(NOTE-LIB "nqthm-boot") 

(DEFINE (^BM^BOARDP X) (IF (^BM^NLISTP X) (EQUAL X (^NIL)) (^BM^AND (^BM^OR (EQUAL (^BM^CAR X) (^BM^PACK (^BM^CONS (^X) (^BM^ZERO)))) (^BM^OR (EQUAL (^BM^CAR X) (^BM^PACK (^BM^CONS (^O) (^BM^ZERO)))) (EQUAL (^BM^CAR X) (^BM^FALSE)))) (^BM^BOARDP (^BM^CDR X))))) 

(DEFINE (^BM^ENDP BOARD) (IF (^BM^NLISTP BOARD) (^BM^TRUE) (IF (^BM^CAR BOARD) (^BM^ENDP (^BM^CDR BOARD)) (^BM^FALSE)))) 

(DEFINE (^BM^LEGAL-MOVEP BOARD1 PLAYER BOARD2) (IF (^BM^NLISTP BOARD1) (^BM^FALSE) (IF (EQUAL (^BM^CAR BOARD1) (^BM^CAR BOARD2)) (^BM^LEGAL-MOVEP (^BM^CDR BOARD1) PLAYER (^BM^CDR BOARD2)) (IF (^BM^AND (EQUAL (^BM^CAR BOARD1) (^BM^FALSE)) (EQUAL (^BM^CAR BOARD2) PLAYER)) (EQUAL (^BM^CDR BOARD1) (^BM^CDR BOARD2)) (IF (^BM^TRUE) (^BM^FALSE) (^NIL)))))) 

(DEFINE (^BM^NTH I BOARD) (IF (^BM^ZEROP I) (^BM^CAR BOARD) (^BM^NTH (^BM^SUB1 I) (^BM^CDR BOARD)))) 

(DEFINE (^BM^WINP1 X LINE BOARD) (IF (^BM^NLISTP LINE) (^BM^TRUE) (IF (EQUAL X (^BM^NTH (^BM^CAR LINE) BOARD)) (^BM^WINP1 X (^BM^CDR LINE) BOARD) (^BM^FALSE)))) 

(DEFINE (^BM^WINP X BOARD) (^BM^OR (^BM^WINP1 X (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))) BOARD) (^BM^OR (^BM^WINP1 X (^BM^CONS (^INT (^BM^CONS (^3) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^4) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^5) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))) BOARD) (^BM^OR (^BM^WINP1 X (^BM^CONS (^INT (^BM^CONS (^6) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^7) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^8) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))) BOARD) (^BM^OR (^BM^WINP1 X (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^CONS (^3) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^6) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))) BOARD) (^BM^OR (^BM^WINP1 X (^BM^CONS (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^4) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^7) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))) BOARD) (^BM^OR (^BM^WINP1 X (^BM^CONS (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^5) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^8) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))) BOARD) (^BM^OR (^BM^WINP1 X (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^CONS (^4) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^8) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))) BOARD) (^BM^WINP1 X (^BM^CONS (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^4) (^BM^ZERO))) (^BM^CONS (^INT (^BM^CONS (^6) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))) BOARD))))))))) 

(DEFINE (^BM^OTHER-PLAYER PLAYER) (IF (EQUAL PLAYER (^BM^PACK (^BM^CONS (^X) (^BM^ZERO)))) (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))))) 

(DEFINE (^BM^END OUTCOME PLAYER LST) (IF (EQUAL LST (^BM^CONS (IF (EQUAL OUTCOME (^BM^PACK (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO)))))) (IF (EQUAL PLAYER (^BM^PACK (^BM^CONS (^O) (^BM^ZERO)))) (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (^BM^PACK (^BM^CONS (^X) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO)))))))) (^BM^PACK (^BM^CONS (^D) (^BM^CONS (^R) (^BM^CONS (^A) (^BM^CONS (^W) (^BM^ZERO))))))) (^NIL))) (IF (EQUAL OUTCOME (^BM^PACK (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO)))))) (IF (EQUAL PLAYER (^BM^PACK (^BM^CONS (^O) (^BM^ZERO)))) (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (^BM^PACK (^BM^CONS (^X) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO)))))))) (^BM^PACK (^BM^CONS (^D) (^BM^CONS (^R) (^BM^CONS (^A) (^BM^CONS (^W) (^BM^ZERO))))))) (^BM^FALSE))) 

