Date: Feb 15, 2013 6:50 AM
Author: fom
Subject: Re: distinguishability - in context, according to definitions

On 2/14/2013 12:40 PM, fom wrote:
> On 2/14/2013 9:32 AM, Shmuel (Seymour J.) Metz wrote:
>> In <qImdnYCz5tRmvITMnZ2dnUVZ_oWdnZ2d@giganews.com>, on 02/11/2013
>> at 10:53 AM, fom <fomJUNK@nyms.net> said:
>>
>> You really need to step back, separate out the philosophy from the
>> mathematics and define any terms that you aren't uisng in accordance
>> with standard practice.
>>




What follows are the difference sets
for each letter of the alphabet. The
first entry of each list is the "given
letter". This entry is followed by a
sign of equality. The "given letter"
is not a member of its difference set.

The construction is a {96,20,4} design.
That is, 96 elements into blocks of 20
that contain quadruples uniquely.

As this part of the construction had been
motivated by the axiom of regularity in
set theory, it is intuitively reasonable
to think of a letter as "a collection
of letters" although I suspect many will
find that objectionable.

These difference sets have numerous
properties. The free orthomodular lattice
on 2 generators contains 6 Boolean blocks
in the configuration of the 16-element
free Boolean lattice on six elements.
No element of a difference set is in the
Boolean block of its "given letter".

One prior formation decision was a
choice of a single column from among
the six columns

TTTFFF
TFFTTF
FFTFTT
FTFTFT

to correspond with a fixed representation
of LEQ as a switching function. Because
the letters have six distinct first coordinates
and sixteen distinct second coordinates,
for any particular second coordinate of any
particular letter, there are six corresponding
letters. Each difference set partitions
one of these six-fold multiplicities into
a 5-set and a singleton. The singleton is
in the same Boolean block as the "given
letter" for the difference set.

Because of the semantical relationships
originating with truth-table semantics
that motivated this 5-set can be taken
as having the form of ortholattice L12
depicted around equation (29) of


http://www.clas.ufl.edu/users/jzeman/quantumlogic/generalized_normal_logic.htm



where the distinguished element of the
lattice, namely c, can be taken to be
XOR. The remaining four labels in the
lattice can be arbitrarily assigned to
FIX, LET, FLIP, and DENY. These are
the four switching functions invariant
under DeMorgan conjugation.

As for the singleton in the same block
as the "given letter" for the difference
set, it may be thought of as an "individuating
mark" in the sense of Leibnizian logic.
Its binding to the "given letter" is
represented by a Steiner Quadruple System
on 14 symbols constructed from the other
14 letters of the Boolean block in which
the "given letter" and its "individuating
mark" are located.

An SQS(14) has 91 4-element blocks.

When the 5-set mentioned above is removed
from the 96-elements of the free orthomodular
lattice on two generators, there remains
a 91-element set. There are 4 projective
planes on 91 symbols. Although the construction
has not yet been done, it is expected that
the block designs can be formulated to express
some uniformity in relation to one another
and in relation to the SQS(14) formed relative
to the absence of the "given letter" and its
"individuating mark".

In addition, the "given letter" and its
"individuating mark" can be bound in a
global sense relative to an

S_5{2,5,89}

design. This design locates any pair
of letters into blocks of 5. The "S_5"
prefix indicates that this relationship
of pairs to blocks will, itself, have a
multiplicity of 5. Thus, every pair will
occur in 5 distinct blocks of 5.

Intuitively, these constructions are
to be thought of as isolating the
5-set mentioned above from the "given
letter" and its "individuating mark".
Without the computational analysis of
how related group actions affect these
constructions, it is difficult to decide
on how to describe the situation. It
is as if the 5-element set is the "object"
and the "given label" with its "individuating
mark" comprise the presentation of
"quantum duality".





=======================

(LEQ,LEQ) =
(FIX,FIX)
(FIX,FLIP)
(FIX,XOR)
(FIX,LEQ)
(XOR,FIX)
(XOR,TRU)
(XOR,NAND)
(XOR,NIMP)
(LET,FIX)
(LET,NTRU)
(LET,OR)
(LET,NIF)
(DENY,FIX)
(DENY,DENY)
(DENY,AND)
(DENY,NOR)
(FLIP,FIX)
(FLIP,LET)
(FLIP,IMP)
(FLIP,IF)


(LEQ,OR) =
(FIX,IMP)
(FIX,NIMP)
(FIX,NOR)
(FIX,OR)
(XOR,IMP)
(XOR,AND)
(XOR,NTRU)
(XOR,FLIP)
(LET,IMP)
(LET,NAND)
(LET,LEQ)
(LET,DENY)
(DENY,IMP)
(DENY,NIF)
(DENY,TRU)
(DENY,XOR)
(FLIP,IMP)
(FLIP,IF)
(FLIP,FIX)
(FLIP,LET)


(LEQ,DENY) =
(FIX,NTRU)
(FIX,TRU)
(FIX,LET)
(FIX,DENY)
(XOR,NTRU)
(XOR,FLIP)
(XOR,IMP)
(XOR,AND)
(LET,NTRU)
(LET,FIX)
(LET,NIF)
(LET,OR)
(DENY,NTRU)
(DENY,LEQ)
(DENY,NIMP)
(DENY,IF)
(FLIP,NTRU)
(FLIP,XOR)
(FLIP,NAND)
(FLIP,NOR)


(LEQ,FLIP) =
(FIX,XOR)
(FIX,LEQ)
(FIX,FIX)
(FIX,FLIP)
(XOR,XOR)
(XOR,DENY)
(XOR,IF)
(XOR,OR)
(LET,XOR)
(LET,LET)
(LET,NIMP)
(LET,AND)
(DENY,XOR)
(DENY,TRU)
(DENY,NIF)
(DENY,IMP)
(FLIP,XOR)
(FLIP,NTRU)
(FLIP,NOR)
(FLIP,NAND)


(LEQ,NIF) =
(FIX,NAND)
(FIX,AND)
(FIX,IF)
(FIX,NIF)
(XOR,NAND)
(XOR,NIMP)
(XOR,FIX)
(XOR,TRU)
(LET,NAND)
(LET,IMP)
(LET,DENY)
(LET,LEQ)
(DENY,NAND)
(DENY,OR)
(DENY,FLIP)
(DENY,LET)
(FLIP,NAND)
(FLIP,NOR)
(FLIP,NTRU)
(FLIP,XOR)


(LEQ,NTRU) =
(FIX,DENY)
(FIX,LET)
(FIX,TRU)
(FIX,NTRU)
(XOR,DENY)
(XOR,XOR)
(XOR,OR)
(XOR,IF)
(LET,DENY)
(LET,LEQ)
(LET,NAND)
(LET,IMP)
(DENY,DENY)
(DENY,FIX)
(DENY,NOR)
(DENY,AND)
(FLIP,DENY)
(FLIP,FLIP)
(FLIP,NIF)
(FLIP,NIMP)


