVertices
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
is non
empty
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
)
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
) is
set
the
ResultSort
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
is
Relation-like
Function-like
V27
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
)
Element
of
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
))
the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
is non
empty
set
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
) is
Relation-like
set
K18
(
K19
( the
carrier'
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
, the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
)) is
set
K538
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
, the
ResultSort
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
) is
Element
of
K18
( the
carrier
of
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
)
)
[
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
]
is non
empty
pair
set
{
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
}
is
functional
set
{
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
}
,
{
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
}
}
is
set
(
x
,
y
,
z
) is
Element
of
InnerVertices
(
x
,
y
,
z
)
the
carrier
of (
x
,
y
,
z
) is non
empty
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
[
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
]
is non
empty
pair
set
{
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
}
is
functional
set
{
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
}
is
functional
V49
()
set
{
{
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
}
,
{
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
}
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
s1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
s1
.
x
is
set
s1
.
y
is
set
s1
.
z
is
set
Following
(
s1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
s1
,2)
)
.
(
x
,
y
,
z
) is
set
(
Following
(
s1
,2)
)
.
(
x
,
y
,
z
) is
set
A2
is
boolean
Element
of
BOOLEAN
s2
is
boolean
Element
of
BOOLEAN
t
is
boolean
Element
of
BOOLEAN
'not'
A2
is
boolean
Element
of
BOOLEAN
K114
(1,
A2
) is
set
'not'
s2
is
boolean
Element
of
BOOLEAN
K114
(1,
s2
) is
set
(
'not'
A2
)
'xor'
(
'not'
s2
)
is
boolean
Element
of
BOOLEAN
K222
(
(
'not'
A2
)
,
(
'not'
s2
)
) is
set
K221
(
(
'not'
A2
)
,
(
'not'
s2
)
) is
set
'not'
(
'not'
A2
)
is
boolean
set
K114
(1,
(
'not'
A2
)
) is
set
K220
(
(
'not'
(
'not'
A2
)
)
,
(
'not'
s2
)
) is
set
'not'
(
'not'
(
'not'
A2
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
A2
)
)
) is
set
'not'
(
'not'
s2
)
is
boolean
set
K114
(1,
(
'not'
s2
)
) is
set
(
'not'
(
'not'
(
'not'
A2
)
)
)
'&'
(
'not'
(
'not'
s2
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
A2
)
)
)
,
(
'not'
(
'not'
s2
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
A2
)
)
)
'&'
(
'not'
(
'not'
s2
)
)
)
is
boolean
set
K221
(
(
'not'
s2
)
,
(
'not'
A2
)
) is
set
K220
(
(
'not'
(
'not'
s2
)
)
,
(
'not'
A2
)
) is
set
'not'
(
'not'
(
'not'
s2
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
s2
)
)
) is
set
(
'not'
(
'not'
(
'not'
s2
)
)
)
'&'
(
'not'
(
'not'
A2
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
s2
)
)
)
,
(
'not'
(
'not'
A2
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
s2
)
)
)
'&'
(
'not'
(
'not'
A2
)
)
)
is
boolean
set
K221
(
(
'not'
A2
)
,
(
'not'
s2
)
)
'&'
K221
(
(
'not'
s2
)
,
(
'not'
A2
)
) is
set
'not'
K222
(
(
'not'
A2
)
,
(
'not'
s2
)
) is
boolean
set
'not'
t
is
boolean
Element
of
BOOLEAN
K114
(1,
t
) is
set
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
'xor'
(
'not'
t
)
is
boolean
Element
of
BOOLEAN
K222
(
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
,
(
'not'
t
)
) is
set
K221
(
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
,
(
'not'
t
)
) is
set
'not'
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
is
boolean
set
K114
(1,
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
) is
set
K220
(
(
'not'
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
)
,
(
'not'
t
)
) is
set
'not'
(
'not'
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
)
is
boolean
set
K114
(1,
(
'not'
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
)
) is
set
'not'
(
'not'
t
)
is
boolean
set
K114
(1,
(
'not'
t
)
) is
set
(
'not'
(
'not'
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
)
)
'&'
(
'not'
(
'not'
t
)
)
is
set
K111
(
(
'not'
(
'not'
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
)
)
,
(
'not'
(
'not'
t
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
)
)
'&'
(
'not'
(
'not'
t
)
)
)
is
boolean
set
K221
(
(
'not'
t
)
,
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
) is
set
K220
(
(
'not'
(
'not'
t
)
)
,
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
) is
set
'not'
(
'not'
(
'not'
t
)
)
is
boolean
set
K114
(1,
(
'not'
(
'not'
t
)
)
) is
set
(
'not'
(
'not'
(
'not'
t
)
)
)
'&'
(
'not'
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
)
is
set
K111
(
(
'not'
(
'not'
(
'not'
t
)
)
)
,
(
'not'
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
)
) is
set
'not'
(
(
'not'
(
'not'
(
'not'
t
)
)
)
'&'
(
'not'
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
)
)
is
boolean
set
K221
(
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
,
(
'not'
t
)
)
'&'
K221
(
(
'not'
t
)
,
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
) is
set
'not'
K222
(
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
,
(
'not'
t
)
) is
boolean
set
'not'
(
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
'xor'
(
'not'
t
)