(DEFINE (^BM^TIC-TAC-TOEP1 BOARD PLAYER LST) (IF (^BM^NLISTP LST) (^BM^END (^BM^PACK (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))) (^BM^OTHER-PLAYER PLAYER) LST) (IF (^BM^NOT (^BM^BOARDP (^BM^CAR LST))) (^BM^FALSE) (IF (^BM^NOT (^BM^LEGAL-MOVEP BOARD PLAYER (^BM^CAR LST))) (^BM^END (^BM^PACK (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))) (^BM^OTHER-PLAYER PLAYER) (^BM^CDR LST)) (IF (^BM^WINP PLAYER (^BM^CAR LST)) (^BM^END (^BM^PACK (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))) PLAYER (^BM^CDR LST)) (IF (^BM^ENDP (^BM^CAR LST)) (^BM^END (^BM^PACK (^BM^CONS (^D) (^BM^CONS (^R) (^BM^CONS (^A) (^BM^CONS (^W) (^BM^ZERO)))))) PLAYER (^BM^CDR LST)) (IF (^BM^TRUE) (^BM^TIC-TAC-TOEP1 (^BM^CAR LST) (^BM^OTHER-PLAYER PLAYER) (^BM^CDR LST)) (^NIL)))))))) 

(DEFINE (^BM^TIC-TAC-TOEP LST) (IF (^BM^AND (^BM^LISTP LST) (EQUAL (^BM^CAR LST) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^NIL)))))))))))) (^BM^TIC-TAC-TOEP1 (^BM^CAR LST) (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CDR LST)) (^BM^FALSE))) 

(DEFINE (^BM^MOVE X I BOARD) (IF (^BM^NLISTP BOARD) BOARD (IF (^BM^ZEROP I) (^BM^CONS X (^BM^CDR BOARD)) (^BM^CONS (^BM^CAR BOARD) (^BM^MOVE X (^BM^SUB1 I) (^BM^CDR BOARD)))))) 

(DEFINE (^BM^LEGALP I BOARD) (^BM^AND (^BM^LESSP I (^INT (^BM^CONS (^9) (^BM^ZERO)))) (EQUAL (^BM^NTH I BOARD) (^BM^FALSE)))) 

(DEFINE (^BM^OPEN-SQUARES BOARD) (IF (^BM^NLISTP BOARD) (^INT (^BM^ZERO)) (IF (^BM^CAR BOARD) (^BM^OPEN-SQUARES (^BM^CDR BOARD)) (^BM^ADD1 (^BM^OPEN-SQUARES (^BM^CDR BOARD)))))) 

(LEMMA (^BM^IMPLIES (^BM^AND X (^BM^LEGALP I BOARD)) (^BM^LESSP (^BM^OPEN-SQUARES (^BM^MOVE X I BOARD)) (^BM^OPEN-SQUARES BOARD)))) 

(LEMMA (^BM^IMPLIES X (^BM^NOT (^BM^LESSP (^BM^OPEN-SQUARES BOARD) (^BM^OPEN-SQUARES (^BM^MOVE X I BOARD)))))) 

(DEFINE (^BM^PICK-MOVE1 BOARD I) (IF (^BM^NLISTP BOARD) (^INT (^BM^ZERO)) (IF (EQUAL (^BM^CAR BOARD) (^BM^FALSE)) I (IF (^BM^TRUE) (^BM^PICK-MOVE1 (^BM^CDR BOARD) (^BM^ADD1 I)) (^NIL))))) 