(LEQ,AND) =
(FIX,IF)
(FIX,NIF)
(FIX,NAND)
(FIX,AND)
(XOR,IF)
(XOR,OR)
(XOR,XOR)
(XOR,DENY)
(LET,IF)
(LET,NOR)
(LET,TRU)
(LET,FLIP)
(DENY,IF)
(DENY,NIMP)
(DENY,LEQ)
(DENY,NTRU)
(FLIP,IF)
(FLIP,IMP)
(FLIP,LET)
(FLIP,FIX)


(LEQ,NIMP) =
(FIX,NOR)
(FIX,OR)
(FIX,IMP)
(FIX,NIMP)
(XOR,NOR)
(XOR,NIF)
(XOR,LET)
(XOR,LEQ)
(LET,NOR)
(LET,IF)
(LET,FLIP)
(LET,TRU)
(DENY,NOR)
(DENY,AND)
(DENY,DENY)
(DENY,FIX)
(FLIP,NOR)
(FLIP,NAND)
(FLIP,XOR)
(FLIP,NTRU)


(LEQ,XOR) =
(FIX,FLIP)
(FIX,FIX)
(FIX,LEQ)
(FIX,XOR)
(XOR,FLIP)
(XOR,NTRU)
(XOR,AND)
(XOR,IMP)
(LET,FLIP)
(LET,TRU)
(LET,NOR)
(LET,IF)
(DENY,FLIP)
(DENY,LET)
(DENY,NAND)
(DENY,OR)
(FLIP,FLIP)
(FLIP,DENY)
(FLIP,NIMP)
(FLIP,NIF)


(LEQ,IMP) =
(FIX,OR)
(FIX,NOR)
(FIX,NIMP)
(FIX,IMP)
(XOR,OR)
(XOR,IF)
(XOR,DENY)
(XOR,XOR)
(LET,OR)
(LET,NIF)
(LET,FIX)
(LET,NTRU)
(DENY,OR)
(DENY,NAND)
(DENY,LET)
(DENY,FLIP)
(FLIP,OR)
(FLIP,AND)
(FLIP,LEQ)
(FLIP,TRU)


(LEQ,NAND) =
(FIX,NIF)
(FIX,IF)
(FIX,AND)
(FIX,NAND)
(XOR,NIF)
(XOR,NOR)
(XOR,LEQ)
(XOR,LET)
(LET,NIF)
(LET,OR)
(LET,NTRU)
(LET,FIX)
(DENY,NIF)
(DENY,IMP)
(DENY,XOR)
(DENY,TRU)
(FLIP,NIF)
(FLIP,NIMP)
(FLIP,DENY)
(FLIP,FLIP)


(LEQ,TRU) =
(FIX,LET)
(FIX,DENY)
(FIX,NTRU)
(FIX,TRU)
(XOR,LET)
(XOR,LEQ)
(XOR,NOR)
(XOR,NIF)
(LET,LET)
(LET,XOR)
(LET,AND)
(LET,NIMP)
(DENY,LET)
(DENY,FLIP)
(DENY,OR)
(DENY,NAND)
(FLIP,LET)
(FLIP,FIX)
(FLIP,IF)
(FLIP,IMP)


(LEQ,IF) =
(FIX,AND)
(FIX,NAND)
(FIX,NIF)
(FIX,IF)
(XOR,AND)
(XOR,IMP)
(XOR,FLIP)
(XOR,NTRU)
(LET,AND)
(LET,NIMP)
(LET,LET)
(LET,XOR)
(DENY,AND)
(DENY,NOR)
(DENY,FIX)
(DENY,DENY)
(FLIP,AND)
(FLIP,OR)
(FLIP,TRU)
(FLIP,LEQ)


(LEQ,FIX) =
(FIX,LEQ)
(FIX,XOR)
(FIX,FLIP)
(FIX,FIX)
(XOR,LEQ)
(XOR,LET)
(XOR,NIF)
(XOR,NOR)
(LET,LEQ)
(LET,DENY)
(LET,IMP)
(LET,NAND)
(DENY,LEQ)
(DENY,NTRU)
(DENY,IF)
(DENY,NIMP)
(FLIP,LEQ)
(FLIP,TRU)
(FLIP,OR)
(FLIP,AND)


(LEQ,LET) =
(FIX,TRU)
(FIX,NTRU)
(FIX,DENY)
(FIX,LET)
(XOR,TRU)
(XOR,FIX)
(XOR,NIMP)
(XOR,NAND)
(LET,TRU)
(LET,FLIP)
(LET,IF)
(LET,NOR)
(DENY,TRU)
(DENY,XOR)
(DENY,IMP)
(DENY,NIF)
(FLIP,TRU)
(FLIP,LEQ)
(FLIP,AND)
(FLIP,OR)


(LEQ,NOR) =
(FIX,NIMP)
(FIX,IMP)
(FIX,OR)
(FIX,NOR)
(XOR,NIMP)
(XOR,NAND)
(XOR,TRU)
(XOR,FIX)
(LET,NIMP)
(LET,AND)
(LET,XOR)
(LET,LET)
(DENY,NIMP)
(DENY,IF)
(DENY,NTRU)
(DENY,LEQ)
(FLIP,NIMP)
(FLIP,NIF)
(FLIP,FLIP)
(FLIP,DENY)


(DENY,LEQ) =
(LET,FIX)
(LET,FLIP)
(LET,XOR)
(LET,LEQ)
(FLIP,FIX)
(FLIP,TRU)
(FLIP,NAND)
(FLIP,NIMP)
(FIX,FIX)
(FIX,NTRU)
(FIX,OR)
(FIX,NIF)
(LEQ,FIX)
(LEQ,DENY)
(LEQ,AND)
(LEQ,NOR)
(XOR,FIX)
(XOR,LET)
(XOR,IMP)
(XOR,IF)


(DENY,OR) =
(LET,IMP)
(LET,NIMP)
(LET,NOR)
(LET,OR)
(FLIP,IMP)
(FLIP,AND)
(FLIP,NTRU)
(FLIP,FLIP)
(FIX,IMP)
(FIX,NAND)
(FIX,LEQ)
(FIX,DENY)
(LEQ,IMP)
(LEQ,NIF)
(LEQ,TRU)
(LEQ,XOR)
(XOR,IMP)
(XOR,IF)
(XOR,FIX)
(XOR,LET)


(DENY,DENY) =
(LET,NTRU)
(LET,TRU)
(LET,LET)
(LET,DENY)
(FLIP,NTRU)
(FLIP,FLIP)
(FLIP,IMP)
(FLIP,AND)
(FIX,NTRU)
(FIX,FIX)
(FIX,NIF)
(FIX,OR)
(LEQ,NTRU)
(LEQ,LEQ)
(LEQ,NIMP)
(LEQ,IF)
(XOR,NTRU)
(XOR,XOR)
(XOR,NAND)
(XOR,NOR)