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
(
'not'
A2
)
'xor'
(
'not'
s2
)
)
'xor'
(
'not'
t
)
)
) is
set
(
'not'
A2
)
'&'
(
'not'
s2
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
A2
)
,
(
'not'
s2
)
) is
set
(
'not'
s2
)
'&'
(
'not'
t
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
s2
)
,
(
'not'
t
)
) is
set
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
is
boolean
set
K114
(1,
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
) is
set
'not'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
is
boolean
set
K114
(1,
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
) is
set
(
'not'
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
)
'&'
(
'not'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
is
set
K111
(
(
'not'
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
)
,
(
'not'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
) is
set
'not'
(
(
'not'
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
)
'&'
(
'not'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
)
is
boolean
set
(
'not'
t
)
'&'
(
'not'
A2
)
is
boolean
Element
of
BOOLEAN
K111
(
(
'not'
t
)
,
(
'not'
A2
)
) is
set
(
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
is
boolean
Element
of
BOOLEAN
'not'
(
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
is
boolean
set
K114
(1,
(
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
) is
set
'not'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
is
boolean
set
K114
(1,
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
) is
set
(
'not'
(
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
)
'&'
(
'not'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
)
is
set
K111
(
(
'not'
(
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
)
,
(
'not'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
)
) is
set
'not'
(
(
'not'
(
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
)
'&'
(
'not'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
)
)
is
boolean
set
'not'
(
(
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
)
is
boolean
Element
of
BOOLEAN
K114
(1,
(
(
(
(
'not'
A2
)
'&'
(
'not'
s2
)
)
'or'
(
(
'not'
s2
)
'&'
(
'not'
t
)
)
)
'or'
(
(
'not'
t
)
'&'
(
'not'
A2
)
)
)
) is
set
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s1
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
S
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
S
is
set
S
.
z
is
set
S
.
y
is
set
the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is
Relation-like
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
-defined
Function-like
V23
( the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
set
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is non
empty
set
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
) is
functional
V49
()
V50
()
set
a
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
Following
(
a
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
a
,2)
)
.
(
x
,
y
,
z
) is
set
Following
(
S
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
S
,2)
)
.
(
x
,
y
,
z
) is
boolean
Element
of
BOOLEAN
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s1
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s2
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
s2
is
set
S
.
x
is
set
(
Following
(
a
,2)
)
.
(
x
,
y
,
z
) is
set
Following
(
s2
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
s2
,2)
)
.
(
x
,
y
,
z
) is
boolean
Element
of
BOOLEAN
s2
.
z
is
set
s2
.
y
is
set
s2
.
x
is
set
z
is
set
x
is
set
y
is
set
<*
x
,
y
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
x
,
y
*>
,
xor2
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
xor2
}
is
functional
set
{
<*
x
,
y
*>
}
is
functional
V49
()
set
{
{
<*
x
,
y
*>
,
xor2
}
,
{
<*
x
,
y
*>
}
}
is
set
<*
y
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
y
,
z
*>
,
and2b
]
is non
empty
pair
set
{
<*
y
,
z
*>
,
and2b
}
is
functional
set
{
<*
y
,
z
*>
}
is
functional
V49
()
set
{
{
<*
y
,
z
*>
,
and2b
}
,
{
<*
y
,
z
*>
}
}
is
set
<*
z
,
x
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
[
<*
z
,
x
*>
,
and2b
]
is non
empty
pair
set
{
<*
z
,
x
*>
,
and2b
}
is
functional
set
{
<*
z
,
x
*>
}
is
functional
V49
()
set
{
{
<*
z
,
x
*>
,
and2b
}
,
{
<*
z
,
x
*>
}
}
is
set
[
<*
x
,
y
*>
,
and2b
]
is non
empty
pair
set
{
<*
x
,
y
*>
,
and2b
}
is
functional
set
{
{
<*
x
,
y
*>
,
and2b
}
,
{
<*
x
,
y
*>
}
}
is
set
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
2GatesCircStr
(
x
,
y
,
z
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(2)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
x
,
y
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
y
,
z
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
1GateCircStr
(
<*
z
,
x
*>
,
and2b
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
is non
empty
Relation-like
NAT
-defined
Function-like
V36
()
V43
(3)
FinSequence-like
FinSubsequence-like
V51
()
set
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is non
empty
non
void
V71
()
strict
Circuit-like
unsplit
gate`1=arity
gate`2isBoolean
gate`2=den
ManySortedSign
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
2GatesCircuit
(
x
,
y
,
z
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
2GatesCircStr
(
x
,
y
,
z
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
2GatesCircStr
(
x
,
y
,
z
,
xor2
)
1GateCircuit
(
x
,
y
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
1GateCircuit
(
<*
x
,
y
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
1GateCircuit
(
[
<*
x
,
y
*>
,
xor2
]
,
z
,
xor2
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
(
1GateCircuit
(
x
,
y
,
xor2
)
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,
