(BOOT-STRAP NQTHM)
[ 0.1 0.1 0.0 ]
GROUND-ZERO
(COMPILE-UNCOMPILED-DEFNS "tmp")
Loading ./basic/tmp.o
Finished loading ./basic/tmp.o
/v/hank/v28/boyer/nqthm-2nd/nqthm-1992/examples/basic/tmp.lisp
(ADD-SHELL BTM NIL BTMP NIL)
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BTM
(DEFN GET
(X ALIST)
(IF (NLISTP ALIST)
(BTM)
(IF (EQUAL X (CAAR ALIST))
(CDAR ALIST)
(GET X (CDR ALIST)))))
Linear arithmetic, the lemmas CDR-LESSEQP and CDR-LESSP, and the
definition of NLISTP inform us that the measure (COUNT ALIST) decreases
according to the well-founded relation LESSP in each recursive call. Hence,
GET is accepted under the definitional principle.
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GET
(DEFN UNSOLV-SUBRP
(FN)
(MEMBER FN
'(ZERO TRUE FALSE ADD1 SUB1 NUMBERP CONS CAR CDR LISTP PACK
UNPACK LITATOM EQUAL LIST)))
From the definition we can conclude that:
(OR (FALSEP (UNSOLV-SUBRP FN))
(TRUEP (UNSOLV-SUBRP FN)))
is a theorem.
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UNSOLV-SUBRP
(DEFN UNSOLV-APPLY-SUBR
(FN LST)
(IF
(EQUAL FN 'ZERO)
(ZERO)
(IF
(EQUAL FN 'TRUE)
(TRUE)
(IF
(EQUAL FN 'FALSE)
(FALSE)
(IF
(EQUAL FN 'ADD1)
(ADD1 (CAR LST))
(IF (EQUAL FN 'SUB1)
(SUB1 (CAR LST))
(IF (EQUAL FN 'NUMBERP)
(NUMBERP (CAR LST))
(IF (EQUAL FN 'CONS)
(CONS (CAR LST) (CADR LST))
(IF (EQUAL FN 'LIST)
LST
(IF (EQUAL FN 'CAR)
(CAR (CAR LST))
(IF (EQUAL FN 'CDR)
(CDR (CAR LST))
(IF (EQUAL FN 'LISTP)
(LISTP (CAR LST))
(IF (EQUAL FN 'PACK)
(PACK (CAR LST))
(IF (EQUAL FN 'UNPACK)
(UNPACK (CAR LST))
(IF (EQUAL FN 'LITATOM)
(LITATOM (CAR LST))
(IF (EQUAL FN 'EQUAL)
(EQUAL (CAR LST) (CADR LST))
0))))))))))))))))
[ 0.0 0.0 0.0 ]
UNSOLV-APPLY-SUBR
(DEFN EV
(FLG X VA FA N)
(IF (EQUAL FLG 'AL)
(IF (NLISTP X)
(IF (NUMBERP X)
X
(IF (EQUAL X 'T)
T
(IF (EQUAL X 'F)
F
(IF (EQUAL X NIL) NIL (GET X VA)))))
(IF (EQUAL (CAR X) 'QUOTE)
(CADR X)
(IF (EQUAL (CAR X) 'IF)
(IF (BTMP (EV 'AL (CADR X) VA FA N))
(BTM)
(IF (EV 'AL (CADR X) VA FA N)
(EV 'AL (CADDR X) VA FA N)
(EV 'AL (CADDDR X) VA FA N)))
(IF (BTMP (EV 'LIST (CDR X) VA FA N))
(BTM)
(IF (UNSOLV-SUBRP (CAR X))
(UNSOLV-APPLY-SUBR (CAR X)
(EV 'LIST (CDR X) VA FA N))
(IF (BTMP (GET (CAR X) FA))
(BTM)
(IF (ZEROP N)
(BTM)
(EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))))))))
(IF (LISTP X)
(IF (BTMP (EV 'AL (CAR X) VA FA N))
(BTM)
(IF (BTMP (EV 'LIST (CDR X) VA FA N))
(BTM)
(CONS (EV 'AL (CAR X) VA FA N)
(EV 'LIST (CDR X) VA FA N))))
NIL))
((ORD-LESSP (CONS (ADD1 N) (COUNT X)))))
Linear arithmetic, the lemmas CAR-CONS, CDR-CONS, SUB1-ADD1, CAR-LESSEQP,
CDR-LESSP, CDR-LESSEQP, ADD1-SUB1, and CAR-LESSP, and the definitions of
ORDINALP, LESSP, ORD-LESSP, EQUAL, NLISTP, BTMP, UNSOLV-SUBRP, CDR, CAR, LISTP,
MEMBER, and ZEROP can be used to establish that the measure:
(CONS (ADD1 N) (COUNT X))
decreases according to the well-founded relation ORD-LESSP in each recursive
call. Hence, EV is accepted under the principle of definition.
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EV
(DEFN PR-EVAL
(X VA FA N)
(EV 'AL X VA FA N))
[ 0.0 0.0 0.0 ]
PR-EVAL
(DEFN EVLIST
(X VA FA N)
(EV 'LIST X VA FA N))
[ 0.0 0.0 0.0 ]
EVLIST
(DEFN SUBLIS
(ALIST X)
(IF (NLISTP X)
(IF (ASSOC X ALIST)
(CDR (ASSOC X ALIST))
X)
(CONS (SUBLIS ALIST (CAR X))
(SUBLIS ALIST (CDR X)))))
Linear arithmetic, the lemmas CDR-LESSEQP, CDR-LESSP, CAR-LESSEQP, and
CAR-LESSP, and the definition of NLISTP establish that the measure (COUNT X)
decreases according to the well-founded relation LESSP in each recursive call.
Hence, SUBLIS is accepted under the principle of definition.
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SUBLIS
(DEFN X
(FA)
(SUBLIS (LIST (CONS 'CIRC (CONS FA 0)))
'(CIRC A)))
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X
(DEFN FA
(FA)
(APPEND (SUBLIS (LIST (CONS 'CIRC (CONS FA 0))
(CONS 'LOOP (CONS FA 1)))
'((CIRC (A)
(IF (HALTS '(CIRC A)
(LIST (CONS 'A A))
A)
(LOOP)
T))
(LOOP NIL (LOOP))))
FA))
Observe that (OR (LISTP (FA FA)) (EQUAL (FA FA) FA)) is a theorem.
[ 0.0 0.0 0.0 ]
FA
(DEFN VA
(FA)
(LIST (CONS 'A (FA FA))))
From the definition we can conclude that (LISTP (VA FA)) is a theorem.
[ 0.0 0.0 0.0 ]
VA
(DEFN K (N) (ADD1 N))
Observe that (NUMBERP (K N)) is a theorem.
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K
(DEFN OCCUR
(X Y)
(IF (EQUAL X Y)
T
(IF (NLISTP Y)
F
(OR (OCCUR X (CAR Y))
(OCCUR X (CDR Y))))))
Linear arithmetic, the lemmas CDR-LESSEQP, CDR-LESSP, CAR-LESSEQP, and
CAR-LESSP, and the definition of NLISTP inform us that the measure (COUNT Y)
decreases according to the well-founded relation LESSP in each recursive call.
Hence, OCCUR is accepted under the definitional principle. Note that:
(OR (FALSEP (OCCUR X Y))
(TRUEP (OCCUR X Y)))
is a theorem.
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OCCUR
(DEFN OCCUR-IN-DEFNS
(X LST)
(IF (NLISTP LST)
F
(OR (OCCUR X (CADDR (CAR LST)))
(OCCUR-IN-DEFNS X (CDR LST))))
NIL)
Linear arithmetic, the lemmas CDR-LESSEQP and CDR-LESSP, and the
definition of NLISTP inform us that the measure (COUNT LST) decreases
according to the well-founded relation LESSP in each recursive call. Hence,
OCCUR-IN-DEFNS is accepted under the principle of definition. Note that:
(OR (FALSEP (OCCUR-IN-DEFNS X LST))
(TRUEP (OCCUR-IN-DEFNS X LST)))
is a theorem.
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OCCUR-IN-DEFNS
(PROVE-LEMMA OCCUR-OCCUR-IN-DEFNS
(REWRITE)
(IMPLIES (AND (NOT (OCCUR-IN-DEFNS FN FA))
(NOT (BTMP (GET X FA))))
(NOT (OCCUR FN (CADR (GET X FA))))))
Name the conjecture *1.
We will try to prove it by induction. The recursive terms in the
conjecture suggest three inductions. However, they merge into one likely
candidate induction. We will induct according to the following scheme:
(AND (IMPLIES (NLISTP FA) (p FN X FA))
(IMPLIES (AND (NOT (NLISTP FA))
(p FN X (CDR FA)))
(p FN X FA))).
Linear arithmetic, the lemmas CDR-LESSEQP and CDR-LESSP, and the definition of
NLISTP can be used to prove that the measure (COUNT FA) decreases according to
the well-founded relation LESSP in each induction step of the scheme. The
above induction scheme generates the following four new conjectures:
Case 4. (IMPLIES (AND (NLISTP FA)
(NOT (OCCUR-IN-DEFNS FN FA))
(NOT (BTMP (GET X FA))))
(NOT (OCCUR FN (CADR (GET X FA))))).
This simplifies, expanding the functions NLISTP, OCCUR-IN-DEFNS, GET, and
BTMP, to:
T.
Case 3. (IMPLIES (AND (NOT (NLISTP FA))
(OCCUR-IN-DEFNS FN (CDR FA))
(NOT (OCCUR-IN-DEFNS FN FA))
(NOT (BTMP (GET X FA))))
(NOT (OCCUR FN (CADR (GET X FA))))).
This simplifies, opening up the functions NLISTP and OCCUR-IN-DEFNS, to:
T.
Case 2. (IMPLIES (AND (NOT (NLISTP FA))
(BTMP (GET X (CDR FA)))
(NOT (OCCUR-IN-DEFNS FN FA))
(NOT (BTMP (GET X FA))))
(NOT (OCCUR FN (CADR (GET X FA))))).
This simplifies, unfolding NLISTP, OCCUR-IN-DEFNS, and GET, to:
T.
Case 1. (IMPLIES (AND (NOT (NLISTP FA))
(NOT (OCCUR FN (CADR (GET X (CDR FA)))))
(NOT (OCCUR-IN-DEFNS FN FA))
(NOT (BTMP (GET X FA))))
(NOT (OCCUR FN (CADR (GET X FA))))).
This simplifies, unfolding the definitions of NLISTP, OCCUR-IN-DEFNS, and
GET, to:
T.
That finishes the proof of *1. Q.E.D.
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OCCUR-OCCUR-IN-DEFNS
(PROVE-LEMMA LEMMA1
(REWRITE)
(IMPLIES (AND (NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N)))
NIL)
Give the conjecture the name *1.
We will appeal to induction. There are four plausible inductions. They
merge into three likely candidate inductions, two of which are unflawed.
However, one of these is more likely than the other. We will induct according
to the following scheme:
(AND
(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NUMBERP X))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(EQUAL X 'T))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(EQUAL X 'F))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(EQUAL X NIL))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(NOT (EQUAL X NIL)))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(EQUAL (CAR X) 'QUOTE))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(p 'AL (CADR X) VA FN DEF FA N))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(p 'AL (CADDR X) VA FN DEF FA N)
(p 'AL (CADR X) VA FN DEF FA N))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(p 'AL (CADDDR X) VA FN DEF FA N)
(p 'AL (CADR X) VA FN DEF FA N))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(p 'LIST (CDR X) VA FN DEF FA N))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(UNSOLV-SUBRP (CAR X))
(p 'LIST (CDR X) VA FN DEF FA N))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) (CONS (CONS FN DEF) FA)))
(p 'LIST (CDR X) VA FN DEF FA N))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(ZEROP N)
(p 'LIST (CDR X) VA FN DEF FA N))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(NOT (ZEROP N))
(p 'LIST (CDR X) VA FN DEF FA N)
(p 'AL
(CADR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(PAIRLIST (CAR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
FN DEF FA
(SUB1 N)))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N))
(p 'AL (CAR X) VA FN DEF FA N))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(p 'AL (CAR X) VA FN DEF FA N)
(p 'LIST (CDR X) VA FN DEF FA N))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(p 'AL (CAR X) VA FN DEF FA N)
(p 'LIST (CDR X) VA FN DEF FA N))
(p FLG X VA FN DEF FA N))
(IMPLIES (AND (NOT (EQUAL FLG 'AL))
(NOT (LISTP X)))
(p FLG X VA FN DEF FA N))).