(DENY,FLIP) =
(LET,XOR)
(LET,LEQ)
(LET,FIX)
(LET,FLIP)
(FLIP,XOR)
(FLIP,DENY)
(FLIP,IF)
(FLIP,OR)
(FIX,XOR)
(FIX,LET)
(FIX,NIMP)
(FIX,AND)
(LEQ,XOR)
(LEQ,TRU)
(LEQ,NIF)
(LEQ,IMP)
(XOR,XOR)
(XOR,NTRU)
(XOR,NOR)
(XOR,NAND)


(DENY,NIF) =
(LET,NAND)
(LET,AND)
(LET,IF)
(LET,NIF)
(FLIP,NAND)
(FLIP,NIMP)
(FLIP,FIX)
(FLIP,TRU)
(FIX,NAND)
(FIX,IMP)
(FIX,DENY)
(FIX,LEQ)
(LEQ,NAND)
(LEQ,OR)
(LEQ,FLIP)
(LEQ,LET)
(XOR,NAND)
(XOR,NOR)
(XOR,NTRU)
(XOR,XOR)


(DENY,NTRU) =
(LET,DENY)
(LET,LET)
(LET,TRU)
(LET,NTRU)
(FLIP,DENY)
(FLIP,XOR)
(FLIP,OR)
(FLIP,IF)
(FIX,DENY)
(FIX,LEQ)
(FIX,NAND)
(FIX,IMP)
(LEQ,DENY)
(LEQ,FIX)
(LEQ,NOR)
(LEQ,AND)
(XOR,DENY)
(XOR,FLIP)
(XOR,NIF)
(XOR,NIMP)


(DENY,AND) =
(LET,IF)
(LET,NIF)
(LET,NAND)
(LET,AND)
(FLIP,IF)
(FLIP,OR)
(FLIP,XOR)
(FLIP,DENY)
(FIX,IF)
(FIX,NOR)
(FIX,TRU)
(FIX,FLIP)
(LEQ,IF)
(LEQ,NIMP)
(LEQ,LEQ)
(LEQ,NTRU)
(XOR,IF)
(XOR,IMP)
(XOR,LET)
(XOR,FIX)


(DENY,NIMP) =
(LET,NOR)
(LET,OR)
(LET,IMP)
(LET,NIMP)
(FLIP,NOR)
(FLIP,NIF)
(FLIP,LET)
(FLIP,LEQ)
(FIX,NOR)
(FIX,IF)
(FIX,FLIP)
(FIX,TRU)
(LEQ,NOR)
(LEQ,AND)
(LEQ,DENY)
(LEQ,FIX)
(XOR,NOR)
(XOR,NAND)
(XOR,XOR)
(XOR,NTRU)


(DENY,XOR) =
(LET,FLIP)
(LET,FIX)
(LET,LEQ)
(LET,XOR)
(FLIP,FLIP)
(FLIP,NTRU)
(FLIP,AND)
(FLIP,IMP)
(FIX,FLIP)
(FIX,TRU)
(FIX,NOR)
(FIX,IF)
(LEQ,FLIP)
(LEQ,LET)
(LEQ,NAND)
(LEQ,OR)
(XOR,FLIP)
(XOR,DENY)
(XOR,NIMP)
(XOR,NIF)


(DENY,IMP) =
(LET,OR)
(LET,NOR)
(LET,NIMP)
(LET,IMP)
(FLIP,OR)
(FLIP,IF)
(FLIP,DENY)
(FLIP,XOR)
(FIX,OR)
(FIX,NIF)
(FIX,FIX)
(FIX,NTRU)
(LEQ,OR)
(LEQ,NAND)
(LEQ,LET)
(LEQ,FLIP)
(XOR,OR)
(XOR,AND)
(XOR,LEQ)
(XOR,TRU)


(DENY,NAND) =
(LET,NIF)
(LET,IF)
(LET,AND)
(LET,NAND)
(FLIP,NIF)
(FLIP,NOR)
(FLIP,LEQ)
(FLIP,LET)
(FIX,NIF)
(FIX,OR)
(FIX,NTRU)
(FIX,FIX)
(LEQ,NIF)
(LEQ,IMP)
(LEQ,XOR)
(LEQ,TRU)
(XOR,NIF)
(XOR,NIMP)
(XOR,DENY)
(XOR,FLIP)


(DENY,TRU) =
(LET,LET)
(LET,DENY)
(LET,NTRU)
(LET,TRU)
(FLIP,LET)
(FLIP,LEQ)
(FLIP,NOR)
(FLIP,NIF)
(FIX,LET)
(FIX,XOR)
(FIX,AND)
(FIX,NIMP)
(LEQ,LET)
(LEQ,FLIP)
(LEQ,OR)
(LEQ,NAND)
(XOR,LET)
(XOR,FIX)
(XOR,IF)
(XOR,IMP)


(DENY,IF) =
(LET,AND)
(LET,NAND)
(LET,NIF)
(LET,IF)
(FLIP,AND)
(FLIP,IMP)
(FLIP,FLIP)
(FLIP,NTRU)
(FIX,AND)
(FIX,NIMP)
(FIX,LET)
(FIX,XOR)
(LEQ,AND)
(LEQ,NOR)
(LEQ,FIX)
(LEQ,DENY)
(XOR,AND)
(XOR,OR)
(XOR,TRU)
(XOR,LEQ)


(DENY,FIX) =
(LET,LEQ)
(LET,XOR)
(LET,FLIP)
(LET,FIX)
(FLIP,LEQ)
(FLIP,LET)
(FLIP,NIF)
(FLIP,NOR)
(FIX,LEQ)
(FIX,DENY)
(FIX,IMP)
(FIX,NAND)
(LEQ,LEQ)
(LEQ,NTRU)
(LEQ,IF)
(LEQ,NIMP)
(XOR,LEQ)
(XOR,TRU)
(XOR,OR)
(XOR,AND)


(DENY,LET) =
(LET,TRU)
(LET,NTRU)
(LET,DENY)
(LET,LET)
(FLIP,TRU)
(FLIP,FIX)
(FLIP,NIMP)
(FLIP,NAND)
(FIX,TRU)
(FIX,FLIP)
(FIX,IF)
(FIX,NOR)
(LEQ,TRU)
(LEQ,XOR)
(LEQ,IMP)
(LEQ,NIF)
(XOR,TRU)
(XOR,LEQ)
(XOR,AND)
(XOR,OR)


(DENY,NOR) =
(LET,NIMP)
(LET,IMP)
(LET,OR)
(LET,NOR)
(FLIP,NIMP)
(FLIP,NAND)
(FLIP,TRU)
(FLIP,FIX)
(FIX,NIMP)
(FIX,AND)
(FIX,XOR)
(FIX,LET)
(LEQ,NIMP)
(LEQ,IF)
(LEQ,NTRU)
(LEQ,LEQ)
(XOR,NIMP)
(XOR,NIF)
(XOR,FLIP)
(XOR,DENY)