(DEFINE (^BM^PICK-MOVE BOARD) (IF (^BM^ASSOC BOARD (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) 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(^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS 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(^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) 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(^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS 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(^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS 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(^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS 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(^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS 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(^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) 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(^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) 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(^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) 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(^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) 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(^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) 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(^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) 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(^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT 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(^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) 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(^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS 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(^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK 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(^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) 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(^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS 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(^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) 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(^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS 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(^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^5) 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(^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))))))))) (^INT (^BM^CONS (^4) (^BM^ZERO)))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (^BM^PICK-MOVE1 BOARD (^INT (^BM^ZERO))))) 

(DEFINE (^BM^TIC-TAC-TOE1 XMOVES BOARD) (IF (^BM^LEGALP (^BM^CAR XMOVES) BOARD) (IF (^BM^ENDP (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^PACK (^BM^CONS (^D) (^BM^CONS (^R) (^BM^CONS (^A) (^BM^CONS (^W) (^BM^ZERO)))))) (^NIL))) (IF (^BM^WINP (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (^NIL)))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^TIC-TAC-TOE1 (^BM^CDR XMOVES) (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD))))))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (^NIL))))) 

(DEFINE (^BM^TIC-TAC-TOE XMOVES) (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^NIL)))))))))) (^BM^TIC-TAC-TOE1 XMOVES (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^NIL))))))))))))) 

(DEFINE (^BM^LENGTH X) (IF (^BM^NLISTP X) (^INT (^BM^ZERO)) (^BM^ADD1 (^BM^LENGTH (^BM^CDR X))))) 

(LEMMA (EQUAL (^BM^LENGTH (^BM^MOVE X I BOARD)) (^BM^LENGTH BOARD))) 

(DEFINE (^BM^LEGAL-BOOKP ALIST) (IF (^BM^NLISTP ALIST) (^BM^TRUE) (^BM^AND (^BM^LEGALP (^BM^CDR (^BM^CAR ALIST)) (^BM^CAR (^BM^CAR ALIST))) (^BM^LEGAL-BOOKP (^BM^CDR ALIST))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^LEGAL-BOOKP ALIST) (^BM^ASSOC BOARD ALIST)) (^BM^LEGALP (^BM^CDR (^BM^ASSOC BOARD ALIST)) BOARD))) 

(DEFINE (^BM^PICK-MOVE2 BOARD) (IF (^BM^NLISTP BOARD) (^INT (^BM^ZERO)) (IF (EQUAL (^BM^CAR BOARD) (^BM^FALSE)) (^INT (^BM^ZERO)) (IF (^BM^TRUE) (^BM^ADD1 (^BM^PICK-MOVE2 (^BM^CDR BOARD))) (^NIL))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NOT (^BM^ENDP BOARD)) (^BM^LESSP (^BM^LENGTH BOARD) (^INT (^BM^CONS (^1) (^BM^CONS (^0) (^BM^ZERO)))))) (^BM^LEGALP (^BM^PICK-MOVE2 BOARD) BOARD))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NOT (^BM^ENDP BOARD)) (^BM^NUMBERP I)) (EQUAL (^BM^PICK-MOVE1 BOARD I) (^BM^PLUS I (^BM^PICK-MOVE2 BOARD))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NOT (^BM^ENDP BOARD)) (^BM^LESSP (^BM^LENGTH BOARD) (^INT (^BM^CONS (^1) (^BM^CONS (^0) (^BM^ZERO)))))) (^BM^LEGALP (^BM^PICK-MOVE BOARD) BOARD))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^BOARDP BOARD) (^BM^OR (EQUAL PLAYER (^BM^PACK (^BM^CONS (^X) (^BM^ZERO)))) (EQUAL PLAYER (^BM^PACK (^BM^CONS (^O) (^BM^ZERO)))))) (^BM^BOARDP (^BM^MOVE PLAYER I BOARD)))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^LEGALP (^BM^CDR (^BM^ASSOC BOARD ALIST)) BOARD) (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO))))) (^BM^LESSP (^BM^CDR (^BM^ASSOC BOARD ALIST)) (^INT (^BM^CONS (^9) (^BM^ZERO)))))) 