Linear arithmetic, the lemmas CAR-CONS, CDR-CONS, SUB1-ADD1, CAR-LESSEQP,
CDR-LESSP, CDR-LESSEQP, ADD1-SUB1, and CAR-LESSP, and the definitions of
ORDINALP, LESSP, ORD-LESSP, EQUAL, NLISTP, BTMP, UNSOLV-SUBRP, CDR, CAR, LISTP,
MEMBER, and ZEROP establish that the measure (CONS (ADD1 N) (COUNT X))
decreases according to the well-founded relation ORD-LESSP in each induction
step of the scheme. Note, however, the inductive instances chosen for FLG and
VA. The above induction scheme generates the following 39 new formulas:
Case 39.(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NUMBERP X)
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, unfolding NLISTP, OCCUR, EQUAL, and EV, to:
T.
Case 38.(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(EQUAL X 'T)
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, opening up the definitions of NLISTP, NUMBERP, LISTP, OCCUR,
EQUAL, and EV, to:
T.
Case 37.(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(EQUAL X 'F)
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, opening up the functions NLISTP, NUMBERP, EQUAL, LISTP,
OCCUR, and EV, to:
T.
Case 36.(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(EQUAL X NIL)
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, opening up NLISTP, NUMBERP, EQUAL, LISTP, OCCUR, and EV, to:
T.
Case 35.(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(NOT (EQUAL X NIL))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, expanding NLISTP, OCCUR, EQUAL, and EV, to:
T.
Case 34.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(EQUAL (CAR X) 'QUOTE)
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, opening up NLISTP, OCCUR, EQUAL, and EV, to:
T.
Case 33.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CADR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, expanding the definitions of NLISTP, EQUAL, OCCUR, and EV,
to the new formula:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (BTM) (EV 'AL X VA FA N))),
which again simplifies, expanding the definitions of LISTP and OCCUR, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (BTM) (EV 'AL X VA FA N))).
However this further simplifies, opening up the function OCCUR, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (EQUAL FN (CDR X)))
(NOT (LISTP (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (BTM) (EV 'AL X VA FA N))).
However this again simplifies, rewriting with the lemma CAR-NLISTP, and
unfolding the definitions of NUMBERP, LISTP, EQUAL, EV, and BTMP, to:
T.
Case 32.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(EQUAL (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))),
which simplifies, opening up the definitions of NLISTP, EQUAL, OCCUR, and EV,
to:
T.
Case 31.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(OCCUR FN (CADDR X))
(OCCUR FN (CADR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))),
which simplifies, unfolding the functions NLISTP, EQUAL, OCCUR, and EV, to
the formula:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(OCCUR FN (CADDR X))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CADDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL X VA FA N))).
However this again simplifies, expanding the functions LISTP and OCCUR, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(OCCUR FN (CADDR X))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CADDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL X VA FA N))).
However this further simplifies, rewriting with the lemma CDR-NLISTP, and
unfolding the definitions of OCCUR, CAR, NUMBERP, LISTP, EQUAL, and EV, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(OCCUR FN (CADDR X))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (EQUAL FN (CDR X)))
(NOT (LISTP (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL 0 (EV 'AL X VA FA N))).
However this again simplifies, rewriting with CAR-NLISTP and CDR-NLISTP, and
opening up NUMBERP, LISTP, EQUAL, EV, BTMP, CAR, and OCCUR, to the new
formula:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(EQUAL FN 0)
(NOT (EQUAL 0 (CDR X)))
(NOT (LISTP (CDR X)))
(NOT (OCCUR-IN-DEFNS 0 FA)))
(EQUAL 0 (EV 'AL X VA FA N))),
which again simplifies, trivially, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (EQUAL 0 (CDR X)))
(NOT (LISTP (CDR X)))
(NOT (OCCUR-IN-DEFNS 0 FA)))
(EQUAL 0 (EV 'AL X VA FA N))).
Applying the lemma CAR-CDR-ELIM, replace X by (CONS Z V) to eliminate
(CAR X) and (CDR X). We thus obtain the new formula:
(IMPLIES (AND (EQUAL Z 'IF)
(NOT (EQUAL 0 V))
(NOT (LISTP V))
(NOT (OCCUR-IN-DEFNS 0 FA)))
(EQUAL 0
(EV 'AL (CONS Z V) VA FA N))),
which finally simplifies, applying the lemmas CDR-NLISTP, CAR-NLISTP,
CDR-CONS, and CAR-CONS, and opening up CDR, CAR, EQUAL, EV, NUMBERP, LISTP,
and BTMP, to:
T.
Case 30.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EQUAL (EV 'AL
(CADDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDR X) VA FA N))
(OCCUR FN (CADR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))),
which simplifies, expanding NLISTP, EQUAL, OCCUR, and EV, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EQUAL (EV 'AL
(CADDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDR X) VA FA N))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL (CADDR X) VA FA N)
(EV 'AL X VA FA N))).
But this again simplifies, expanding the definitions of LISTP and OCCUR, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EQUAL (EV 'AL
(CADDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDR X) VA FA N))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL (CADDR X) VA FA N)
(EV 'AL X VA FA N))).
However this further simplifies, rewriting with the lemma CDR-NLISTP, and
opening up OCCUR, CAR, NUMBERP, LISTP, EQUAL, and EV, to the conjecture:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EQUAL (EV 'AL
(CADDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDR X) VA FA N))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (EQUAL FN (CDR X)))
(NOT (LISTP (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL 0 (EV 'AL X VA FA N))).
But this again simplifies, applying CAR-NLISTP and CDR-NLISTP, and expanding
the functions NUMBERP, LISTP, EQUAL, EV, BTMP, CAR, and OCCUR, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(EQUAL FN 0)
(NOT (EQUAL 0 (CDR X)))
(NOT (LISTP (CDR X)))
(NOT (OCCUR-IN-DEFNS 0 FA)))
(EQUAL 0 (EV 'AL X VA FA N))),
which again simplifies, clearly, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (EQUAL 0 (CDR X)))
(NOT (LISTP (CDR X)))
(NOT (OCCUR-IN-DEFNS 0 FA)))
(EQUAL 0 (EV 'AL X VA FA N))).
Applying the lemma CAR-CDR-ELIM, replace X by (CONS Z V) to eliminate
(CAR X) and (CDR X). We thus obtain the new goal:
(IMPLIES (AND (EQUAL Z 'IF)
(NOT (EQUAL 0 V))
(NOT (LISTP V))
(NOT (OCCUR-IN-DEFNS 0 FA)))
(EQUAL 0
(EV 'AL (CONS Z V) VA FA N))),
which finally simplifies, applying CDR-NLISTP, CAR-NLISTP, CDR-CONS, and
CAR-CONS, and expanding the functions CDR, CAR, EQUAL, EV, NUMBERP, LISTP,
and BTMP, to:
T.
Case 29.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(OCCUR FN (CADDR X))
(EQUAL (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, expanding NLISTP, EQUAL, OCCUR, and EV, to the new goal:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(OCCUR FN (CADDR X))
(EQUAL (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADR X) VA FA N))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CADDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDR X) VA FA N))),
which again simplifies, expanding LISTP and OCCUR, to the formula:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(OCCUR FN (CADDR X))
(EQUAL (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADR X) VA FA N))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CADDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDR X) VA FA N))).
But this further simplifies, applying the lemmas CAR-NLISTP and CDR-NLISTP,
and expanding OCCUR, NUMBERP, LISTP, EQUAL, EV, and CAR, to:
T.
Case 28.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EQUAL (EV 'AL
(CADDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDR X) VA FA N))
(EQUAL (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))),
which simplifies, expanding the definitions of NLISTP, EQUAL, OCCUR, and EV,
to:
T.
Case 27.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CADDDR X))
(OCCUR FN (CADR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))),
which simplifies, opening up the definitions of NLISTP, EQUAL, BTMP, OCCUR,
and EV, to the formula:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CADDDR X))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CADDDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL X VA FA N))).
However this again simplifies, expanding the functions LISTP and OCCUR, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CADDDR X))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CADDDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL X VA FA N))).
But this further simplifies, rewriting with CDR-NLISTP, and expanding the
functions OCCUR, CDR, CAR, NUMBERP, LISTP, EQUAL, and EV, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CADDDR X))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (EQUAL FN (CDR X)))
(NOT (LISTP (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL 0 (EV 'AL X VA FA N))),
which again simplifies, applying CAR-NLISTP, and unfolding the definitions
of NUMBERP, LISTP, EQUAL, and EV, to:
T.
Case 26.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(EQUAL (EV 'AL
(CADDDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDDR X) VA FA N))
(OCCUR FN (CADR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, expanding the definitions of NLISTP, EQUAL, BTMP, OCCUR,
and EV, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(EQUAL (EV 'AL
(CADDDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDDR X) VA FA N))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL (CADDDR X) VA FA N)
(EV 'AL X VA FA N))),
which again simplifies, unfolding LISTP and OCCUR, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(EQUAL (EV 'AL
(CADDDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDDR X) VA FA N))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL (CADDDR X) VA FA N)
(EV 'AL X VA FA N))).
But this further simplifies, applying CDR-NLISTP, and opening up the
definitions of OCCUR, CDR, CAR, NUMBERP, LISTP, EQUAL, and EV, to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(EQUAL (EV 'AL
(CADDDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDDR X) VA FA N))
(OCCUR FN (CADR X))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (EQUAL FN (CDR X)))
(NOT (LISTP (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL 0 (EV 'AL X VA FA N))),
which again simplifies, applying CAR-NLISTP, and expanding NUMBERP, LISTP,
EQUAL, and EV, to:
T.
Case 25.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CADDDR X))
(EQUAL (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, expanding the functions NLISTP, EQUAL, OCCUR, BTMP, and EV,
to:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (EV 'AL (CADR X) VA FA N))
(OCCUR FN (CADDDR X))
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CADDDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDDR X) VA FA N))),
which again simplifies, expanding LISTP and OCCUR, to the goal:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (EV 'AL (CADR X) VA FA N))
(OCCUR FN (CADDDR X))
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CADDDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDDR X) VA FA N))).
However this further simplifies, rewriting with the lemma CDR-NLISTP, and
expanding the functions OCCUR, CDR, CAR, NUMBERP, LISTP, EQUAL, and EV, to
the goal:
(IMPLIES (AND (LISTP X)
(EQUAL (CAR X) 'IF)
(NOT (EV 'AL (CADR X) VA FA N))
(OCCUR FN (CADDDR X))
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(NOT (EQUAL FN X))
(NOT (EQUAL FN 'IF))
(NOT (EQUAL FN (CDR X)))
(NOT (OCCUR FN (CADR X)))
(NOT (OCCUR FN (CDDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CADDDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDDR X) VA FA N))).
Appealing to the lemma CAR-CDR-ELIM, we now replace X by (CONS Z V) to
eliminate (CAR X) and (CDR X), V by (CONS W D) to eliminate (CAR V) and
(CDR V), D by (CONS C V) to eliminate (CDR D) and (CAR D), and V by
(CONS D X1) to eliminate (CAR V) and (CDR V). We must thus prove four new
goals:
Case 25.4.
(IMPLIES (AND (NOT (LISTP V))
(EQUAL Z 'IF)
(NOT (EV 'AL (CAR V) VA FA N))
(OCCUR FN (CADDR V))
(NOT (EV 'AL
(CAR V)
VA
(CONS (CONS FN DEF) FA)
N))
(NOT (EQUAL FN (CONS Z V)))
(NOT (EQUAL FN 'IF))
(NOT (EQUAL FN V))
(NOT (OCCUR FN (CAR V)))
(NOT (OCCUR FN (CDR V)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CADDR V)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDR V) VA FA N))),
which further simplifies, applying CAR-NLISTP, and expanding NUMBERP,
LISTP, EQUAL, and EV, to:
T.
Case 25.3.
(IMPLIES (AND (NOT (LISTP D))
(EQUAL Z 'IF)
(NOT (EV 'AL W VA FA N))
(OCCUR FN (CADR D))
(NOT (EV 'AL
W VA
(CONS (CONS FN DEF) FA)
N))
(NOT (EQUAL FN (CONS Z (CONS W D))))
(NOT (EQUAL FN 'IF))
(NOT (EQUAL FN (CONS W D)))
(NOT (OCCUR FN W))
(NOT (OCCUR FN D))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CADR D)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADR D) VA FA N))).
But this further simplifies, applying CDR-NLISTP, and opening up CAR,
LISTP, OCCUR, EQUAL, NUMBERP, and EV, to:
T.
Case 25.2.