(FLIP,LEQ) =
(XOR,FIX)
(XOR,FLIP)
(XOR,XOR)
(XOR,LEQ)
(FIX,FIX)
(FIX,TRU)
(FIX,NAND)
(FIX,NIMP)
(DENY,FIX)
(DENY,NTRU)
(DENY,OR)
(DENY,NIF)
(LET,FIX)
(LET,DENY)
(LET,AND)
(LET,NOR)
(LEQ,FIX)
(LEQ,LET)
(LEQ,IMP)
(LEQ,IF)


(FLIP,OR) =
(XOR,IMP)
(XOR,NIMP)
(XOR,NOR)
(XOR,OR)
(FIX,IMP)
(FIX,AND)
(FIX,NTRU)
(FIX,FLIP)
(DENY,IMP)
(DENY,NAND)
(DENY,LEQ)
(DENY,DENY)
(LET,IMP)
(LET,NIF)
(LET,TRU)
(LET,XOR)
(LEQ,IMP)
(LEQ,IF)
(LEQ,FIX)
(LEQ,LET)


(FLIP,DENY) =
(XOR,NTRU)
(XOR,TRU)
(XOR,LET)
(XOR,DENY)
(FIX,NTRU)
(FIX,FLIP)
(FIX,IMP)
(FIX,AND)
(DENY,NTRU)
(DENY,FIX)
(DENY,NIF)
(DENY,OR)
(LET,NTRU)
(LET,LEQ)
(LET,NIMP)
(LET,IF)
(LEQ,NTRU)
(LEQ,XOR)
(LEQ,NAND)
(LEQ,NOR)


(FLIP,FLIP) =
(XOR,XOR)
(XOR,LEQ)
(XOR,FIX)
(XOR,FLIP)
(FIX,XOR)
(FIX,DENY)
(FIX,IF)
(FIX,OR)
(DENY,XOR)
(DENY,LET)
(DENY,NIMP)
(DENY,AND)
(LET,XOR)
(LET,TRU)
(LET,NIF)
(LET,IMP)
(LEQ,XOR)
(LEQ,NTRU)
(LEQ,NOR)
(LEQ,NAND)


(FLIP,NIF) =
(XOR,NAND)
(XOR,AND)
(XOR,IF)
(XOR,NIF)
(FIX,NAND)
(FIX,NIMP)
(FIX,FIX)
(FIX,TRU)
(DENY,NAND)
(DENY,IMP)
(DENY,DENY)
(DENY,LEQ)
(LET,NAND)
(LET,OR)
(LET,FLIP)
(LET,LET)
(LEQ,NAND)
(LEQ,NOR)
(LEQ,NTRU)
(LEQ,XOR)


(FLIP,NTRU) =
(XOR,DENY)
(XOR,LET)
(XOR,TRU)
(XOR,NTRU)
(FIX,DENY)
(FIX,XOR)
(FIX,OR)
(FIX,IF)
(DENY,DENY)
(DENY,LEQ)
(DENY,NAND)
(DENY,IMP)
(LET,DENY)
(LET,FIX)
(LET,NOR)
(LET,AND)
(LEQ,DENY)
(LEQ,FLIP)
(LEQ,NIF)
(LEQ,NIMP)


(FLIP,AND) =
(XOR,IF)
(XOR,NIF)
(XOR,NAND)
(XOR,AND)
(FIX,IF)
(FIX,OR)
(FIX,XOR)
(FIX,DENY)
(DENY,IF)
(DENY,NOR)
(DENY,TRU)
(DENY,FLIP)
(LET,IF)
(LET,NIMP)
(LET,LEQ)
(LET,NTRU)
(LEQ,IF)
(LEQ,IMP)
(LEQ,LET)
(LEQ,FIX)


(FLIP,NIMP) =
(XOR,NOR)
(XOR,OR)
(XOR,IMP)
(XOR,NIMP)
(FIX,NOR)
(FIX,NIF)
(FIX,LET)
(FIX,LEQ)
(DENY,NOR)
(DENY,IF)
(DENY,FLIP)
(DENY,TRU)
(LET,NOR)
(LET,AND)
(LET,DENY)
(LET,FIX)
(LEQ,NOR)
(LEQ,NAND)
(LEQ,XOR)
(LEQ,NTRU)


(FLIP,XOR) =
(XOR,FLIP)
(XOR,FIX)
(XOR,LEQ)
(XOR,XOR)
(FIX,FLIP)
(FIX,NTRU)
(FIX,AND)
(FIX,IMP)
(DENY,FLIP)
(DENY,TRU)
(DENY,NOR)
(DENY,IF)
(LET,FLIP)
(LET,LET)
(LET,NAND)
(LET,OR)
(LEQ,FLIP)
(LEQ,DENY)
(LEQ,NIMP)
(LEQ,NIF)


(FLIP,IMP) =
(XOR,OR)
(XOR,NOR)
(XOR,NIMP)
(XOR,IMP)
(FIX,OR)
(FIX,IF)
(FIX,DENY)
(FIX,XOR)
(DENY,OR)
(DENY,NIF)
(DENY,FIX)
(DENY,NTRU)
(LET,OR)
(LET,NAND)
(LET,LET)
(LET,FLIP)
(LEQ,OR)
(LEQ,AND)
(LEQ,LEQ)
(LEQ,TRU)


(FLIP,NAND) =
(XOR,NIF)
(XOR,IF)
(XOR,AND)
(XOR,NAND)
(FIX,NIF)
(FIX,NOR)
(FIX,LEQ)
(FIX,LET)
(DENY,NIF)
(DENY,OR)
(DENY,NTRU)
(DENY,FIX)
(LET,NIF)
(LET,IMP)
(LET,XOR)
(LET,TRU)
(LEQ,NIF)
(LEQ,NIMP)
(LEQ,DENY)
(LEQ,FLIP)


(FLIP,TRU) =
(XOR,LET)
(XOR,DENY)
(XOR,NTRU)
(XOR,TRU)
(FIX,LET)
(FIX,LEQ)
(FIX,NOR)
(FIX,NIF)
(DENY,LET)
(DENY,XOR)
(DENY,AND)
(DENY,NIMP)
(LET,LET)
(LET,FLIP)
(LET,OR)
(LET,NAND)
(LEQ,LET)
(LEQ,FIX)
(LEQ,IF)
(LEQ,IMP)


(FLIP,IF) =
(XOR,AND)
(XOR,NAND)
(XOR,NIF)
(XOR,IF)
(FIX,AND)
(FIX,IMP)
(FIX,FLIP)
(FIX,NTRU)
(DENY,AND)
(DENY,NIMP)
(DENY,LET)
(DENY,XOR)
(LET,AND)
(LET,NOR)
(LET,FIX)
(LET,DENY)
(LEQ,AND)
(LEQ,OR)
(LEQ,TRU)
(LEQ,LEQ)