(LEMMA (^BM^IMPLIES (^BM^ENDP BOARD) (EQUAL (^BM^PICK-MOVE1 BOARD I) (^INT (^BM^ZERO))))) 

(LEMMA (^BM^IMPLIES (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^LESSP (^BM^PICK-MOVE BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))))) 

(LEMMA (EQUAL (^BM^TIC-TAC-TOE1 XMOVES (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL))))))))))) (IF (^BM^LEGALP (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL))))))))))) (IF (^BM^ENDP (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL)))))))))))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL))))))))))) (^BM^CONS (^BM^PACK (^BM^CONS (^D) (^BM^CONS (^R) (^BM^CONS (^A) (^BM^CONS (^W) (^BM^ZERO)))))) (^NIL))) (IF (^BM^WINP (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL)))))))))))) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL))))))))))))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL))))))))))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL)))))))))))) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL)))))))))))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (^NIL)))) (IF (^BM^TRUE) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL))))))))))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL)))))))))))) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL)))))))))))) (^BM^TIC-TAC-TOE1 (^BM^CDR XMOVES) (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL)))))))))))) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL))))))))))))))) (^NIL)))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL))))))))))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (^NIL)))))) 

(DEFINE (^BM^LEGALP1 X BOARD) (IF (^BM^ZEROP X) (^BM^NOT (^BM^CAR BOARD)) (IF (^BM^NLISTP BOARD) (^BM^FALSE) (^BM^LEGALP1 (^BM^SUB1 X) (^BM^CDR BOARD))))) 

(LEMMA (^BM^IMPLIES (^BM^NOT (^BM^LESSP X (^BM^LENGTH BOARD))) (^BM^NOT (^BM^LEGALP1 X BOARD)))) 

(LEMMA (^BM^IMPLIES (^BM^NTH X BOARD) (^BM^NOT (^BM^LEGALP1 X BOARD)))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^LESSP X (^BM^LENGTH BOARD)) (^BM^NOT (^BM^NTH X BOARD))) (^BM^LEGALP1 X BOARD))) 

(LEMMA (^BM^IMPLIES (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))) (EQUAL (^BM^LEGALP X BOARD) (^BM^LEGALP1 X BOARD)))) 

(DEFINE (^BM^LEGALP2 X BOARD I) (IF (^BM^NLISTP BOARD) (^BM^FALSE) (IF (^BM^AND (^BM^NOT (^BM^CAR BOARD)) (EQUAL (^BM^FIX X) I)) (^BM^TRUE) (^BM^LEGALP2 X (^BM^CDR BOARD) (^BM^ADD1 I))))) 

(LEMMA (^BM^IMPLIES (^BM^LESSP X I) (^BM^NOT (^BM^LEGALP2 X BOARD I)))) 

(LEMMA (EQUAL (^BM^SUB1 (^BM^DIFFERENCE X Y)) (^BM^DIFFERENCE (^BM^SUB1 X) Y))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NUMBERP I) (^BM^NOT (^BM^LESSP X I))) (EQUAL (^BM^LEGALP1 (^BM^DIFFERENCE X I) BOARD) (^BM^LEGALP2 X BOARD I)))) 

(LEMMA (EQUAL (^BM^LEGALP1 X BOARD) (^BM^LEGALP2 X BOARD (^INT (^BM^ZERO))))) 