(IMPLIES (AND (NOT (LISTP V))
(EQUAL Z 'IF)
(NOT (EV 'AL W VA FA N))
(OCCUR FN (CAR V))
(NOT (EV 'AL
W VA
(CONS (CONS FN DEF) FA)
N))
(NOT (EQUAL FN
(CONS Z (CONS W (CONS C V)))))
(NOT (EQUAL FN 'IF))
(NOT (EQUAL FN (CONS W (CONS C V))))
(NOT (OCCUR FN W))
(NOT (OCCUR FN (CONS C V)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
(CAR V)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CAR V) VA FA N))).
However this further simplifies, applying CAR-NLISTP, CDR-CONS, and
CAR-CONS, and unfolding the definitions of LISTP, OCCUR, EQUAL, NUMBERP,
and EV, to:
T.
Case 25.1.
(IMPLIES (AND (EQUAL Z 'IF)
(NOT (EV 'AL W VA FA N))
(OCCUR FN D)
(NOT (EV 'AL
W VA
(CONS (CONS FN DEF) FA)
N))
(NOT (EQUAL FN
(CONS Z
(CONS W (CONS C (CONS D X1))))))
(NOT (EQUAL FN 'IF))
(NOT (EQUAL FN
(CONS W (CONS C (CONS D X1)))))
(NOT (OCCUR FN W))
(NOT (OCCUR FN (CONS C (CONS D X1))))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
D VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL D VA FA N))).
This further simplifies, rewriting with CDR-CONS and CAR-CONS, and opening
up the function OCCUR, to:
T.
Case 24.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N))
(EQUAL (EV 'AL
(CADDDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADDDR X) VA FA N))
(EQUAL (EV 'AL
(CADR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CADR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, opening up NLISTP, EQUAL, OCCUR, BTMP, and EV, to:
T.
Case 23.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CDR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, opening up the definitions of NLISTP and OCCUR, to:
T.
Case 22.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, expanding NLISTP, OCCUR, EQUAL, and EV, to:
T.
Case 21.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(UNSOLV-SUBRP (CAR X))
(OCCUR FN (CDR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, opening up the definitions of NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, and OCCUR, to:
T.
Case 20.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(UNSOLV-SUBRP (CAR X))
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, expanding the functions NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, OCCUR, UNSOLV-APPLY-SUBR, EQUAL, and EV, to:
T.
Case 19.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) (CONS (CONS FN DEF) FA)))
(OCCUR FN (CDR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, rewriting with CDR-CONS and CAR-CONS, and unfolding NLISTP,
MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP, GET, and OCCUR, to:
T.
Case 18.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) (CONS (CONS FN DEF) FA)))
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))),
which simplifies, rewriting with the lemmas CDR-CONS and CAR-CONS, and
opening up the definitions of NLISTP, MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP,
GET, OCCUR, EQUAL, and EV, to the goal:
(IMPLIES (AND (LISTP X)
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR X) 'ZERO))
(NOT (EQUAL (CAR X) 'TRUE))
(NOT (EQUAL (CAR X) 'FALSE))
(NOT (EQUAL (CAR X) 'ADD1))
(NOT (EQUAL (CAR X) 'SUB1))
(NOT (EQUAL (CAR X) 'NUMBERP))
(NOT (EQUAL (CAR X) 'CONS))
(NOT (EQUAL (CAR X) 'CAR))
(NOT (EQUAL (CAR X) 'CDR))
(NOT (EQUAL (CAR X) 'LISTP))
(NOT (EQUAL (CAR X) 'PACK))
(NOT (EQUAL (CAR X) 'UNPACK))
(NOT (EQUAL (CAR X) 'LITATOM))
(NOT (EQUAL (CAR X) 'EQUAL))
(NOT (EQUAL (CAR X) 'LIST))
(EQUAL (CAR X) FN)
(BTMP DEF)
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
X VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL X VA FA N))).
However this again simplifies, expanding OCCUR, to:
T.
Case 17.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(ZEROP N)
(OCCUR FN (CDR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))),
which simplifies, rewriting with CDR-CONS and CAR-CONS, and unfolding NLISTP,
MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP, GET, ZEROP, and OCCUR, to:
T.
Case 16.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(ZEROP N)
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, rewriting with CDR-CONS and CAR-CONS, and unfolding NLISTP,
MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP, GET, ZEROP, OCCUR, EQUAL, and EV, to
two new goals:
Case 16.2.
(IMPLIES (AND (LISTP X)
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR X) 'ZERO))
(NOT (EQUAL (CAR X) 'TRUE))
(NOT (EQUAL (CAR X) 'FALSE))
(NOT (EQUAL (CAR X) 'ADD1))
(NOT (EQUAL (CAR X) 'SUB1))
(NOT (EQUAL (CAR X) 'NUMBERP))
(NOT (EQUAL (CAR X) 'CONS))
(NOT (EQUAL (CAR X) 'CAR))
(NOT (EQUAL (CAR X) 'CDR))
(NOT (EQUAL (CAR X) 'LISTP))
(NOT (EQUAL (CAR X) 'PACK))
(NOT (EQUAL (CAR X) 'UNPACK))
(NOT (EQUAL (CAR X) 'LITATOM))
(NOT (EQUAL (CAR X) 'EQUAL))
(NOT (EQUAL (CAR X) 'LIST))
(EQUAL (CAR X) FN)
(NOT (BTMP DEF))
(EQUAL N 0)
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA 0))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
X VA
(CONS (CONS FN DEF) FA)
0)
(EV 'AL X VA FA 0))),
which again simplifies, opening up OCCUR, to:
T.
Case 16.1.
(IMPLIES (AND (LISTP X)
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR X) 'ZERO))
(NOT (EQUAL (CAR X) 'TRUE))
(NOT (EQUAL (CAR X) 'FALSE))
(NOT (EQUAL (CAR X) 'ADD1))
(NOT (EQUAL (CAR X) 'SUB1))
(NOT (EQUAL (CAR X) 'NUMBERP))
(NOT (EQUAL (CAR X) 'CONS))
(NOT (EQUAL (CAR X) 'CAR))
(NOT (EQUAL (CAR X) 'CDR))
(NOT (EQUAL (CAR X) 'LISTP))
(NOT (EQUAL (CAR X) 'PACK))
(NOT (EQUAL (CAR X) 'UNPACK))
(NOT (EQUAL (CAR X) 'LITATOM))
(NOT (EQUAL (CAR X) 'EQUAL))
(NOT (EQUAL (CAR X) 'LIST))
(EQUAL (CAR X) FN)
(NOT (BTMP DEF))
(NOT (NUMBERP N))
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
X VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL X VA FA N))),
which again simplifies, opening up the function OCCUR, to:
T.
Case 15.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(NOT (ZEROP N))
(OCCUR FN (CDR X))
(OCCUR FN
(CADR (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))),
which simplifies, applying CDR-CONS and CAR-CONS, and unfolding NLISTP,
MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP, GET, ZEROP, and OCCUR, to:
T.
Case 14.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(NOT (ZEROP N))
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(OCCUR FN
(CADR (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, applying the lemmas CDR-CONS and CAR-CONS, and opening up
the functions NLISTP, MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP, GET, ZEROP, and
OCCUR, to the following two new conjectures:
Case 14.2.
(IMPLIES (AND (LISTP X)
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR X) 'ZERO))
(NOT (EQUAL (CAR X) 'TRUE))
(NOT (EQUAL (CAR X) 'FALSE))
(NOT (EQUAL (CAR X) 'ADD1))
(NOT (EQUAL (CAR X) 'SUB1))
(NOT (EQUAL (CAR X) 'NUMBERP))
(NOT (EQUAL (CAR X) 'CONS))
(NOT (EQUAL (CAR X) 'CAR))
(NOT (EQUAL (CAR X) 'CDR))
(NOT (EQUAL (CAR X) 'LISTP))
(NOT (EQUAL (CAR X) 'PACK))
(NOT (EQUAL (CAR X) 'UNPACK))
(NOT (EQUAL (CAR X) 'LITATOM))
(NOT (EQUAL (CAR X) 'EQUAL))
(NOT (EQUAL (CAR X) 'LIST))
(NOT (EQUAL (CAR X) FN))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (EQUAL N 0))
(NUMBERP N)
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(OCCUR FN
(CADR (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
X VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL X VA FA N))).
This further simplifies, rewriting with CDR-CONS, CAR-CONS, and
OCCUR-OCCUR-IN-DEFNS, and opening up the definition of GET, to:
T.
Case 14.1.
(IMPLIES (AND (LISTP X)
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR X) 'ZERO))
(NOT (EQUAL (CAR X) 'TRUE))
(NOT (EQUAL (CAR X) 'FALSE))
(NOT (EQUAL (CAR X) 'ADD1))
(NOT (EQUAL (CAR X) 'SUB1))
(NOT (EQUAL (CAR X) 'NUMBERP))
(NOT (EQUAL (CAR X) 'CONS))
(NOT (EQUAL (CAR X) 'CAR))
(NOT (EQUAL (CAR X) 'CDR))
(NOT (EQUAL (CAR X) 'LISTP))
(NOT (EQUAL (CAR X) 'PACK))
(NOT (EQUAL (CAR X) 'UNPACK))
(NOT (EQUAL (CAR X) 'LITATOM))
(NOT (EQUAL (CAR X) 'EQUAL))
(NOT (EQUAL (CAR X) 'LIST))
(EQUAL (CAR X) FN)
(NOT (BTMP DEF))
(NOT (EQUAL N 0))
(NUMBERP N)
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(OCCUR FN
(CADR (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
X VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL X VA FA N))).
However this again simplifies, applying CDR-CONS and CAR-CONS, and
expanding GET and OCCUR, to:
T.
Case 13.(IMPLIES
(AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(NOT (ZEROP N))
(OCCUR FN (CDR X))
(EQUAL (EV 'AL
(CADR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(PAIRLIST (CAR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(CONS (CONS FN DEF) FA)
(SUB1 N))
(EV 'AL
(CADR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(PAIRLIST (CAR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
FA
(SUB1 N)))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, rewriting with CDR-CONS and CAR-CONS, and unfolding NLISTP,
MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP, GET, ZEROP, and OCCUR, to:
T.
Case 12.(IMPLIES
(AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X)
(CONS (CONS FN DEF) FA))))
(NOT (ZEROP N))
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(EQUAL (EV 'AL
(CADR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(PAIRLIST (CAR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(CONS (CONS FN DEF) FA)
(SUB1 N))
(EV 'AL
(CADR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(PAIRLIST (CAR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
FA
(SUB1 N)))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))),
which simplifies, applying CDR-CONS and CAR-CONS, and opening up NLISTP,
MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP, GET, ZEROP, and OCCUR, to the
following two new conjectures:
Case 12.2.
(IMPLIES
(AND
(LISTP X)
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR X) 'ZERO))
(NOT (EQUAL (CAR X) 'TRUE))
(NOT (EQUAL (CAR X) 'FALSE))
(NOT (EQUAL (CAR X) 'ADD1))
(NOT (EQUAL (CAR X) 'SUB1))
(NOT (EQUAL (CAR X) 'NUMBERP))
(NOT (EQUAL (CAR X) 'CONS))
(NOT (EQUAL (CAR X) 'CAR))
(NOT (EQUAL (CAR X) 'CDR))
(NOT (EQUAL (CAR X) 'LISTP))
(NOT (EQUAL (CAR X) 'PACK))
(NOT (EQUAL (CAR X) 'UNPACK))
(NOT (EQUAL (CAR X) 'LITATOM))
(NOT (EQUAL (CAR X) 'EQUAL))
(NOT (EQUAL (CAR X) 'LIST))
(NOT (EQUAL (CAR X) FN))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (EQUAL N 0))
(NUMBERP N)
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(EQUAL (EV 'AL
(CADR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(PAIRLIST (CAR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(CONS (CONS FN DEF) FA)
(SUB1 N))
(EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
X VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL X VA FA N))).
This again simplifies, applying CAR-CONS and CDR-CONS, and opening up GET,
UNSOLV-SUBRP, CDR, CAR, LISTP, MEMBER, EQUAL, and EV, to:
T.
Case 12.1.
(IMPLIES
(AND
(LISTP X)
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR X) 'ZERO))
(NOT (EQUAL (CAR X) 'TRUE))
(NOT (EQUAL (CAR X) 'FALSE))
(NOT (EQUAL (CAR X) 'ADD1))
(NOT (EQUAL (CAR X) 'SUB1))
(NOT (EQUAL (CAR X) 'NUMBERP))
(NOT (EQUAL (CAR X) 'CONS))
(NOT (EQUAL (CAR X) 'CAR))
(NOT (EQUAL (CAR X) 'CDR))
(NOT (EQUAL (CAR X) 'LISTP))
(NOT (EQUAL (CAR X) 'PACK))
(NOT (EQUAL (CAR X) 'UNPACK))
(NOT (EQUAL (CAR X) 'LITATOM))
(NOT (EQUAL (CAR X) 'EQUAL))
(NOT (EQUAL (CAR X) 'LIST))
(EQUAL (CAR X) FN)
(NOT (BTMP DEF))
(NOT (EQUAL N 0))
(NUMBERP N)
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(EQUAL (EV 'AL
(CADR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(PAIRLIST (CAR (GET (CAR X) (CONS (CONS FN DEF) FA)))
(EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(CONS (CONS FN DEF) FA)
(SUB1 N))
(EV 'AL
(CADR DEF)
(PAIRLIST (CAR DEF)
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))
(NOT (EQUAL FN X))
(NOT (OCCUR FN (CAR X)))
(NOT (OCCUR FN (CDR X)))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV 'AL
X VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL X VA FA N))).