(FLIP,FIX) =
(XOR,LEQ)
(XOR,XOR)
(XOR,FLIP)
(XOR,FIX)
(FIX,LEQ)
(FIX,LET)
(FIX,NIF)
(FIX,NOR)
(DENY,LEQ)
(DENY,DENY)
(DENY,IMP)
(DENY,NAND)
(LET,LEQ)
(LET,NTRU)
(LET,IF)
(LET,NIMP)
(LEQ,LEQ)
(LEQ,TRU)
(LEQ,OR)
(LEQ,AND)


(FLIP,LET) =
(XOR,TRU)
(XOR,NTRU)
(XOR,DENY)
(XOR,LET)
(FIX,TRU)
(FIX,FIX)
(FIX,NIMP)
(FIX,NAND)
(DENY,TRU)
(DENY,FLIP)
(DENY,IF)
(DENY,NOR)
(LET,TRU)
(LET,XOR)
(LET,IMP)
(LET,NIF)
(LEQ,TRU)
(LEQ,LEQ)
(LEQ,AND)
(LEQ,OR)


(FLIP,NOR) =
(XOR,NIMP)
(XOR,IMP)
(XOR,OR)
(XOR,NOR)
(FIX,NIMP)
(FIX,NAND)
(FIX,TRU)
(FIX,FIX)
(DENY,NIMP)
(DENY,AND)
(DENY,XOR)
(DENY,LET)
(LET,NIMP)
(LET,IF)
(LET,NTRU)
(LET,LEQ)
(LEQ,NIMP)
(LEQ,NIF)
(LEQ,FLIP)
(LEQ,DENY)


(XOR,LEQ) =
(FLIP,FIX)
(FLIP,FLIP)
(FLIP,XOR)
(FLIP,LEQ)
(LET,FIX)
(LET,TRU)
(LET,NAND)
(LET,NIMP)
(LEQ,FIX)
(LEQ,NTRU)
(LEQ,OR)
(LEQ,NIF)
(FIX,FIX)
(FIX,DENY)
(FIX,AND)
(FIX,NOR)
(DENY,FIX)
(DENY,LET)
(DENY,IMP)
(DENY,IF)


(XOR,OR) =
(FLIP,IMP)
(FLIP,NIMP)
(FLIP,NOR)
(FLIP,OR)
(LET,IMP)
(LET,AND)
(LET,NTRU)
(LET,FLIP)
(LEQ,IMP)
(LEQ,NAND)
(LEQ,LEQ)
(LEQ,DENY)
(FIX,IMP)
(FIX,NIF)
(FIX,TRU)
(FIX,XOR)
(DENY,IMP)
(DENY,IF)
(DENY,FIX)
(DENY,LET)


(XOR,DENY) =
(FLIP,NTRU)
(FLIP,TRU)
(FLIP,LET)
(FLIP,DENY)
(LET,NTRU)
(LET,FLIP)
(LET,IMP)
(LET,AND)
(LEQ,NTRU)
(LEQ,FIX)
(LEQ,NIF)
(LEQ,OR)
(FIX,NTRU)
(FIX,LEQ)
(FIX,NIMP)
(FIX,IF)
(DENY,NTRU)
(DENY,XOR)
(DENY,NAND)
(DENY,NOR)


(XOR,FLIP) =
(FLIP,XOR)
(FLIP,LEQ)
(FLIP,FIX)
(FLIP,FLIP)
(LET,XOR)
(LET,DENY)
(LET,IF)
(LET,OR)
(LEQ,XOR)
(LEQ,LET)
(LEQ,NIMP)
(LEQ,AND)
(FIX,XOR)
(FIX,TRU)
(FIX,NIF)
(FIX,IMP)
(DENY,XOR)
(DENY,NTRU)
(DENY,NOR)
(DENY,NAND)


(XOR,NIF) =
(FLIP,NAND)
(FLIP,AND)
(FLIP,IF)
(FLIP,NIF)
(LET,NAND)
(LET,NIMP)
(LET,FIX)
(LET,TRU)
(LEQ,NAND)
(LEQ,IMP)
(LEQ,DENY)
(LEQ,LEQ)
(FIX,NAND)
(FIX,OR)
(FIX,FLIP)
(FIX,LET)
(DENY,NAND)
(DENY,NOR)
(DENY,NTRU)
(DENY,XOR)


(XOR,NTRU) =
(FLIP,DENY)
(FLIP,LET)
(FLIP,TRU)
(FLIP,NTRU)
(LET,DENY)
(LET,XOR)
(LET,OR)
(LET,IF)
(LEQ,DENY)
(LEQ,LEQ)
(LEQ,NAND)
(LEQ,IMP)
(FIX,DENY)
(FIX,FIX)
(FIX,NOR)
(FIX,AND)
(DENY,DENY)
(DENY,FLIP)
(DENY,NIF)
(DENY,NIMP)


(XOR,AND) =
(FLIP,IF)
(FLIP,NIF)
(FLIP,NAND)
(FLIP,AND)
(LET,IF)
(LET,OR)
(LET,XOR)
(LET,DENY)
(LEQ,IF)
(LEQ,NOR)
(LEQ,TRU)
(LEQ,FLIP)
(FIX,IF)
(FIX,NIMP)
(FIX,LEQ)
(FIX,NTRU)
(DENY,IF)
(DENY,IMP)
(DENY,LET)
(DENY,FIX)


(XOR,NIMP) =
(FLIP,NOR)
(FLIP,OR)
(FLIP,IMP)
(FLIP,NIMP)
(LET,NOR)
(LET,NIF)
(LET,LET)
(LET,LEQ)
(LEQ,NOR)
(LEQ,IF)
(LEQ,FLIP)
(LEQ,TRU)
(FIX,NOR)
(FIX,AND)
(FIX,DENY)
(FIX,FIX)
(DENY,NOR)
(DENY,NAND)
(DENY,XOR)
(DENY,NTRU)


(XOR,XOR) =
(FLIP,FLIP)
(FLIP,FIX)
(FLIP,LEQ)
(FLIP,XOR)
(LET,FLIP)
(LET,NTRU)
(LET,AND)
(LET,IMP)
(LEQ,FLIP)
(LEQ,TRU)
(LEQ,NOR)
(LEQ,IF)
(FIX,FLIP)
(FIX,LET)
(FIX,NAND)
(FIX,OR)
(DENY,FLIP)
(DENY,DENY)
(DENY,NIMP)
(DENY,NIF)


(XOR,IMP) =
(FLIP,OR)
(FLIP,NOR)
(FLIP,NIMP)
(FLIP,IMP)
(LET,OR)
(LET,IF)
(LET,DENY)
(LET,XOR)
(LEQ,OR)
(LEQ,NIF)
(LEQ,FIX)
(LEQ,NTRU)
(FIX,OR)
(FIX,NAND)
(FIX,LET)
(FIX,FLIP)
(DENY,OR)
(DENY,AND)
(DENY,LEQ)
(DENY,TRU)