(LEMMA (^BM^IMPLIES (^BM^NUMBERP I) (EQUAL (^BM^LEGALP2 X (^BM^CONS (^BM^FALSE) BOARD) I) (^BM^OR (IF (EQUAL I (^INT (^BM^ZERO))) (^BM^ZEROP X) (EQUAL X I)) (^BM^LEGALP2 X BOARD (^BM^ADD1 I)))))) 

(LEMMA (EQUAL (^BM^LEGALP2 X (^BM^CONS (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) BOARD) I) (^BM^LEGALP2 X BOARD (^BM^ADD1 I)))) 

(LEMMA (EQUAL (^BM^LEGALP2 X (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) BOARD) I) (^BM^LEGALP2 X BOARD (^BM^ADD1 I)))) 

(LEMMA (EQUAL (^BM^LEGALP2 X (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO))))) I) (^BM^FALSE))) 

(LEMMA (EQUAL (^BM^LEGALP X (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL))))))))))) (^BM^LEGALP2 X (^BM^CONS S0 (^BM^CONS S1 (^BM^CONS S2 (^BM^CONS S3 (^BM^CONS S4 (^BM^CONS S5 (^BM^CONS S6 (^BM^CONS S7 (^BM^CONS S8 (^NIL)))))))))) (^INT (^BM^ZERO))))) 

(LEMMA (^BM^IMPLIES (^BM^NOT (^BM^LESSP I (^BM^LENGTH BOARD))) (EQUAL (^BM^MOVE X I BOARD) BOARD))) 

(LEMMA (^BM^IMPLIES (^BM^AND (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^AND (^BM^NUMBERP I) (^BM^AND (^BM^NOT (EQUAL I (^INT (^BM^ZERO)))) (^BM^AND (^BM^NOT (EQUAL I (^INT (^BM^CONS (^1) (^BM^ZERO))))) (^BM^AND (^BM^NOT (EQUAL I (^INT (^BM^CONS (^2) (^BM^ZERO))))) (^BM^AND (^BM^NOT (EQUAL I (^INT (^BM^CONS (^3) (^BM^ZERO))))) (^BM^AND (^BM^NOT (EQUAL I (^INT (^BM^CONS (^4) (^BM^ZERO))))) (^BM^AND (^BM^NOT (EQUAL I (^INT (^BM^CONS (^5) (^BM^ZERO))))) (^BM^AND (^BM^NOT (EQUAL I (^INT (^BM^CONS (^6) (^BM^ZERO))))) (^BM^AND (^BM^NOT (EQUAL I (^INT (^BM^CONS (^7) (^BM^ZERO))))) (^BM^NOT (EQUAL I (^INT (^BM^CONS (^8) (^BM^ZERO))))))))))))))) (EQUAL (^BM^MOVE X I BOARD) BOARD))) 

(LEMMA (^BM^IMPLIES (^BM^AND (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^NOT (^BM^NUMBERP I))) (EQUAL (^BM^MOVE X I BOARD) (^BM^CONS X (^BM^CDR BOARD))))) 

(LEMMA (^BM^NOT (^BM^LEGAL-MOVEP BOARD (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) BOARD))) 

(LEMMA (^BM^IMPLIES (^BM^NTH I BOARD) (^BM^NOT (^BM^LEGAL-MOVEP BOARD (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) I BOARD))))) 

(LEMMA (^BM^IMPLIES (^BM^NOT (^BM^LESSP I (^BM^LENGTH BOARD))) (^BM^NOT (^BM^LEGAL-MOVEP BOARD (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) I BOARD))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^BOARDP BOARD) (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO))))) (EQUAL (^BM^LEGAL-MOVEP BOARD (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) I BOARD)) (^BM^LEGALP I BOARD)))) 

(LEMMA (^BM^MEMBER (^BM^TIC-TAC-TOEP (^BM^TIC-TAC-TOE XMOVES)) (^BM^CONS (^BM^PACK (^BM^CONS (^D) (^BM^CONS (^R) (^BM^CONS (^A) (^BM^CONS (^W) (^BM^ZERO)))))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO))))))))) 