This again simplifies, applying CDR-CONS and CAR-CONS, and unfolding the
functions GET and OCCUR, to:
T.
Case 11.(IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CAR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, expanding the function OCCUR, to:
T.
Case 10.(IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N))
(EQUAL (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CAR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, unfolding the functions OCCUR, EV, and EQUAL, to:
T.
Case 9. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CAR X))
(OCCUR FN (CDR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, unfolding the definition of OCCUR, to:
T.
Case 8. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(EQUAL (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CAR X) VA FA N))
(OCCUR FN (CDR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, expanding OCCUR, to:
T.
Case 7. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(OCCUR FN (CAR X))
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, opening up the function OCCUR, to:
T.
Case 6. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N))
(EQUAL (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CAR X) VA FA N))
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, unfolding the functions OCCUR, EV, and EQUAL, to:
T.
Case 5. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(OCCUR FN (CAR X))
(OCCUR FN (CDR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, expanding the definition of OCCUR, to:
T.
Case 4. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EQUAL (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CAR X) VA FA N))
(OCCUR FN (CDR X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, opening up the function OCCUR, to:
T.
Case 3. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(OCCUR FN (CAR X))
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, opening up the definition of OCCUR, to:
T.
Case 2. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(NOT (BTMP (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)))
(EQUAL (EV 'AL
(CAR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'AL (CAR X) VA FA N))
(EQUAL (EV 'LIST
(CDR X)
VA
(CONS (CONS FN DEF) FA)
N)
(EV 'LIST (CDR X) VA FA N))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, opening up the definitions of OCCUR and EV, to:
T.
Case 1. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(NOT (LISTP X))
(NOT (OCCUR FN X))
(NOT (OCCUR-IN-DEFNS FN FA)))
(EQUAL (EV FLG X VA
(CONS (CONS FN DEF) FA)
N)
(EV FLG X VA FA N))).
This simplifies, unfolding OCCUR, EV, and EQUAL, to:
T.
That finishes the proof of *1. Q.E.D.
[ 0.0 1.1 0.1 ]
LEMMA1
(PROVE-LEMMA COUNT-OCCUR
(REWRITE)
(IMPLIES (LESSP (COUNT Y) (COUNT X))
(NOT (OCCUR X Y)))
NIL)
Call the conjecture *1.
Perhaps we can prove it by induction. There is only one plausible
induction. We will induct according to the following scheme:
(AND (IMPLIES (EQUAL X Y) (p X Y))
(IMPLIES (AND (NOT (EQUAL X Y)) (NLISTP Y))
(p X Y))
(IMPLIES (AND (NOT (EQUAL X Y))
(NOT (NLISTP Y))
(p X (CDR Y))
(p X (CAR Y)))
(p X Y))).
Linear arithmetic, the lemmas CDR-LESSEQP, CDR-LESSP, CAR-LESSEQP, and
CAR-LESSP, and the definition of NLISTP can be used to prove that the measure
(COUNT Y) decreases according to the well-founded relation LESSP in each
induction step of the scheme. The above induction scheme leads to six new
goals:
Case 6. (IMPLIES (AND (EQUAL X Y)
(LESSP (COUNT Y) (COUNT X)))
(NOT (OCCUR X Y))),
which simplifies, using linear arithmetic, to:
T.
Case 5. (IMPLIES (AND (NOT (EQUAL X Y))
(NLISTP Y)
(LESSP (COUNT Y) (COUNT X)))
(NOT (OCCUR X Y))),
which simplifies, opening up the definitions of NLISTP and OCCUR, to:
T.
Case 4. (IMPLIES (AND (NOT (EQUAL X Y))
(NOT (NLISTP Y))
(NOT (LESSP (COUNT (CDR Y)) (COUNT X)))
(NOT (LESSP (COUNT (CAR Y)) (COUNT X)))
(LESSP (COUNT Y) (COUNT X)))
(NOT (OCCUR X Y))),
which simplifies, using linear arithmetic and rewriting with CAR-LESSEQP, to:
T.
Case 3. (IMPLIES (AND (NOT (EQUAL X Y))
(NOT (NLISTP Y))
(NOT (OCCUR X (CDR Y)))
(NOT (LESSP (COUNT (CAR Y)) (COUNT X)))
(LESSP (COUNT Y) (COUNT X)))
(NOT (OCCUR X Y))).
This simplifies, using linear arithmetic and applying CAR-LESSEQP, to:
T.
Case 2. (IMPLIES (AND (NOT (EQUAL X Y))
(NOT (NLISTP Y))
(NOT (LESSP (COUNT (CDR Y)) (COUNT X)))
(NOT (OCCUR X (CAR Y)))
(LESSP (COUNT Y) (COUNT X)))
(NOT (OCCUR X Y))),
which simplifies, using linear arithmetic and rewriting with CDR-LESSEQP, to:
T.
Case 1. (IMPLIES (AND (NOT (EQUAL X Y))
(NOT (NLISTP Y))
(NOT (OCCUR X (CDR Y)))
(NOT (OCCUR X (CAR Y)))
(LESSP (COUNT Y) (COUNT X)))
(NOT (OCCUR X Y))).
This simplifies, expanding the functions NLISTP and OCCUR, to:
T.
That finishes the proof of *1. Q.E.D.
[ 0.0 0.0 0.0 ]
COUNT-OCCUR
(PROVE-LEMMA COUNT-GET
(REWRITE)
(LESSP (COUNT (CADR (GET FN FA)))
(ADD1 (COUNT FA)))
NIL)
WARNING: Note that the proposed lemma COUNT-GET is to be stored as zero type
prescription rules, zero compound recognizer rules, one linear rule, and zero
replacement rules.
This conjecture simplifies, rewriting with SUB1-ADD1, and unfolding LESSP, to:
(IMPLIES (NOT (EQUAL (COUNT (CADR (GET FN FA))) 0))
(LESSP (SUB1 (COUNT (CADR (GET FN FA))))
(COUNT FA))),
which we will name *1.
Perhaps we can prove it by induction. There are two plausible inductions.
However, they merge into one likely candidate induction. We will induct
according to the following scheme:
(AND (IMPLIES (NLISTP FA) (p FN FA))
(IMPLIES (AND (NOT (NLISTP FA))
(EQUAL FN (CAAR FA)))
(p FN FA))
(IMPLIES (AND (NOT (NLISTP FA))
(NOT (EQUAL FN (CAAR FA)))
(p FN (CDR FA)))
(p FN FA))).
Linear arithmetic, the lemmas CDR-LESSEQP and CDR-LESSP, and the definition of
NLISTP can be used to prove that the measure (COUNT FA) decreases according to
the well-founded relation LESSP in each induction step of the scheme. The
above induction scheme generates four new goals:
Case 4. (IMPLIES (AND (NLISTP FA)
(NOT (EQUAL (COUNT (CADR (GET FN FA))) 0)))
(LESSP (SUB1 (COUNT (CADR (GET FN FA))))
(COUNT FA))),
which simplifies, unfolding the functions NLISTP, GET, CDR, CAR, COUNT, and
EQUAL, to:
T.
Case 3. (IMPLIES (AND (NOT (NLISTP FA))
(EQUAL FN (CAAR FA))
(NOT (EQUAL (COUNT (CADR (GET FN FA))) 0)))
(LESSP (SUB1 (COUNT (CADR (GET FN FA))))
(COUNT FA))),
which simplifies, expanding the definitions of NLISTP and GET, to the
conjecture:
(IMPLIES (AND (LISTP FA)
(NOT (EQUAL (COUNT (CADDAR FA)) 0)))
(LESSP (SUB1 (COUNT (CADDAR FA)))
(COUNT FA))).
However this again simplifies, using linear arithmetic and applying
CDR-LESSEQP and CAR-LESSEQP, to:
T.
Case 2. (IMPLIES (AND (NOT (NLISTP FA))
(NOT (EQUAL FN (CAAR FA)))
(EQUAL (COUNT (CADR (GET FN (CDR FA))))
0)
(NOT (EQUAL (COUNT (CADR (GET FN FA))) 0)))
(LESSP (SUB1 (COUNT (CADR (GET FN FA))))
(COUNT FA))).
This simplifies, expanding the functions NLISTP, GET, and EQUAL, to:
T.
Case 1. (IMPLIES (AND (NOT (NLISTP FA))
(NOT (EQUAL FN (CAAR FA)))
(LESSP (SUB1 (COUNT (CADR (GET FN (CDR FA)))))
(COUNT (CDR FA)))
(NOT (EQUAL (COUNT (CADR (GET FN FA))) 0)))
(LESSP (SUB1 (COUNT (CADR (GET FN FA))))
(COUNT FA))).
This simplifies, opening up the definitions of NLISTP and GET, to:
(IMPLIES (AND (LISTP FA)
(NOT (EQUAL FN (CAAR FA)))
(LESSP (SUB1 (COUNT (CADR (GET FN (CDR FA)))))
(COUNT (CDR FA)))
(NOT (EQUAL (COUNT (CADR (GET FN (CDR FA))))
0)))
(LESSP (SUB1 (COUNT (CADR (GET FN (CDR FA)))))
(COUNT FA))),
which again simplifies, using linear arithmetic and rewriting with the lemma
CDR-LESSEQP, to:
T.
That finishes the proof of *1. Q.E.D.
[ 0.0 0.0 0.0 ]
COUNT-GET
(PROVE-LEMMA COUNT-OCCUR-IN-DEFNS
(REWRITE)
(IMPLIES (LESSP (COUNT FA) (COUNT X))
(NOT (OCCUR-IN-DEFNS X FA)))
NIL)
Call the conjecture *1.
Perhaps we can prove it by induction. There is only one plausible
induction. We will induct according to the following scheme:
(AND (IMPLIES (NLISTP FA) (p X FA))
(IMPLIES (AND (NOT (NLISTP FA)) (p X (CDR FA)))
(p X FA))).
Linear arithmetic, the lemmas CDR-LESSEQP and CDR-LESSP, and the definition of
NLISTP can be used to prove that the measure (COUNT FA) decreases according to
the well-founded relation LESSP in each induction step of the scheme. The
above induction scheme leads to three new goals:
Case 3. (IMPLIES (AND (NLISTP FA)
(LESSP (COUNT FA) (COUNT X)))
(NOT (OCCUR-IN-DEFNS X FA))),
which simplifies, opening up the definitions of NLISTP and OCCUR-IN-DEFNS,
to:
T.
Case 2. (IMPLIES (AND (NOT (NLISTP FA))
(NOT (LESSP (COUNT (CDR FA)) (COUNT X)))
(LESSP (COUNT FA) (COUNT X)))
(NOT (OCCUR-IN-DEFNS X FA))),
which simplifies, using linear arithmetic and applying CDR-LESSEQP, to:
T.
Case 1. (IMPLIES (AND (NOT (NLISTP FA))
(NOT (OCCUR-IN-DEFNS X (CDR FA)))
(LESSP (COUNT FA) (COUNT X)))
(NOT (OCCUR-IN-DEFNS X FA))).
This simplifies, using linear arithmetic, appealing to the lemmas
CAR-LESSEQP, CDR-LESSEQP, and COUNT-OCCUR, and expanding the functions
NLISTP and OCCUR-IN-DEFNS, to:
T.
That finishes the proof of *1. Q.E.D.
[ 0.0 0.0 0.0 ]
COUNT-OCCUR-IN-DEFNS
(PROVE-LEMMA COROLLARY1
(REWRITE)
(EQUAL (EV 'AL
(CADR (GET 'HALTS FA))
VA
(CONS (CONS (CONS FA 0) DEF0)
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))
N)
(EV 'AL
(CADR (GET 'HALTS FA))
VA FA N))
NIL)
This simplifies, using linear arithmetic, rewriting with CAR-CONS, CDR-CONS,
COUNT-OCCUR-IN-DEFNS, COUNT-OCCUR, COUNT-CONS, COUNT-GET, and LEMMA1, and
expanding the definitions of OCCUR-IN-DEFNS, OCCUR, EQUAL, LISTP, and COUNT,
to:
T.