(XOR,NAND) =
(FLIP,NIF)
(FLIP,IF)
(FLIP,AND)
(FLIP,NAND)
(LET,NIF)
(LET,NOR)
(LET,LEQ)
(LET,LET)
(LEQ,NIF)
(LEQ,OR)
(LEQ,NTRU)
(LEQ,FIX)
(FIX,NIF)
(FIX,IMP)
(FIX,XOR)
(FIX,TRU)
(DENY,NIF)
(DENY,NIMP)
(DENY,DENY)
(DENY,FLIP)


(XOR,TRU) =
(FLIP,LET)
(FLIP,DENY)
(FLIP,NTRU)
(FLIP,TRU)
(LET,LET)
(LET,LEQ)
(LET,NOR)
(LET,NIF)
(LEQ,LET)
(LEQ,XOR)
(LEQ,AND)
(LEQ,NIMP)
(FIX,LET)
(FIX,FLIP)
(FIX,OR)
(FIX,NAND)
(DENY,LET)
(DENY,FIX)
(DENY,IF)
(DENY,IMP)


(XOR,IF) =
(FLIP,AND)
(FLIP,NAND)
(FLIP,NIF)
(FLIP,IF)
(LET,AND)
(LET,IMP)
(LET,FLIP)
(LET,NTRU)
(LEQ,AND)
(LEQ,NIMP)
(LEQ,LET)
(LEQ,XOR)
(FIX,AND)
(FIX,NOR)
(FIX,FIX)
(FIX,DENY)
(DENY,AND)
(DENY,OR)
(DENY,TRU)
(DENY,LEQ)


(XOR,FIX) =
(FLIP,LEQ)
(FLIP,XOR)
(FLIP,FLIP)
(FLIP,FIX)
(LET,LEQ)
(LET,LET)
(LET,NIF)
(LET,NOR)
(LEQ,LEQ)
(LEQ,DENY)
(LEQ,IMP)
(LEQ,NAND)
(FIX,LEQ)
(FIX,NTRU)
(FIX,IF)
(FIX,NIMP)
(DENY,LEQ)
(DENY,TRU)
(DENY,OR)
(DENY,AND)


(XOR,LET) =
(FLIP,TRU)
(FLIP,NTRU)
(FLIP,DENY)
(FLIP,LET)
(LET,TRU)
(LET,FIX)
(LET,NIMP)
(LET,NAND)
(LEQ,TRU)
(LEQ,FLIP)
(LEQ,IF)
(LEQ,NOR)
(FIX,TRU)
(FIX,XOR)
(FIX,IMP)
(FIX,NIF)
(DENY,TRU)
(DENY,LEQ)
(DENY,AND)
(DENY,OR)


(XOR,NOR) =
(FLIP,NIMP)
(FLIP,IMP)
(FLIP,OR)
(FLIP,NOR)
(LET,NIMP)
(LET,NAND)
(LET,TRU)
(LET,FIX)
(LEQ,NIMP)
(LEQ,AND)
(LEQ,XOR)
(LEQ,LET)
(FIX,NIMP)
(FIX,IF)
(FIX,NTRU)
(FIX,LEQ)
(DENY,NIMP)
(DENY,NIF)
(DENY,FLIP)
(DENY,DENY)


(FIX,LEQ) =
(LEQ,FIX)
(LEQ,FLIP)
(LEQ,XOR)
(LEQ,LEQ)
(DENY,FIX)
(DENY,TRU)
(DENY,NAND)
(DENY,NIMP)
(FLIP,FIX)
(FLIP,NTRU)
(FLIP,OR)
(FLIP,NIF)
(XOR,FIX)
(XOR,DENY)
(XOR,AND)
(XOR,NOR)
(LET,FIX)
(LET,LET)
(LET,IMP)
(LET,IF)


(FIX,OR) =
(LEQ,IMP)
(LEQ,NIMP)
(LEQ,NOR)
(LEQ,OR)
(DENY,IMP)
(DENY,AND)
(DENY,NTRU)
(DENY,FLIP)
(FLIP,IMP)
(FLIP,NAND)
(FLIP,LEQ)
(FLIP,DENY)
(XOR,IMP)
(XOR,NIF)
(XOR,TRU)
(XOR,XOR)
(LET,IMP)
(LET,IF)
(LET,FIX)
(LET,LET)


(FIX,DENY) =
(LEQ,NTRU)
(LEQ,TRU)
(LEQ,LET)
(LEQ,DENY)
(DENY,NTRU)
(DENY,FLIP)
(DENY,IMP)
(DENY,AND)
(FLIP,NTRU)
(FLIP,FIX)
(FLIP,NIF)
(FLIP,OR)
(XOR,NTRU)
(XOR,LEQ)
(XOR,NIMP)
(XOR,IF)
(LET,NTRU)
(LET,XOR)
(LET,NAND)
(LET,NOR)


(FIX,FLIP) =
(LEQ,XOR)
(LEQ,LEQ)
(LEQ,FIX)
(LEQ,FLIP)
(DENY,XOR)
(DENY,DENY)
(DENY,IF)
(DENY,OR)
(FLIP,XOR)
(FLIP,LET)
(FLIP,NIMP)
(FLIP,AND)
(XOR,XOR)
(XOR,TRU)
(XOR,NIF)
(XOR,IMP)
(LET,XOR)
(LET,NTRU)
(LET,NOR)
(LET,NAND)


(FIX,NIF) =
(LEQ,NAND)
(LEQ,AND)
(LEQ,IF)
(LEQ,NIF)
(DENY,NAND)
(DENY,NIMP)
(DENY,FIX)
(DENY,TRU)
(FLIP,NAND)
(FLIP,IMP)
(FLIP,DENY)
(FLIP,LEQ)
(XOR,NAND)
(XOR,OR)
(XOR,FLIP)
(XOR,LET)
(LET,NAND)
(LET,NOR)
(LET,NTRU)
(LET,XOR)


(FIX,NTRU) =
(LEQ,DENY)
(LEQ,LET)
(LEQ,TRU)
(LEQ,NTRU)
(DENY,DENY)
(DENY,XOR)
(DENY,OR)
(DENY,IF)
(FLIP,DENY)
(FLIP,LEQ)
(FLIP,NAND)
(FLIP,IMP)
(XOR,DENY)
(XOR,FIX)
(XOR,NOR)
(XOR,AND)
(LET,DENY)
(LET,FLIP)
(LET,NIF)
(LET,NIMP)


(FIX,AND) =
(LEQ,IF)
(LEQ,NIF)
(LEQ,NAND)
(LEQ,AND)
(DENY,IF)
(DENY,OR)
(DENY,XOR)
(DENY,DENY)
(FLIP,IF)
(FLIP,NOR)
(FLIP,TRU)
(FLIP,FLIP)
(XOR,IF)
(XOR,NIMP)
(XOR,LEQ)
(XOR,NTRU)
(LET,IF)
(LET,IMP)
(LET,LET)
(LET,FIX)