(DEFINE (^BM^X-MOVES-HONORED1 BOARD XMOVES LST) (IF (^BM^NLISTP LST) (^BM^TRUE) (IF (^BM^NLISTP (^BM^CDR LST)) (^BM^TRUE) (IF (^BM^TRUE) (^BM^AND (EQUAL (^BM^CAR LST) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^X-MOVES-HONORED1 (^BM^CAR (^BM^CDR LST)) (^BM^CDR XMOVES) (^BM^CDR (^BM^CDR LST)))) (^NIL))))) 

(DEFINE (^BM^X-MOVES-HONORED XMOVES LST) (^BM^X-MOVES-HONORED1 (^BM^CAR LST) XMOVES (^BM^CDR LST))) 

(LEMMA (^BM^IMPLIES (^BM^BOARDP BOARD) (^BM^X-MOVES-HONORED1 BOARD XMOVES (^BM^TIC-TAC-TOE1 XMOVES BOARD)))) 

(LEMMA (^BM^X-MOVES-HONORED XMOVES (^BM^TIC-TAC-TOE XMOVES))) 

(DEFINE (^BM^INIT-GAME1 N LST) (IF (^BM^ZEROP N) (^NIL) (IF (^BM^NLISTP LST) (^NIL) (IF (^BM^NLISTP (^BM^CDR LST)) (^BM^CONS (^BM^CAR LST) (^NIL)) (^BM^CONS (^BM^CAR LST) (^BM^CONS (^BM^CAR (^BM^CDR LST)) (^BM^INIT-GAME1 (^BM^SUB1 N) (^BM^CDR (^BM^CDR LST))))))))) 

(DEFINE (^BM^INIT-GAME N LST) (^BM^CONS (^BM^CAR LST) (^BM^INIT-GAME1 N (^BM^CDR LST)))) 

(LEMMA (EQUAL (EQUAL (^BM^INIT-GAME1 (^BM^LENGTH OPENING) (^BM^TIC-TAC-TOE1 (^BM^APPEND OPENING XMOVES1) BOARD)) (^BM^INIT-GAME1 (^BM^LENGTH OPENING) (^BM^TIC-TAC-TOE1 (^BM^APPEND OPENING XMOVES2) BOARD))) (^BM^TRUE))) 

(LEMMA (EQUAL (EQUAL (^BM^INIT-GAME (^BM^LENGTH OPENING) (^BM^TIC-TAC-TOE (^BM^APPEND OPENING XMOVES1))) (^BM^INIT-GAME (^BM^LENGTH OPENING) (^BM^TIC-TAC-TOE (^BM^APPEND OPENING XMOVES2)))) (^BM^TRUE))) 

(LEMMA (^BM^AND (^BM^MEMBER (^BM^TIC-TAC-TOEP (^BM^TIC-TAC-TOE XMOVES)) (^BM^CONS (^BM^PACK (^BM^CONS (^D) (^BM^CONS (^R) (^BM^CONS (^A) (^BM^CONS (^W) (^BM^ZERO)))))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))) (^BM^AND (^BM^X-MOVES-HONORED XMOVES (^BM^TIC-TAC-TOE XMOVES)) (EQUAL (^BM^INIT-GAME (^BM^LENGTH OPENING) (^BM^TIC-TAC-TOE (^BM^APPEND OPENING XMOVES1))) (^BM^INIT-GAME (^BM^LENGTH OPENING) (^BM^TIC-TAC-TOE (^BM^APPEND OPENING XMOVES2))))))) 

(LEMMA (^BM^IMPLIES (^BM^TIC-TAC-TOEP1 BOARD PLAYER LST) (EQUAL (^BM^TIC-TAC-TOEP1 BOARD PLAYER LST) (^BM^NTH (^BM^SUB1 (^BM^LENGTH LST)) LST)))) 