Q.E.D.
[ 0.0 0.1 0.0 ]
COROLLARY1
(DISABLE LEMMA1)
[ 0.0 0.0 0.0 ]
LEMMA1-OFF
(PROVE-LEMMA LEMMA2 NIL
(IMPLIES (AND (NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K)))
NIL)
Name the conjecture *1.
We will appeal to induction. There are four plausible inductions.
However, they merge into one likely candidate induction. We will induct
according to the following scheme:
(AND (IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NUMBERP X))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(EQUAL X 'T))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(EQUAL X 'F))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(EQUAL X NIL))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(NOT (EQUAL X NIL)))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(EQUAL (CAR X) 'QUOTE))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(BTMP (EV 'AL (CADR X) VA FA N))
(p 'AL (CADR X) VA FA N K))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(p 'AL (CADR X) VA FA N K)
(p 'AL (CADDR X) VA FA N K))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(p 'AL (CADR X) VA FA N K)
(p 'AL (CADDDR X) VA FA N K))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST (CDR X) VA FA N))
(p 'LIST (CDR X) VA FA N K))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(UNSOLV-SUBRP (CAR X))
(p 'LIST (CDR X) VA FA N K))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) FA))
(p 'LIST (CDR X) VA FA N K))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(ZEROP N)
(p 'LIST (CDR X) VA FA N K))
(p FLG X VA FA N K))
(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(p 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)
(SUB1 K))
(p 'LIST (CDR X) VA FA N K))
(p FLG X VA FA N K))
(IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(BTMP (EV 'AL (CAR X) VA FA N))
(p 'AL (CAR X) VA FA N K))
(p FLG X VA FA N K))
(IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(p 'LIST (CDR X) VA FA N K)
(p 'AL (CAR X) VA FA N K))
(p FLG X VA FA N K))
(IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(p 'LIST (CDR X) VA FA N K)
(p 'AL (CAR X) VA FA N K))
(p FLG X VA FA N K))
(IMPLIES (AND (NOT (EQUAL FLG 'AL))
(NOT (LISTP X)))
(p FLG X VA FA N K))).
Linear arithmetic, the lemmas CAR-CONS, CDR-CONS, SUB1-ADD1, CAR-LESSEQP,
CDR-LESSP, CDR-LESSEQP, ADD1-SUB1, and CAR-LESSP, and the definitions of
ORDINALP, LESSP, ORD-LESSP, EQUAL, NLISTP, BTMP, UNSOLV-SUBRP, CDR, CAR, LISTP,
MEMBER, and ZEROP can be used to show that the measure:
(CONS (ADD1 N) (COUNT X))
decreases according to the well-founded relation ORD-LESSP in each induction
step of the scheme. Note, however, the inductive instances chosen for K, FLG,
and VA. The above induction scheme generates 40 new conjectures:
Case 40.(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NUMBERP X)
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the functions NLISTP, EQUAL, and EV, to:
T.
Case 39.(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(EQUAL X 'T)
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the definitions of NLISTP, NUMBERP, LISTP,
EQUAL, EV, and BTMP, to:
T.
Case 38.(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(EQUAL X 'F)
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding the functions NLISTP, NUMBERP, EQUAL, LISTP, EV,
and BTMP, to:
T.
Case 37.(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(EQUAL X NIL)
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the definitions of NLISTP, NUMBERP, EQUAL,
LISTP, EV, and BTMP, to:
T.
Case 36.(IMPLIES (AND (EQUAL FLG 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(NOT (EQUAL X NIL))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding the functions NLISTP, EQUAL, and EV, to:
T.
Case 35.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(EQUAL (CAR X) 'QUOTE)
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, unfolding NLISTP, EQUAL, and EV, to:
T.
Case 34.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(BTMP (EV 'AL (CADR X) VA FA K))
(BTMP (EV 'AL (CADDR X) VA FA N))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the definitions of NLISTP, EQUAL, and EV, to:
T.
Case 33.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(EQUAL (EV 'AL (CADR X) VA FA N)
(EV 'AL (CADR X) VA FA K))
(BTMP (EV 'AL (CADDR X) VA FA N))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, unfolding NLISTP, EQUAL, and EV, to:
T.
Case 32.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(BTMP (EV 'AL (CADR X) VA FA K))
(BTMP (EV 'AL (CADDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding the functions NLISTP, EQUAL, EV, and BTMP, to:
T.
Case 31.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(EQUAL (EV 'AL (CADR X) VA FA N)
(EV 'AL (CADR X) VA FA K))
(BTMP (EV 'AL (CADDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding NLISTP, EQUAL, and EV, to:
T.
Case 30.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(BTMP (EV 'AL (CADR X) VA FA K))
(EQUAL (EV 'AL (CADDR X) VA FA N)
(EV 'AL (CADDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the functions NLISTP, EQUAL, EV, and BTMP, to:
T.
Case 29.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(EQUAL (EV 'AL (CADR X) VA FA N)
(EV 'AL (CADR X) VA FA K))
(EQUAL (EV 'AL (CADDR X) VA FA N)
(EV 'AL (CADDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, unfolding the functions NLISTP, EQUAL, and EV, to:
T.
Case 28.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(BTMP (EV 'AL (CADR X) VA FA K))
(BTMP (EV 'AL (CADDDR X) VA FA N))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the definitions of NLISTP, EQUAL, BTMP, and EV,
to:
T.
Case 27.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(EQUAL (EV 'AL (CADR X) VA FA N)
(EV 'AL (CADR X) VA FA K))
(BTMP (EV 'AL (CADDDR X) VA FA N))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, unfolding NLISTP, EQUAL, BTMP, and EV, to:
T.
Case 26.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(BTMP (EV 'AL (CADR X) VA FA K))
(BTMP (EV 'AL (CADDDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up NLISTP, EQUAL, BTMP, and EV, to:
T.
Case 25.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(EQUAL (EV 'AL (CADR X) VA FA N)
(EV 'AL (CADR X) VA FA K))
(BTMP (EV 'AL (CADDDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up NLISTP, EQUAL, BTMP, and EV, to:
T.
Case 24.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(BTMP (EV 'AL (CADR X) VA FA N))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding NLISTP, EQUAL, EV, and BTMP, to:
T.
Case 23.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(BTMP (EV 'AL (CADR X) VA FA K))
(EQUAL (EV 'AL (CADDDR X) VA FA N)
(EV 'AL (CADDDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, unfolding the functions NLISTP, EQUAL, BTMP, and EV, to:
T.
Case 22.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(EQUAL (EV 'AL (CADR X) VA FA N)
(EV 'AL (CADR X) VA FA K))
(EQUAL (EV 'AL (CADDDR X) VA FA N)
(EV 'AL (CADDDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding the functions NLISTP, EQUAL, BTMP, and EV, to:
T.
Case 21.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(UNSOLV-SUBRP (CAR X))
(BTMP (EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding NLISTP, MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP,
UNSOLV-APPLY-SUBR, EQUAL, EV, and BTMP, to:
T.
Case 20.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(UNSOLV-SUBRP (CAR X))
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up NLISTP, MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP,
UNSOLV-APPLY-SUBR, EQUAL, EV, and BTMP, to:
T.
Case 19.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) FA))
(BTMP (EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding NLISTP, MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP,
EQUAL, EV, and BTMP, to:
T.
Case 18.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) FA))
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the definitions of NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, EQUAL, EV, and BTMP, to:
T.
Case 17.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(ZEROP N)
(BTMP (EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the functions NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, ZEROP, EQUAL, EV, and BTMP, to:
T.
Case 16.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(ZEROP N)
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, unfolding NLISTP, MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP,
ZEROP, EQUAL, EV, and BTMP, to:
T.
Case 15.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up NLISTP, EQUAL, EV, and BTMP, to:
T.
Case 14.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))
(BTMP (EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the functions NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, ZEROP, EQUAL, and EV, to:
T.
Case 13.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 K)))
(BTMP (EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the definitions of NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, ZEROP, EQUAL, EV, and BTMP, to:
T.
Case 12.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(EQUAL (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N))
(EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 K)))
(BTMP (EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, unfolding the functions NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, ZEROP, EQUAL, EV, and BTMP, to:
T.
Case 11.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding NLISTP, MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP,
ZEROP, EQUAL, and EV, to:
T.
Case 10.(IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 K)))
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the functions NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
(IMPLIES (AND (LISTP X)
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA K)))
(NOT (EQUAL (CAR X) 'ZERO))
(NOT (EQUAL (CAR X) 'TRUE))
(NOT (EQUAL (CAR X) 'FALSE))
(NOT (EQUAL (CAR X) 'ADD1))
(NOT (EQUAL (CAR X) 'SUB1))
(NOT (EQUAL (CAR X) 'NUMBERP))
(NOT (EQUAL (CAR X) 'CONS))
(NOT (EQUAL (CAR X) 'CAR))
(NOT (EQUAL (CAR X) 'CDR))
(NOT (EQUAL (CAR X) 'LISTP))
(NOT (EQUAL (CAR X) 'PACK))
(NOT (EQUAL (CAR X) 'UNPACK))
(NOT (EQUAL (CAR X) 'LITATOM))
(NOT (EQUAL (CAR X) 'EQUAL))
(NOT (EQUAL (CAR X) 'LIST))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (EQUAL N 0))
(NUMBERP N)
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 K)))
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV 'AL X VA FA N)))
(NOT (BTMP (EV 'AL X VA FA K))))
(EQUAL (EV 'AL X VA FA N)
(EV 'AL X VA FA K))).
This further simplifies, trivially, to:
(IMPLIES (AND (LISTP X)
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA K)))
(NOT (EQUAL (CAR X) 'ZERO))
(NOT (EQUAL (CAR X) 'TRUE))
(NOT (EQUAL (CAR X) 'FALSE))
(NOT (EQUAL (CAR X) 'ADD1))
(NOT (EQUAL (CAR X) 'SUB1))
(NOT (EQUAL (CAR X) 'NUMBERP))
(NOT (EQUAL (CAR X) 'CONS))
(NOT (EQUAL (CAR X) 'CAR))
(NOT (EQUAL (CAR X) 'CDR))
(NOT (EQUAL (CAR X) 'LISTP))
(NOT (EQUAL (CAR X) 'PACK))
(NOT (EQUAL (CAR X) 'UNPACK))
(NOT (EQUAL (CAR X) 'LITATOM))
(NOT (EQUAL (CAR X) 'EQUAL))
(NOT (EQUAL (CAR X) 'LIST))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (EQUAL N 0))
(NUMBERP N)
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA K))
FA
(SUB1 K)))
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV 'AL X VA FA N)))
(NOT (BTMP (EV 'AL X VA FA K))))
(EQUAL (EV 'AL X VA FA N)
(EV 'AL X VA FA K))),
which again simplifies, unfolding the functions UNSOLV-SUBRP, CDR, CAR,
LISTP, MEMBER, EQUAL, and EV, to:
T.
Case 9. (IMPLIES (AND (EQUAL FLG 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(EQUAL (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N))
(EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 K)))
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding the definitions of NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, ZEROP, EQUAL, and EV, to:
(IMPLIES (AND (LISTP X)
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA K)))
(NOT (EQUAL (CAR X) 'ZERO))
(NOT (EQUAL (CAR X) 'TRUE))
(NOT (EQUAL (CAR X) 'FALSE))
(NOT (EQUAL (CAR X) 'ADD1))
(NOT (EQUAL (CAR X) 'SUB1))
(NOT (EQUAL (CAR X) 'NUMBERP))
(NOT (EQUAL (CAR X) 'CONS))
(NOT (EQUAL (CAR X) 'CAR))
(NOT (EQUAL (CAR X) 'CDR))
(NOT (EQUAL (CAR X) 'LISTP))
(NOT (EQUAL (CAR X) 'PACK))
(NOT (EQUAL (CAR X) 'UNPACK))
(NOT (EQUAL (CAR X) 'LITATOM))
(NOT (EQUAL (CAR X) 'EQUAL))
(NOT (EQUAL (CAR X) 'LIST))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (EQUAL N 0))
(NUMBERP N)
(EQUAL (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N))
(EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 K)))
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 K))))
(NOT (BTMP (EV 'AL X VA FA K))))
(EQUAL (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 K))
(EV 'AL X VA FA K))).