xor2
]
,
z
,
xor2
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,
xor2
)
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
xor2
]
,
z
*>
,
xor2
)
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
1GateCircuit
(
x
,
y
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
1GateCircuit
(
<*
x
,
y
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
1GateCircuit
(
y
,
z
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
1GateCircuit
(
<*
y
,
z
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
(
1GateCircuit
(
x
,
y
,
and2b
)
)
+*
(
1GateCircuit
(
y
,
z
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
1GateCircuit
(
z
,
x
,
and2b
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
1GateCircuit
(
<*
z
,
x
*>
,
and2b
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
(
(
1GateCircuit
(
x
,
y
,
and2b
)
)
+*
(
1GateCircuit
(
y
,
z
,
and2b
)
)
)
+*
(
1GateCircuit
(
z
,
x
,
and2b
)
)
is
strict
non-empty
finitely-generated
V107
(
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
)
gate`2=den
Boolean
MSAlgebra
over
(
(
1GateCircStr
(
<*
x
,
y
*>
,
and2b
)
)
+*
(
1GateCircStr
(
<*
y
,
z
*>
,
and2b
)
)
)
+*
(
1GateCircStr
(
<*
z
,
x
*>
,
and2b
)
)
1GateCircuit
(
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
,
nor3
) is
strict
non-empty
finitely-generated
V107
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
))
gate`2=den
Boolean
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
1GateCircuit
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
) is
strict
non-empty
gate`2=den
MSAlgebra
over
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
(
x
,
y
,
z
)
+*
(
1GateCircuit
(
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
,
nor3
)
)
is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
)
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
1GateCircStr
(
<*
[
<*
x
,
y
*>
,
and2b
]
,
[
<*
y
,
z
*>
,
and2b
]
,
[
<*
z
,
x
*>
,
and2b
]
*>
,
nor3
)
)
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
) is
strict
non-empty
finitely-generated
V107
((
x
,
y
,
z
)
+*
(
x
,
y
,
z
))
gate`2=den
Boolean
MSAlgebra
over (
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
{
x
,
y
,
z
}
is
set
InputVertices
(
x
,
y
,
z
) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
) is non
empty
set
K18
( the
carrier
of (
x
,
y
,
z
)) is
set
the
ResultSort
of (
x
,
y
,
z
) is
Relation-like
Function-like
V27
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))
Element
of
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)))
the
carrier'
of (
x
,
y
,
z
) is non
empty
set
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
)) is
Relation-like
set
K18
(
K19
( the
carrier'
of (
x
,
y
,
z
), the
carrier
of (
x
,
y
,
z
))) is
set
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
carrier
of (
x
,
y
,
z
)
\
K538
( the
carrier
of (
x
,
y
,
z
), the
ResultSort
of (
x
,
y
,
z
)) is
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s1
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s1
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
Following
(
s1
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
2
+
1 is
V9
()
V10
()
V11
()
V15
() non
pair
Element
of
NAT
Following
(
s1
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
the
Sorts
of (
x
,
y
,
z
) is
Relation-like
the
carrier
of (
x
,
y
,
z
)
-defined
Function-like
V23
( the
carrier
of (
x
,
y
,
z
))
set
K230
( the
Sorts
of (
x
,
y
,
z
)) is
functional
V49
()
V50
()
set
s
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
s2
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s2
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
Following
(
s2
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
s2
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is
Relation-like
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
-defined
Function-like
V23
( the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
set
the
carrier
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
is non
empty
set
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
) is
functional
V49
()
V50
()
set
Following
(
s
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
(
Following
(
s
,3)
)
is
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
t
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
Following
(
t
,2) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
t
,2)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
Following
(
s1
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
Following
(
t
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of
(
(
x
,
y
,
z
)
+*
(
x
,
y
,
z
)
)
)
(
Following
(
t
,3)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
InnerVertices
(
x
,
y
,
z
) is non
empty
Element
of
K18
( the
carrier
of (
x
,
y
,
z
))
(
Following
(
t
,2)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
Following
(
s2
,3) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
t
,3)
)
|
the
carrier
of (
x
,
y
,
z
) is
Relation-like
Function-like
set
the
carrier
of (
x
,
y
,
z
)
\/
the
carrier
of (
x
,
y
,
z
) is
set
proj1
(
Following
(
s1
,2)
)
is
set
proj1
(
Following
(
s2
,2)
)
is
set
a
is
set
(
Following
(
s
,2)
)
.
a
is
set
(
Following
(
s1
,2)
)
.
a
is
set
(
Following
(
s
,3)
)
.
a
is
set
(
Following
(
s1
,3)
)
.
a
is
set
(
Following
(
s2
,2)
)
.
a
is
set
(
Following
(
s2
,3)
)
.
a
is
set
Following
(
Following
(
s
,2)
)
is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
(
Following
(
Following
(
s
,2)
)
)
.
a
is
set
Following
(
s
,
(
2
+
1
)
) is
Relation-like
Function-like
Element
of
K230
( the
Sorts
of (
x
,
y
,
z
))
proj1
(
Following
(
s
,2)
)
is
set