(LEMMA (^BM^IMPLIES (^BM^TIC-TAC-TOEP LST) (EQUAL (^BM^TIC-TAC-TOEP LST) (^BM^NTH (^BM^SUB1 (^BM^LENGTH LST)) LST)))) 

(LEMMA (EQUAL (^BM^PLUS X (^BM^ADD1 Y)) (^BM^ADD1 (^BM^PLUS X Y)))) 

(LEMMA (EQUAL (^BM^PLUS X Y) (^BM^PLUS Y X))) 

(LEMMA (EQUAL (^BM^PLUS X (^BM^PLUS Y Z)) (^BM^PLUS Y (^BM^PLUS X Z)))) 

(LEMMA (EQUAL (^BM^PLUS (^BM^PLUS X Y) Z) (^BM^PLUS X (^BM^PLUS Y Z)))) 

(LEMMA (EQUAL (^BM^TIMES X (^INT (^BM^ZERO))) (^INT (^BM^ZERO)))) 

(LEMMA (^BM^IMPLIES (^BM^NOT (^BM^NUMBERP Z)) (EQUAL (^BM^TIMES X Z) (^INT (^BM^ZERO))))) 

(LEMMA (EQUAL (^BM^TIMES X (^BM^ADD1 Y)) (^BM^PLUS X (^BM^TIMES X Y)))) 

(LEMMA (EQUAL (^BM^TIMES X (^BM^PLUS Y Z)) (^BM^PLUS (^BM^TIMES X Y) (^BM^TIMES X Z)))) 

(LEMMA (EQUAL (^BM^TIMES X Y) (^BM^TIMES Y X))) 

(LEMMA (EQUAL (^BM^TIMES X (^BM^TIMES Y Z)) (^BM^TIMES Y (^BM^TIMES X Z)))) 

(LEMMA (EQUAL (^BM^TIMES (^BM^TIMES X Y) Z) (^BM^TIMES X (^BM^TIMES Y Z)))) 

(LEMMA (EQUAL (^BM^TIMES (^BM^PLUS X Y) Z) (^BM^PLUS (^BM^TIMES X Z) (^BM^TIMES Y Z)))) 

(LEMMA (^BM^IMPLIES (^BM^NOT (^BM^LESSP Y X)) (EQUAL (^BM^DIFFERENCE X Y) (^INT (^BM^ZERO))))) 

(LEMMA (EQUAL (^BM^DIFFERENCE (^BM^PLUS I X) I) (^BM^FIX X))) 

(LEMMA (EQUAL (^BM^DIFFERENCE (^BM^PLUS I X) (^BM^PLUS I Y)) (^BM^DIFFERENCE X Y))) 

(LEMMA (EQUAL (^BM^DIFFERENCE (^BM^PLUS I (^BM^PLUS J X)) J) (^BM^PLUS I X))) 

(LEMMA (EQUAL (^BM^LESSP (^BM^REMAINDER X Y) Y) (^BM^NOT (^BM^ZEROP Y)))) 

(LEMMA (^BM^IMPLIES (^BM^NUMBERP X) (EQUAL (^BM^PLUS (^BM^REMAINDER X Y) (^BM^TIMES Y (^BM^QUOTIENT X Y))) X))) 

(DEFINE (^BM^TIC-TAC-TOE1-A XMOVES BOARD I) (IF (^BM^LEGALP (^BM^CAR XMOVES) BOARD) (IF (^BM^LESSP I (^INT (^BM^CONS (^9) (^BM^ZERO)))) (IF (^BM^WINP (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (^NIL)))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^TIC-TAC-TOE1-A (^BM^CDR XMOVES) (^BM^MOVE (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))) (^BM^PICK-MOVE (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^ADD1 (^BM^ADD1 I)))))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^PACK (^BM^CONS (^D) (^BM^CONS (^R) (^BM^CONS (^A) (^BM^CONS (^W) (^BM^ZERO)))))) (^NIL)))) (^BM^CONS (^BM^MOVE (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (^NIL))))) 