This further simplifies, obviously, to the new formula:
(IMPLIES (AND (LISTP X)
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA K)))
(NOT (EQUAL (CAR X) 'ZERO))
(NOT (EQUAL (CAR X) 'TRUE))
(NOT (EQUAL (CAR X) 'FALSE))
(NOT (EQUAL (CAR X) 'ADD1))
(NOT (EQUAL (CAR X) 'SUB1))
(NOT (EQUAL (CAR X) 'NUMBERP))
(NOT (EQUAL (CAR X) 'CONS))
(NOT (EQUAL (CAR X) 'CAR))
(NOT (EQUAL (CAR X) 'CDR))
(NOT (EQUAL (CAR X) 'LISTP))
(NOT (EQUAL (CAR X) 'PACK))
(NOT (EQUAL (CAR X) 'UNPACK))
(NOT (EQUAL (CAR X) 'LITATOM))
(NOT (EQUAL (CAR X) 'EQUAL))
(NOT (EQUAL (CAR X) 'LIST))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (EQUAL N 0))
(NUMBERP N)
(EQUAL (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA K))
FA
(SUB1 N))
(EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA K))
FA
(SUB1 K)))
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(NOT (BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA K))
FA
(SUB1 K))))
(NOT (BTMP (EV 'AL X VA FA K))))
(EQUAL (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA K))
FA
(SUB1 K))
(EV 'AL X VA FA K))),
which again simplifies, unfolding UNSOLV-SUBRP, CDR, CAR, LISTP, MEMBER,
EQUAL, and EV, to:
T.
Case 8. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(BTMP (EV 'AL (CAR X) VA FA N))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, unfolding the definitions of EV and BTMP, to:
T.
Case 7. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(BTMP (EV 'AL (CAR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the functions EV and BTMP, to:
T.
Case 6. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA K))
(BTMP (EV 'AL (CAR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the definitions of EV and BTMP, to:
T.
Case 5. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(BTMP (EV 'AL (CAR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, unfolding the definitions of EV and BTMP, to:
T.
Case 4. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(EQUAL (EV 'AL (CAR X) VA FA N)
(EV 'AL (CAR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding the definitions of EV and BTMP, to:
T.
Case 3. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA K))
(EQUAL (EV 'AL (CAR X) VA FA N)
(EV 'AL (CAR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, expanding the definitions of EV and BTMP, to:
T.
Case 2. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(EQUAL (EV 'LIST (CDR X) VA FA N)
(EV 'LIST (CDR X) VA FA K))
(EQUAL (EV 'AL (CAR X) VA FA N)
(EV 'AL (CAR X) VA FA K))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the function EV, to:
T.
Case 1. (IMPLIES (AND (NOT (EQUAL FLG 'AL))
(NOT (LISTP X))
(NOT (BTMP (EV FLG X VA FA N)))
(NOT (BTMP (EV FLG X VA FA K))))
(EQUAL (EV FLG X VA FA N)
(EV FLG X VA FA K))),
which simplifies, opening up the definitions of EV, BTMP, and EQUAL, to:
T.
That finishes the proof of *1. Q.E.D.
[ 0.0 1.0 0.1 ]
LEMMA2
(PROVE-LEMMA COROLLARY2
(REWRITE)
(IMPLIES (EQUAL (EV FLG X VA FA N) T)
(EV FLG X VA FA K))
((USE (LEMMA2))))
WARNING: Note that COROLLARY2 contains the free variable N which will be
chosen by instantiating the hypothesis (EQUAL (EV FLG X VA FA N) T).
This formula simplifies, unfolding BTMP, NOT, AND, EQUAL, and IMPLIES, to:
T.
Q.E.D.
[ 0.0 0.0 0.0 ]
COROLLARY2
(PROVE-LEMMA LEMMA3
(REWRITE)
(IMPLIES (AND (LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))))
This formula can be simplified, using the abbreviations NLISTP, AND, and
IMPLIES, to the new conjecture:
(IMPLIES (AND (LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
Applying the lemma CAR-CDR-ELIM, replace X by (CONS Z V) to eliminate (CAR X)
and (CDR X). This produces the new goal:
(IMPLIES (AND (LISTP Z)
(NOT (LISTP V))
(LISTP (GET Z FA))
(EQUAL (CAR (GET Z FA)) NIL)
(EQUAL (CADR (GET Z FA)) (CONS Z V)))
(BTMP (EV 'AL (CONS Z V) VA FA N))),
which we would normally push and work on later by induction. But if we must
use induction to prove the input conjecture, we prefer to induct on the
original formulation of the problem. Thus we will disregard all that we have
previously done, give the name *1 to the original input, and work on it.
So now let us return to:
(IMPLIES (AND (LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
named *1. Let us appeal to the induction principle. There are four plausible
inductions. They merge into two likely candidate inductions. However, only
one is unflawed. We will induct according to the following scheme:
(AND (IMPLIES (AND (EQUAL 'AL 'AL)
(NLISTP X)
(NUMBERP X))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(EQUAL X 'T))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(EQUAL X 'F))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(EQUAL X NIL))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(NOT (EQUAL X NIL)))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(EQUAL (CAR X) 'QUOTE))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(BTMP (EV 'AL (CADR X) VA FA N))
(p (CADR X) VA FA N))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(p (CADR X) VA FA N)
(p (CADDR X) VA FA N))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(p (CADR X) VA FA N)
(p (CADDDR X) VA FA N))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST (CDR X) VA FA N))
(p (CDR X) VA FA N))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(UNSOLV-SUBRP (CAR X))
(p (CDR X) VA FA N))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) FA))
(p (CDR X) VA FA N))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(ZEROP N)
(p (CDR X) VA FA N))
(p X VA FA N))
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(p (CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N))
(p (CDR X) VA FA N))
(p X VA FA N))
(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(LISTP X)
(BTMP (EV 'AL (CAR X) VA FA N))
(p (CAR X) VA FA N))
(p X VA FA N))
(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(p (CDR X) VA FA N)
(p (CAR X) VA FA N))
(p X VA FA N))
(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(LISTP X)
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(p (CDR X) VA FA N)
(p (CAR X) VA FA N))
(p X VA FA N))
(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (LISTP X)))
(p X VA FA N))).
Linear arithmetic, the lemmas CAR-CONS, CDR-CONS, SUB1-ADD1, CAR-LESSEQP,
CDR-LESSP, CDR-LESSEQP, ADD1-SUB1, and CAR-LESSP, and the definitions of
ORDINALP, LESSP, ORD-LESSP, EQUAL, NLISTP, BTMP, UNSOLV-SUBRP, CDR, CAR, LISTP,
MEMBER, and ZEROP establish that the measure (CONS (ADD1 N) (COUNT X))
decreases according to the well-founded relation ORD-LESSP in each induction
step of the scheme. Note, however, the inductive instances chosen for VA.
The above induction scheme leads to 239 new goals:
Case 239.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NLISTP X)
(NUMBERP X)
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, clearly, to:
T.
Case 238.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(EQUAL X 'T)
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 237.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(EQUAL X 'F)
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 236.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(EQUAL X NIL)
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 235.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NLISTP X)
(NOT (NUMBERP X))
(NOT (EQUAL X 'T))
(NOT (EQUAL X 'F))
(NOT (EQUAL X NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding the definitions of EQUAL and NLISTP, to:
T.
Case 234.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(EQUAL (CAR X) 'QUOTE)
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 233.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CADR X)))
(NOT (LISTP (CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 232.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CAADR X)))
(NOT (LISTP (CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 231.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (NLISTP (CDADR X)))
(NOT (LISTP (CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 230.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (LISTP (CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 229.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (LISTP (CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 228.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (LISTP (CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 227.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CADR X)))
(NOT (LISTP (CAADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 226.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CAADR X)))
(NOT (LISTP (CAADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 225.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (NLISTP (CDADR X)))
(NOT (LISTP (CAADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 224.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (LISTP (CAADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 223.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (LISTP (CAADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 222.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (LISTP (CAADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 221.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CADR X)))
(NOT (NLISTP (CDADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 220.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CAADR X)))
(NOT (NLISTP (CDADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 219.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (NLISTP (CDADR X)))
(NOT (NLISTP (CDADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 218.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (NLISTP (CDADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 217.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (NLISTP (CDADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 216.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (NLISTP (CDADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 215.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CADR X)))
(NOT (LISTP (GET (CAADDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 214.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CAADR X)))
(NOT (LISTP (GET (CAADDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 213.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (NLISTP (CDADR X)))
(NOT (LISTP (GET (CAADDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 212.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (LISTP (GET (CAADDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 211.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (LISTP (GET (CAADDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 210.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (LISTP (GET (CAADDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 209.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CADR X)))
(NOT (EQUAL (CAR (GET (CAADDR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 208.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CAADR X)))
(NOT (EQUAL (CAR (GET (CAADDR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 207.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (NLISTP (CDADR X)))
(NOT (EQUAL (CAR (GET (CAADDR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 206.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (EQUAL (CAR (GET (CAADDR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 205.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (EQUAL (CAR (GET (CAADDR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 204.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (EQUAL (CAR (GET (CAADDR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 203.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CADR X)))
(NOT (EQUAL (CADR (GET (CAADDR X) FA))
(CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 202.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CAADR X)))
(NOT (EQUAL (CADR (GET (CAADDR X) FA))
(CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 201.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (NLISTP (CDADR X)))
(NOT (EQUAL (CADR (GET (CAADDR X) FA))
(CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 200.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (EQUAL (CADR (GET (CAADDR X) FA))
(CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 199.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (EQUAL (CADR (GET (CAADDR X) FA))
(CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 198.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (EQUAL (CADR (GET (CAADDR X) FA))
(CADDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 197.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CADR X)))
(BTMP (EV 'AL (CADDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 196.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (CAADR X)))
(BTMP (EV 'AL (CADDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 195.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (NLISTP (CDADR X)))
(BTMP (EV 'AL (CADDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 194.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (LISTP (GET (CAADR X) FA)))
(BTMP (EV 'AL (CADDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 193.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(BTMP (EV 'AL (CADDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 192.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(EV 'AL (CADR X) VA FA N)
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(BTMP (EV 'AL (CADDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 191.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CADR X)))
(NOT (LISTP (CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 190.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CAADR X)))
(NOT (LISTP (CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 189.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (NLISTP (CDADR X)))
(NOT (LISTP (CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 188.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (LISTP (CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 187.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (LISTP (CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 186.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (LISTP (CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 185.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CADR X)))
(NOT (LISTP (CAADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 184.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CAADR X)))
(NOT (LISTP (CAADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 183.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (NLISTP (CDADR X)))
(NOT (LISTP (CAADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 182.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (LISTP (CAADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 181.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (LISTP (CAADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 180.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (LISTP (CAADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 179.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CADR X)))
(NOT (NLISTP (CDADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 178.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CAADR X)))
(NOT (NLISTP (CDADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 177.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (NLISTP (CDADR X)))
(NOT (NLISTP (CDADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 176.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (NLISTP (CDADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 175.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (NLISTP (CDADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 174.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (NLISTP (CDADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 173.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CADR X)))
(NOT (LISTP (GET (CAADDDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 172.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CAADR X)))
(NOT (LISTP (GET (CAADDDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 171.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (NLISTP (CDADR X)))
(NOT (LISTP (GET (CAADDDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 170.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (LISTP (GET (CAADDDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 169.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (LISTP (GET (CAADDDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 168.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (LISTP (GET (CAADDDR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 167.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CADR X)))
(NOT (EQUAL (CAR (GET (CAADDDR X) FA))
NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 166.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CAADR X)))
(NOT (EQUAL (CAR (GET (CAADDDR X) FA))
NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 165.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (NLISTP (CDADR X)))
(NOT (EQUAL (CAR (GET (CAADDDR X) FA))
NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 164.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (EQUAL (CAR (GET (CAADDDR X) FA))
NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 163.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (EQUAL (CAR (GET (CAADDDR X) FA))
NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 162.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (EQUAL (CAR (GET (CAADDDR X) FA))
NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 161.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CADR X)))
(NOT (EQUAL (CADR (GET (CAADDDR X) FA))
(CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 160.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CAADR X)))
(NOT (EQUAL (CADR (GET (CAADDDR X) FA))
(CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 159.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (NLISTP (CDADR X)))
(NOT (EQUAL (CADR (GET (CAADDDR X) FA))
(CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 158.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (GET (CAADR X) FA)))
(NOT (EQUAL (CADR (GET (CAADDDR X) FA))
(CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 157.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(NOT (EQUAL (CADR (GET (CAADDDR X) FA))
(CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 156.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(NOT (EQUAL (CADR (GET (CAADDDR X) FA))
(CADDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 155.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CADR X)))
(BTMP (EV 'AL (CADDDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 154.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (CAADR X)))
(BTMP (EV 'AL (CADDDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 153.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (NLISTP (CDADR X)))
(BTMP (EV 'AL (CADDDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 152.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (LISTP (GET (CAADR X) FA)))
(BTMP (EV 'AL (CADDDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 151.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CAR (GET (CAADR X) FA)) NIL))
(BTMP (EV 'AL (CADDDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 150.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(NOT (BTMP (EV 'AL (CADR X) VA FA N)))
(NOT (EV 'AL (CADR X) VA FA N))
(NOT (EQUAL (CADR (GET (CAADR X) FA))
(CADR X)))
(BTMP (EV 'AL (CADDDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 149.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(EQUAL (CAR X) 'IF)
(BTMP (EV 'AL (CADR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 148.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding EQUAL, NLISTP, EV, and BTMP, to:
T.