(FIX,NIMP) =
(LEQ,NOR)
(LEQ,OR)
(LEQ,IMP)
(LEQ,NIMP)
(DENY,NOR)
(DENY,NIF)
(DENY,LET)
(DENY,LEQ)
(FLIP,NOR)
(FLIP,IF)
(FLIP,FLIP)
(FLIP,TRU)
(XOR,NOR)
(XOR,AND)
(XOR,DENY)
(XOR,FIX)
(LET,NOR)
(LET,NAND)
(LET,XOR)
(LET,NTRU)


(FIX,XOR) =
(LEQ,FLIP)
(LEQ,FIX)
(LEQ,LEQ)
(LEQ,XOR)
(DENY,FLIP)
(DENY,NTRU)
(DENY,AND)
(DENY,IMP)
(FLIP,FLIP)
(FLIP,TRU)
(FLIP,NOR)
(FLIP,IF)
(XOR,FLIP)
(XOR,LET)
(XOR,NAND)
(XOR,OR)
(LET,FLIP)
(LET,DENY)
(LET,NIMP)
(LET,NIF)


(FIX,IMP) =
(LEQ,OR)
(LEQ,NOR)
(LEQ,NIMP)
(LEQ,IMP)
(DENY,OR)
(DENY,IF)
(DENY,DENY)
(DENY,XOR)
(FLIP,OR)
(FLIP,NIF)
(FLIP,FIX)
(FLIP,NTRU)
(XOR,OR)
(XOR,NAND)
(XOR,LET)
(XOR,FLIP)
(LET,OR)
(LET,AND)
(LET,LEQ)
(LET,TRU)


(FIX,NAND) =
(LEQ,NIF)
(LEQ,IF)
(LEQ,AND)
(LEQ,NAND)
(DENY,NIF)
(DENY,NOR)
(DENY,LEQ)
(DENY,LET)
(FLIP,NIF)
(FLIP,OR)
(FLIP,NTRU)
(FLIP,FIX)
(XOR,NIF)
(XOR,IMP)
(XOR,XOR)
(XOR,TRU)
(LET,NIF)
(LET,NIMP)
(LET,DENY)
(LET,FLIP)


(FIX,TRU) =
(LEQ,LET)
(LEQ,DENY)
(LEQ,NTRU)
(LEQ,TRU)
(DENY,LET)
(DENY,LEQ)
(DENY,NOR)
(DENY,NIF)
(FLIP,LET)
(FLIP,XOR)
(FLIP,AND)
(FLIP,NIMP)
(XOR,LET)
(XOR,FLIP)
(XOR,OR)
(XOR,NAND)
(LET,LET)
(LET,FIX)
(LET,IF)
(LET,IMP)


(FIX,IF) =
(LEQ,AND)
(LEQ,NAND)
(LEQ,NIF)
(LEQ,IF)
(DENY,AND)
(DENY,IMP)
(DENY,FLIP)
(DENY,NTRU)
(FLIP,AND)
(FLIP,NIMP)
(FLIP,LET)
(FLIP,XOR)
(XOR,AND)
(XOR,NOR)
(XOR,FIX)
(XOR,DENY)
(LET,AND)
(LET,OR)
(LET,TRU)
(LET,LEQ)


(FIX,FIX) =
(LEQ,LEQ)
(LEQ,XOR)
(LEQ,FLIP)
(LEQ,FIX)
(DENY,LEQ)
(DENY,LET)
(DENY,NIF)
(DENY,NOR)
(FLIP,LEQ)
(FLIP,DENY)
(FLIP,IMP)
(FLIP,NAND)
(XOR,LEQ)
(XOR,NTRU)
(XOR,IF)
(XOR,NIMP)
(LET,LEQ)
(LET,TRU)
(LET,OR)
(LET,AND)


(FIX,LET) =
(LEQ,TRU)
(LEQ,NTRU)
(LEQ,DENY)
(LEQ,LET)
(DENY,TRU)
(DENY,FIX)
(DENY,NIMP)
(DENY,NAND)
(FLIP,TRU)
(FLIP,FLIP)
(FLIP,IF)
(FLIP,NOR)
(XOR,TRU)
(XOR,XOR)
(XOR,IMP)
(XOR,NIF)
(LET,TRU)
(LET,LEQ)
(LET,AND)
(LET,OR)


(FIX,NOR) =
(LEQ,NIMP)
(LEQ,IMP)
(LEQ,OR)
(LEQ,NOR)
(DENY,NIMP)
(DENY,NAND)
(DENY,TRU)
(DENY,FIX)
(FLIP,NIMP)
(FLIP,AND)
(FLIP,XOR)
(FLIP,LET)
(XOR,NIMP)
(XOR,IF)
(XOR,NTRU)
(XOR,LEQ)
(LET,NIMP)
(LET,NIF)
(LET,FLIP)
(LET,DENY)


(LET,LEQ) =
(DENY,FIX)
(DENY,FLIP)
(DENY,XOR)
(DENY,LEQ)
(LEQ,FIX)
(LEQ,TRU)
(LEQ,NAND)
(LEQ,NIMP)
(XOR,FIX)
(XOR,NTRU)
(XOR,OR)
(XOR,NIF)
(FLIP,FIX)
(FLIP,DENY)
(FLIP,AND)
(FLIP,NOR)
(FIX,FIX)
(FIX,LET)
(FIX,IMP)
(FIX,IF)


(LET,OR) =
(DENY,IMP)
(DENY,NIMP)
(DENY,NOR)
(DENY,OR)
(LEQ,IMP)
(LEQ,AND)
(LEQ,NTRU)
(LEQ,FLIP)
(XOR,IMP)
(XOR,NAND)
(XOR,LEQ)
(XOR,DENY)
(FLIP,IMP)
(FLIP,NIF)
(FLIP,TRU)
(FLIP,XOR)
(FIX,IMP)
(FIX,IF)
(FIX,FIX)
(FIX,LET)


(LET,DENY) =
(DENY,NTRU)
(DENY,TRU)
(DENY,LET)
(DENY,DENY)
(LEQ,NTRU)
(LEQ,FLIP)
(LEQ,IMP)
(LEQ,AND)
(XOR,NTRU)
(XOR,FIX)
(XOR,NIF)
(XOR,OR)
(FLIP,NTRU)
(FLIP,LEQ)
(FLIP,NIMP)
(FLIP,IF)
(FIX,NTRU)
(FIX,XOR)
(FIX,NAND)
(FIX,NOR)