Case 147.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up the definitions of EQUAL, NLISTP, EV, BTMP,
MEMBER, LISTP, CAR, CDR, and UNSOLV-SUBRP, to:
(IMPLIES (AND (BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X)
(NOT (EQUAL N 0))
(NUMBERP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))),
which again simplifies, unfolding EQUAL, EV, and BTMP, to:
T.
Case 146.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (NLISTP (CDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, expanding EQUAL, NLISTP, EV, BTMP, MEMBER, LISTP, CAR, CDR,
and UNSOLV-SUBRP, to:
(IMPLIES (AND (BTMP (EV 'LIST (CDR X) VA FA N))
(LISTP (CDDR X))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X)
(NOT (EQUAL N 0))
(NUMBERP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))).
This again simplifies, opening up EQUAL, EV, and BTMP, to:
T.
Case 145.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, expanding EQUAL, NLISTP, EV, BTMP, MEMBER, LISTP, CAR, CDR,
and UNSOLV-SUBRP, to:
(IMPLIES (AND (BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X)
(NOT (EQUAL N 0))
(NUMBERP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))).
This again simplifies, expanding EQUAL, EV, and BTMP, to:
T.
Case 144.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, opening up the functions EQUAL, NLISTP, EV, BTMP, MEMBER,
LISTP, CAR, CDR, and UNSOLV-SUBRP, to:
(IMPLIES (AND (BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X)
(NOT (EQUAL N 0))
(NUMBERP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))).
But this again simplifies, unfolding the functions EQUAL, EV, and BTMP, to:
T.
Case 143.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, opening up EQUAL, NLISTP, EV, BTMP, MEMBER, LISTP, CAR,
CDR, and UNSOLV-SUBRP, to:
(IMPLIES (AND (BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X)
(NOT (EQUAL N 0))
(NUMBERP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))).
This again simplifies, opening up the functions EQUAL, EV, and BTMP, to:
T.
Case 142.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(BTMP (EV 'LIST (CDR X) VA FA N))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, opening up EQUAL, NLISTP, EV, BTMP, MEMBER, LISTP, CAR,
CDR, and UNSOLV-SUBRP, to the conjecture:
(IMPLIES (AND (BTMP (EV 'LIST (CDR X) VA FA N))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X)
(NOT (EQUAL N 0))
(NUMBERP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))).
But this again simplifies, expanding EQUAL, EV, and BTMP, to:
T.
Case 141.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(UNSOLV-SUBRP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, expanding the definitions of EQUAL, NLISTP, EV, BTMP,
MEMBER, LISTP, CAR, CDR, and UNSOLV-SUBRP, to:
T.
Case 140.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(UNSOLV-SUBRP (CAR X))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, expanding the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, and UNSOLV-SUBRP, to:
T.
Case 139.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(UNSOLV-SUBRP (CAR X))
(NOT (NLISTP (CDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, unfolding the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, and UNSOLV-SUBRP, to:
T.
Case 138.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(UNSOLV-SUBRP (CAR X))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, opening up the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, and UNSOLV-SUBRP, to:
T.
Case 137.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(UNSOLV-SUBRP (CAR X))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, opening up the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, and UNSOLV-SUBRP, to:
T.
Case 136.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(UNSOLV-SUBRP (CAR X))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, opening up the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, and UNSOLV-SUBRP, to:
T.
Case 135.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(UNSOLV-SUBRP (CAR X))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, unfolding the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, and UNSOLV-SUBRP, to:
T.
Case 134.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) FA))
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, obviously, to:
T.
Case 133.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) FA))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 132.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) FA))
(NOT (NLISTP (CDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 131.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) FA))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 130.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) FA))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 129.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) FA))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 128.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(BTMP (GET (CAR X) FA))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 127.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(ZEROP N)
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up EQUAL, NLISTP, EV, BTMP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 126.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(ZEROP N)
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, ZEROP, EV, and BTMP, to:
T.
Case 125.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(ZEROP N)
(NOT (NLISTP (CDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, ZEROP, EV, and BTMP, to:
T.
Case 124.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(ZEROP N)
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, ZEROP, EV, and BTMP, to:
T.
Case 123.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(ZEROP N)
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, ZEROP, EV, and BTMP, to:
T.
Case 122.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(ZEROP N)
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, ZEROP, EV, and BTMP, to:
T.
Case 121.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(ZEROP N)
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, ZEROP, EV, and BTMP, to:
T.
Case 120.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CADR (GET (CAR X) FA))))
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 119.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CAADR (GET (CAR X) FA))))
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding EQUAL, NLISTP, EV, BTMP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 118.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (NLISTP (CDADR (GET (CAR X) FA))))
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up the functions EQUAL, NLISTP, EV, BTMP, MEMBER,
LISTP, CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 117.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (GET (CAADR (GET (CAR X) FA)) FA)))
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding the definitions of EQUAL, NLISTP, EV, BTMP,
MEMBER, LISTP, CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 116.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CAR (GET (CAADR (GET (CAR X) FA)) FA))
NIL))
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up EQUAL, NLISTP, EV, BTMP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 115.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CADR (GET (CAADR (GET (CAR X) FA)) FA))
(CADR (GET (CAR X) FA))))
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding EQUAL, NLISTP, EV, BTMP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 114.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding the functions EQUAL, NLISTP, EV, BTMP, MEMBER,
LISTP, CAR, CDR, UNSOLV-SUBRP, ZEROP, and PAIRLIST, to:
(IMPLIES (AND (NOT (EQUAL N 0))
(NUMBERP N)
(BTMP (EV 'AL X NIL FA (SUB1 N)))
(NOT (LISTP (CDR X)))
(LISTP X)
(LISTP (CAR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))),
which again simplifies, expanding the functions EQUAL, EV, and PAIRLIST, to:
T.
Case 113.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CADR (GET (CAR X) FA))))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, trivially, to:
T.
Case 112.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CAADR (GET (CAR X) FA))))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 111.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (NLISTP (CDADR (GET (CAR X) FA))))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 110.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (GET (CAADR (GET (CAR X) FA)) FA)))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 109.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CAR (GET (CAADR (GET (CAR X) FA)) FA))
NIL))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 108.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CADR (GET (CAADR (GET (CAR X) FA)) FA))
(CADR (GET (CAR X) FA))))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 107.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, ZEROP, PAIRLIST, EV, and BTMP, to:
(IMPLIES (AND (NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL N 0))
(NUMBERP N)
(BTMP (EV 'AL X NIL FA (SUB1 N)))
(NOT (LISTP (CADR X)))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))),
which again simplifies, applying CAR-NLISTP, and opening up the functions
EQUAL, EV, BTMP, LISTP, and PAIRLIST, to:
T.
Case 106.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CADR (GET (CAR X) FA))))
(NOT (NLISTP (CDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 105.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CAADR (GET (CAR X) FA))))
(NOT (NLISTP (CDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 104.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (NLISTP (CDADR (GET (CAR X) FA))))
(NOT (NLISTP (CDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 103.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (GET (CAADR (GET (CAR X) FA)) FA)))
(NOT (NLISTP (CDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 102.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CAR (GET (CAADR (GET (CAR X) FA)) FA))
NIL))
(NOT (NLISTP (CDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 101.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CADR (GET (CAADR (GET (CAR X) FA)) FA))
(CADR (GET (CAR X) FA))))
(NOT (NLISTP (CDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 100.
(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))
(NOT (NLISTP (CDDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, ZEROP, PAIRLIST, EV, and BTMP, to:
(IMPLIES (AND (NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL N 0))
(NUMBERP N)
(BTMP (EV 'AL X NIL FA (SUB1 N)))
(LISTP (CDDR X))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))),
which again simplifies, rewriting with CDR-NLISTP, and expanding the
functions EQUAL, EV, BTMP, and LISTP, to:
T.
Case 99.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CADR (GET (CAR X) FA))))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 98.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CAADR (GET (CAR X) FA))))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 97.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (NLISTP (CDADR (GET (CAR X) FA))))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 96.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (GET (CAADR (GET (CAR X) FA)) FA)))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 95.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CAR (GET (CAADR (GET (CAR X) FA)) FA))
NIL))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 94.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CADR (GET (CAADR (GET (CAR X) FA)) FA))
(CADR (GET (CAR X) FA))))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 93.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, ZEROP, PAIRLIST, EV, and BTMP, to:
(IMPLIES (AND (NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL N 0))
(NUMBERP N)
(BTMP (EV 'AL X NIL FA (SUB1 N)))
(NOT (LISTP (GET (CADR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))),
which again simplifies, rewriting with the lemma CAR-NLISTP, and unfolding
EQUAL, EV, BTMP, and PAIRLIST, to:
T.
Case 92.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CADR (GET (CAR X) FA))))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, obviously, to:
T.
Case 91.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CAADR (GET (CAR X) FA))))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 90.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (NLISTP (CDADR (GET (CAR X) FA))))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 89.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (GET (CAADR (GET (CAR X) FA)) FA)))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 88.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CAR (GET (CAADR (GET (CAR X) FA)) FA))
NIL))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 87.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CADR (GET (CAADR (GET (CAR X) FA)) FA))
(CADR (GET (CAR X) FA))))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 86.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, ZEROP, PAIRLIST, EV, and BTMP, to:
(IMPLIES (AND (NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL N 0))
(NUMBERP N)
(BTMP (EV 'AL X NIL FA (SUB1 N)))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))),
which again simplifies, applying CAR-NLISTP, and opening up the definitions
of EQUAL, EV, BTMP, and PAIRLIST, to:
T.
Case 85.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CADR (GET (CAR X) FA))))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 84.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CAADR (GET (CAR X) FA))))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding the functions EQUAL, NLISTP, MEMBER, LISTP, CAR,
CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 83.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (NLISTP (CDADR (GET (CAR X) FA))))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 82.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (GET (CAADR (GET (CAR X) FA)) FA)))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, unfolding EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 81.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CAR (GET (CAADR (GET (CAR X) FA)) FA))
NIL))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 80.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CADR (GET (CAADR (GET (CAR X) FA)) FA))
(CADR (GET (CAR X) FA))))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 79.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, ZEROP, PAIRLIST, EV, and BTMP, to the new goal:
(IMPLIES (AND (NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL N 0))
(NUMBERP N)
(BTMP (EV 'AL X NIL FA (SUB1 N)))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))),
which again simplifies, applying CAR-NLISTP, and unfolding the definitions
of EQUAL, EV, BTMP, and PAIRLIST, to:
T.
Case 78.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CADR (GET (CAR X) FA))))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 77.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (CAADR (GET (CAR X) FA))))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 76.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (NLISTP (CDADR (GET (CAR X) FA))))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 75.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (LISTP (GET (CAADR (GET (CAR X) FA)) FA)))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, and ZEROP, to:
T.
Case 74.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CAR (GET (CAADR (GET (CAR X) FA)) FA))
NIL))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 73.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(NOT (EQUAL (CADR (GET (CAADR (GET (CAR X) FA)) FA))
(CADR (GET (CAR X) FA))))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, expanding EQUAL, NLISTP, MEMBER, LISTP, CAR, CDR,
UNSOLV-SUBRP, and ZEROP, to:
T.
Case 72.(IMPLIES (AND (EQUAL 'AL 'AL)
(NOT (NLISTP X))
(NOT (EQUAL (CAR X) 'QUOTE))
(NOT (EQUAL (CAR X) 'IF))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (UNSOLV-SUBRP (CAR X)))
(NOT (BTMP (GET (CAR X) FA)))
(NOT (ZEROP N))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, opening up the definitions of EQUAL, NLISTP, MEMBER, LISTP,
CAR, CDR, UNSOLV-SUBRP, ZEROP, PAIRLIST, EV, and BTMP, to the new conjecture:
(IMPLIES (AND (NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL N 0))
(NUMBERP N)
(BTMP (EV 'AL X NIL FA (SUB1 N)))
(BTMP (EV 'AL (CDR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NOT (LISTP (CDR X)))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL
(CADR (GET (CAR X) FA))
(PAIRLIST (CAR (GET (CAR X) FA))
(EV 'LIST (CDR X) VA FA N))
FA
(SUB1 N)))),
which again simplifies, expanding the definitions of EQUAL, EV, BTMP, and
PAIRLIST, to:
T.
Case 71.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CDR X)))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))),
which simplifies, clearly, to:
T.
Case 70.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CADR X)))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 69.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (NLISTP (CDDR X)))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 68.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (GET (CADR X) FA)))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 67.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 66.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 65.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(BTMP (EV 'AL (CDR X) VA FA N))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 64.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CDR X)))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 63.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CADR X)))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 62.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (NLISTP (CDDR X)))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 61.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (GET (CADR X) FA)))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 60.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 59.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 58.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(BTMP (EV 'AL (CDR X) VA FA N))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 57.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CDR X)))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 56.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CADR X)))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 55.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (NLISTP (CDDR X)))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 54.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (GET (CADR X) FA)))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 53.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 52.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 51.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(BTMP (EV 'AL (CDR X) VA FA N))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 50.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CDR X)))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 49.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CADR X)))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 48.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (NLISTP (CDDR X)))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 47.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (GET (CADR X) FA)))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 46.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 45.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 44.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(BTMP (EV 'AL (CDR X) VA FA N))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 43.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CDR X)))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 42.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (CADR X)))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 41.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (NLISTP (CDDR X)))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 40.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (LISTP (GET (CADR X) FA)))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 39.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 38.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 37.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(BTMP (EV 'LIST (CDR X) VA FA N))
(BTMP (EV 'AL (CDR X) VA FA N))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 36.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (CDR X)))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 35.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (CADR X)))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 34.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (NLISTP (CDDR X)))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 33.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (GET (CADR X) FA)))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 32.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 31.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 30.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(BTMP (EV 'AL (CDR X) VA FA N))
(NOT (LISTP (CAAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 29.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (CDR X)))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 28.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (CADR X)))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 27.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (NLISTP (CDDR X)))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 26.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (GET (CADR X) FA)))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 25.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 24.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 23.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(BTMP (EV 'AL (CDR X) VA FA N))
(NOT (NLISTP (CDAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 22.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (CDR X)))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 21.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (CADR X)))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 20.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (NLISTP (CDDR X)))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 19.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (GET (CADR X) FA)))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 18.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 17.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 16.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(BTMP (EV 'AL (CDR X) VA FA N))
(NOT (LISTP (GET (CAAR X) FA)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 15.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (CDR X)))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 14.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (CADR X)))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 13.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (NLISTP (CDDR X)))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 12.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (GET (CADR X) FA)))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 11.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 10.(IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
Case 9. (IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(BTMP (EV 'AL (CDR X) VA FA N))
(NOT (EQUAL (CAR (GET (CAAR X) FA)) NIL))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 8. (IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (CDR X)))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 7. (IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (CADR X)))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 6. (IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (NLISTP (CDDR X)))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 5. (IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (LISTP (GET (CADR X) FA)))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 4. (IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CAR (GET (CADR X) FA)) NIL))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, obviously, to:
T.
Case 3. (IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(NOT (EQUAL (CADR (GET (CADR X) FA))
(CDR X)))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 2. (IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(NOT (BTMP (EV 'AL (CAR X) VA FA N)))
(NOT (BTMP (EV 'LIST (CDR X) VA FA N)))
(BTMP (EV 'AL (CDR X) VA FA N))
(NOT (EQUAL (CADR (GET (CAAR X) FA))
(CAR X)))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, trivially, to:
T.
Case 1. (IMPLIES (AND (NOT (EQUAL 'AL 'AL))
(BTMP (EV 'AL (CAR X) VA FA N))
(LISTP X)
(LISTP (CAR X))
(NLISTP (CDR X))
(LISTP (GET (CAR X) FA))
(EQUAL (CAR (GET (CAR X) FA)) NIL)
(EQUAL (CADR (GET (CAR X) FA)) X))
(BTMP (EV 'AL X VA FA N))).
This simplifies, clearly, to:
T.
That finishes the proof of *1. Q.E.D.
[ 0.0 1.6 0.3 ]
LEMMA3
(PROVE-LEMMA EXPAND-CIRC
(REWRITE)
(IMPLIES (AND (NOT (BTMP VAL))
(NOT (BTMP (GET (CONS FN 0) FA))))
(EQUAL (EV 'AL
(CONS (CONS FN 0) '(A))
(LIST (CONS 'A VAL))
FA J)
(IF (ZEROP J)
(BTM)
(EV 'AL
(CADR (GET (CONS FN 0) FA))
(PAIRLIST (CAR (GET (CONS FN 0) FA))
(EV 'LIST
'(A)
(LIST (CONS 'A VAL))
FA J))
FA
(SUB1 J)))))
NIL)
This formula simplifies, rewriting with the lemmas CDR-CONS and CAR-CONS, and
expanding UNSOLV-SUBRP, CDR, CAR, LISTP, MEMBER, EQUAL, EV, GET, NUMBERP, BTMP,
and ZEROP, to:
T.
Q.E.D.
[ 0.0 0.0 0.0 ]
EXPAND-CIRC
(DEFN SEXP
(X)
(IF (EQUAL X T)
T
(IF (EQUAL X F)
T
(IF (NUMBERP X)
T
(IF (LISTP X)
(AND (SEXP (CAR X)) (SEXP (CDR X)))
(IF (LITATOM X)
(SEXP (UNPACK X))
F))))))
Linear arithmetic and the lemmas CDR-LESSP, CAR-LESSP, and UNPACK-LESSP
can be used to show that the measure (COUNT X) decreases according to the
well-founded relation LESSP in each recursive call. Hence, SEXP is accepted
under the principle of definition. Note that:
(OR (FALSEP (SEXP X))
(TRUEP (SEXP X)))
is a theorem.
[ 0.0 0.0 0.0 ]
SEXP
(PROVE-LEMMA UNSOLVABILITY-OF-THE-HALTING-PROBLEM NIL
(AND (IMPLIES (EQUAL H
(PR-EVAL (LIST 'HALTS
(LIST 'QUOTE (X FA))
(LIST 'QUOTE (VA FA))
(LIST 'QUOTE (FA FA)))
NIL FA N))
(AND (IMPLIES (EQUAL H F)
(NOT (BTMP (PR-EVAL (X FA)
(VA FA)
(FA FA)
(K N)))))
(IMPLIES (EQUAL H T)
(BTMP (PR-EVAL (X FA) (VA FA) (FA FA) K)))))
(IMPLIES (SEXP FA)
(AND (SEXP (X FA))
(SEXP (VA FA))
(SEXP (FA FA))))))
This conjecture can be simplified, using the abbreviations IMPLIES, AND, K, VA,
X, and PR-EVAL, to two new formulas:
Case 2. (IMPLIES
(EQUAL H
(EV 'AL
(LIST 'HALTS
(LIST 'QUOTE
(SUBLIS (LIST (CONS 'CIRC (CONS FA 0)))
'(CIRC A)))
(LIST 'QUOTE
(LIST (CONS 'A (FA FA))))
(LIST 'QUOTE (FA FA)))
NIL FA N))
(AND (IMPLIES (EQUAL H F)
(NOT (BTMP (EV 'AL
(SUBLIS (LIST (CONS 'CIRC (CONS FA 0)))
'(CIRC A))
(LIST (CONS 'A (FA FA)))
(FA FA)
(ADD1 N)))))
(IMPLIES (EQUAL H T)
(BTMP (EV 'AL
(SUBLIS (LIST (CONS 'CIRC (CONS FA 0)))
'(CIRC A))
(LIST (CONS 'A (FA FA)))
(FA FA)
K))))),
which simplifies, applying CDR-CONS, CAR-CONS, SUB1-ADD1, COROLLARY1, and
EXPAND-CIRC, and opening up the definitions of CDR, CAR, LISTP, SUBLIS,
ASSOC, EQUAL, CONS, APPEND, FA, UNSOLV-SUBRP, EV, BTMP, GET, NUMBERP,
PAIRLIST, UNSOLV-APPLY-SUBR, NOT, IMPLIES, and AND, to the following three
new goals:
Case 2.3.
(IMPLIES
(AND
(NOT (BTMP (GET 'HALTS FA)))
(NOT (EQUAL N 0))
(NUMBERP N)
(EQUAL
(EV 'AL
(CADR (GET 'HALTS FA))
(PAIRLIST
(CAR (GET 'HALTS FA))
(LIST
(CONS (CONS FA 0) '(A))
(LIST
(CONS 'A
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
FA
(SUB1 N))
T)
(NOT (EQUAL K 0))
(NUMBERP K)
(NOT (EQUAL (SUB1 K) 0))
(NOT
(BTMP
(EV 'AL
(CADR (GET 'HALTS FA))
(PAIRLIST
(CAR (GET 'HALTS FA))
(LIST
(CONS (CONS FA 0) '(A))
(LIST
(CONS 'A
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
FA
(SUB1 (SUB1 K))))))
(BTMP
(EV 'AL
(LIST (CONS FA 1))
(LIST
(CONS 'A
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))
(SUB1 K)))).
However this again simplifies, rewriting with CDR-CONS, CAR-CONS, and
LEMMA3, and unfolding the functions GET, EQUAL, and LISTP, to:
T.
Case 2.2.
(IMPLIES
(AND
(NOT (BTMP (GET 'HALTS FA)))
(NOT (EQUAL N 0))
(NUMBERP N)
(EQUAL
(EV 'AL
(CADR (GET 'HALTS FA))
(PAIRLIST
(CAR (GET 'HALTS FA))
(LIST
(CONS (CONS FA 0) '(A))
(LIST
(CONS 'A
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
FA
(SUB1 N))
T)
(NOT (EQUAL K 0))
(NUMBERP K)
(NOT (EQUAL (SUB1 K) 0))
(NOT
(BTMP
(EV 'AL
(CADR (GET 'HALTS FA))
(PAIRLIST
(CAR (GET 'HALTS FA))
(LIST
(CONS (CONS FA 0) '(A))
(LIST
(CONS 'A
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
FA
(SUB1 (SUB1 K))))))
(EV 'AL
(CADR (GET 'HALTS FA))
(PAIRLIST
(CAR (GET 'HALTS FA))
(LIST
(CONS (CONS FA 0) '(A))
(LIST
(CONS 'A
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
FA
(SUB1 (SUB1 K)))).
However this again simplifies, appealing to the lemma COROLLARY2, and
expanding BTMP, to:
T.
Case 2.1.
(IMPLIES
(AND
(NOT (BTMP (GET 'HALTS FA)))
(NOT (EQUAL N 0))
(NUMBERP N)
(NOT
(EV 'AL
(CADR (GET 'HALTS FA))
(PAIRLIST
(CAR (GET 'HALTS FA))
(LIST
(CONS (CONS FA 0) '(A))
(LIST
(CONS 'A
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
FA
(SUB1 N))))
(NOT
(BTMP
(EV 'AL
(CADR (GET 'HALTS FA))
(PAIRLIST
(CAR (GET 'HALTS FA))
(LIST
(CONS (CONS FA 0) '(A))
(LIST
(CONS 'A
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
(CONS
(LIST
(CONS FA 0)
'(A)
(CONS 'IF
(CONS (CONS 'HALTS
(CONS (LIST 'QUOTE (CONS (CONS FA 0) '(A)))
'((LIST (CONS 'A A)) A)))
(CONS (LIST (CONS FA 1)) '(T)))))
(CONS (LIST (CONS FA 1)
NIL
(LIST (CONS FA 1)))
FA))))
FA
(SUB1 N))))),
which again simplifies, trivially, to:
T.
Case 1. (IMPLIES (SEXP FA)
(AND (SEXP (SUBLIS (LIST (CONS 'CIRC (CONS FA 0)))
'(CIRC A)))
(SEXP (LIST (CONS 'A (FA FA))))
(SEXP (FA FA)))).
This simplifies, rewriting with the lemmas CDR-CONS and CAR-CONS, and
opening up the definitions of CDR, CAR, LISTP, SUBLIS, ASSOC, EQUAL, CONS,
SEXP, APPEND, FA, and AND, to:
T.
Q.E.D.
[ 0.0 5.5 0.0 ]
UNSOLVABILITY-OF-THE-HALTING-PROBLEM
(MAKE-LIB "unsolv" T)
Making the lib for "unsolv".
Compiling the lib for "unsolv".
Loading ./basic/unsolv.o
Finished loading ./basic/unsolv.o
Finished compiling the lib for "unsolv".
Finished making the lib for "unsolv".
(/v/hank/v28/boyer/nqthm-2nd/nqthm-1992/examples/basic/unsolv.lib
/v/hank/v28/boyer/nqthm-2nd/nqthm-1992/examples/basic/unsolv.lisp)