(LET,FLIP) =
(DENY,XOR)
(DENY,LEQ)
(DENY,FIX)
(DENY,FLIP)
(LEQ,XOR)
(LEQ,DENY)
(LEQ,IF)
(LEQ,OR)
(XOR,XOR)
(XOR,LET)
(XOR,NIMP)
(XOR,AND)
(FLIP,XOR)
(FLIP,TRU)
(FLIP,NIF)
(FLIP,IMP)
(FIX,XOR)
(FIX,NTRU)
(FIX,NOR)
(FIX,NAND)


(LET,NIF) =
(DENY,NAND)
(DENY,AND)
(DENY,IF)
(DENY,NIF)
(LEQ,NAND)
(LEQ,NIMP)
(LEQ,FIX)
(LEQ,TRU)
(XOR,NAND)
(XOR,IMP)
(XOR,DENY)
(XOR,LEQ)
(FLIP,NAND)
(FLIP,OR)
(FLIP,FLIP)
(FLIP,LET)
(FIX,NAND)
(FIX,NOR)
(FIX,NTRU)
(FIX,XOR)


(LET,NTRU) =
(DENY,DENY)
(DENY,LET)
(DENY,TRU)
(DENY,NTRU)
(LEQ,DENY)
(LEQ,XOR)
(LEQ,OR)
(LEQ,IF)
(XOR,DENY)
(XOR,LEQ)
(XOR,NAND)
(XOR,IMP)
(FLIP,DENY)
(FLIP,FIX)
(FLIP,NOR)
(FLIP,AND)
(FIX,DENY)
(FIX,FLIP)
(FIX,NIF)
(FIX,NIMP)


(LET,AND) =
(DENY,IF)
(DENY,NIF)
(DENY,NAND)
(DENY,AND)
(LEQ,IF)
(LEQ,OR)
(LEQ,XOR)
(LEQ,DENY)
(XOR,IF)
(XOR,NOR)
(XOR,TRU)
(XOR,FLIP)
(FLIP,IF)
(FLIP,NIMP)
(FLIP,LEQ)
(FLIP,NTRU)
(FIX,IF)
(FIX,IMP)
(FIX,LET)
(FIX,FIX)


(LET,NIMP) =
(DENY,NOR)
(DENY,OR)
(DENY,IMP)
(DENY,NIMP)
(LEQ,NOR)
(LEQ,NIF)
(LEQ,LET)
(LEQ,LEQ)
(XOR,NOR)
(XOR,IF)
(XOR,FLIP)
(XOR,TRU)
(FLIP,NOR)
(FLIP,AND)
(FLIP,DENY)
(FLIP,FIX)
(FIX,NOR)
(FIX,NAND)
(FIX,XOR)
(FIX,NTRU)


(LET,XOR) =
(DENY,FLIP)
(DENY,FIX)
(DENY,LEQ)
(DENY,XOR)
(LEQ,FLIP)
(LEQ,NTRU)
(LEQ,AND)
(LEQ,IMP)
(XOR,FLIP)
(XOR,TRU)
(XOR,NOR)
(XOR,IF)
(FLIP,FLIP)
(FLIP,LET)
(FLIP,NAND)
(FLIP,OR)
(FIX,FLIP)
(FIX,DENY)
(FIX,NIMP)
(FIX,NIF)


(LET,IMP) =
(DENY,OR)
(DENY,NOR)
(DENY,NIMP)
(DENY,IMP)
(LEQ,OR)
(LEQ,IF)
(LEQ,DENY)
(LEQ,XOR)
(XOR,OR)
(XOR,NIF)
(XOR,FIX)
(XOR,NTRU)
(FLIP,OR)
(FLIP,NAND)
(FLIP,LET)
(FLIP,FLIP)
(FIX,OR)
(FIX,AND)
(FIX,LEQ)
(FIX,TRU)


(LET,NAND) =
(DENY,NIF)
(DENY,IF)
(DENY,AND)
(DENY,NAND)
(LEQ,NIF)
(LEQ,NOR)
(LEQ,LEQ)
(LEQ,LET)
(XOR,NIF)
(XOR,OR)
(XOR,NTRU)
(XOR,FIX)
(FLIP,NIF)
(FLIP,IMP)
(FLIP,XOR)
(FLIP,TRU)
(FIX,NIF)
(FIX,NIMP)
(FIX,DENY)
(FIX,FLIP)


(LET,TRU) =
(DENY,LET)
(DENY,DENY)
(DENY,NTRU)
(DENY,TRU)
(LEQ,LET)
(LEQ,LEQ)
(LEQ,NOR)
(LEQ,NIF)
(XOR,LET)
(XOR,XOR)
(XOR,AND)
(XOR,NIMP)
(FLIP,LET)
(FLIP,FLIP)
(FLIP,OR)
(FLIP,NAND)
(FIX,LET)
(FIX,FIX)
(FIX,IF)
(FIX,IMP)


(LET,IF) =
(DENY,AND)
(DENY,NAND)
(DENY,NIF)
(DENY,IF)
(LEQ,AND)
(LEQ,IMP)
(LEQ,FLIP)
(LEQ,NTRU)
(XOR,AND)
(XOR,NIMP)
(XOR,LET)
(XOR,XOR)
(FLIP,AND)
(FLIP,NOR)
(FLIP,FIX)
(FLIP,DENY)
(FIX,AND)
(FIX,OR)
(FIX,TRU)
(FIX,LEQ)


(LET,FIX) =
(DENY,LEQ)
(DENY,XOR)
(DENY,FLIP)
(DENY,FIX)
(LEQ,LEQ)
(LEQ,LET)
(LEQ,NIF)
(LEQ,NOR)
(XOR,LEQ)
(XOR,DENY)
(XOR,IMP)
(XOR,NAND)
(FLIP,LEQ)
(FLIP,NTRU)
(FLIP,IF)
(FLIP,NIMP)
(FIX,LEQ)
(FIX,TRU)
(FIX,OR)
(FIX,AND)


(LET,LET) =
(DENY,TRU)
(DENY,NTRU)
(DENY,DENY)
(DENY,LET)
(LEQ,TRU)
(LEQ,FIX)
(LEQ,NIMP)
(LEQ,NAND)
(XOR,TRU)
(XOR,FLIP)
(XOR,IF)
(XOR,NOR)
(FLIP,TRU)
(FLIP,XOR)
(FLIP,IMP)
(FLIP,NIF)
(FIX,TRU)
(FIX,LEQ)
(FIX,AND)
(FIX,OR)


(LET,NOR) =
(DENY,NIMP)
(DENY,IMP)
(DENY,OR)
(DENY,NOR)
(LEQ,NIMP)
(LEQ,NAND)
(LEQ,TRU)
(LEQ,FIX)
(XOR,NIMP)
(XOR,AND)
(XOR,XOR)
(XOR,LET)
(FLIP,NIMP)
(FLIP,IF)
(FLIP,NTRU)
(FLIP,LEQ)
(FIX,NIMP)
(FIX,NIF)
(FIX,FLIP)
(FIX,DENY)