(DEFINE (^BM^TIC-TAC-TOE-A XMOVES) (^BM^CONS (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^NIL)))))))))) (^BM^TIC-TAC-TOE1-A XMOVES (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^BM^CONS (^BM^FALSE) (^NIL)))))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))))) 

(LEMMA (EQUAL (^BM^ENDP BOARD) (^BM^ZEROP (^BM^OPEN-SQUARES BOARD)))) 

(LEMMA (^BM^IMPLIES (^BM^AND X (^BM^LEGALP I BOARD)) (EQUAL (^BM^OPEN-SQUARES (^BM^MOVE X I BOARD)) (^BM^SUB1 (^BM^OPEN-SQUARES BOARD))))) 

(LEMMA (^BM^IMPLIES (^BM^NOT (^BM^LESSP X Y)) (EQUAL (^BM^ADD1 (^BM^DIFFERENCE X Y)) (^BM^DIFFERENCE (^BM^ADD1 X) Y)))) 

(LEMMA (^BM^NOT (^BM^LESSP (^BM^LENGTH BOARD) (^BM^OPEN-SQUARES BOARD)))) 

(LEMMA (^BM^IMPLIES (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))) (EQUAL (^BM^TIC-TAC-TOE1 XMOVES BOARD) (^BM^TIC-TAC-TOE1-A XMOVES BOARD (^BM^DIFFERENCE (^INT (^BM^CONS (^1) (^BM^CONS (^0) (^BM^ZERO)))) (^BM^OPEN-SQUARES BOARD)))))) 

(LEMMA (EQUAL (^BM^TIC-TAC-TOE XMOVES) (^BM^TIC-TAC-TOE-A XMOVES))) 

(DEFINE (^BM^PIECE->NUMBER X) (IF (EQUAL X (^BM^FALSE)) (^INT (^BM^ZERO)) (IF (EQUAL X (^BM^PACK (^BM^CONS (^X) (^BM^ZERO)))) (^INT (^BM^CONS (^1) (^BM^ZERO))) (^INT (^BM^CONS (^2) (^BM^ZERO)))))) 

(DEFINE (^BM^NUMBER->PIECE J) (IF (EQUAL J (^INT (^BM^ZERO))) (^BM^FALSE) (IF (EQUAL J (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^PACK (^BM^CONS (^X) (^BM^ZERO))) (^BM^PACK (^BM^CONS (^O) (^BM^ZERO)))))) 

(DEFINE (^BM^BOARD->NUMBER BOARD) (IF (^BM^NLISTP BOARD) (^INT (^BM^ZERO)) (^BM^PLUS (^BM^PIECE->NUMBER (^BM^CAR BOARD)) (^BM^TIMES (^INT (^BM^CONS (^4) (^BM^ZERO))) (^BM^BOARD->NUMBER (^BM^CDR BOARD)))))) 

(DEFINE (^BM^NUMBER->BOARD N LEN) (IF (^BM^ZEROP LEN) (^NIL) (^BM^CONS (^BM^NUMBER->PIECE (^BM^REMAINDER N (^INT (^BM^CONS (^4) (^BM^ZERO))))) (^BM^NUMBER->BOARD (^BM^QUOTIENT N (^INT (^BM^CONS (^4) (^BM^ZERO)))) (^BM^SUB1 LEN))))) 

(DEFINE (^BM^BOARDP* LST LEN) (IF (^BM^NLISTP LST) (EQUAL LST (^NIL)) (^BM^AND (^BM^BOARDP (^BM^CAR LST)) (^BM^AND (EQUAL (^BM^LENGTH (^BM^CAR LST)) LEN) (^BM^BOARDP* (^BM^CDR LST) LEN))))) 

(DEFINE (^BM^NUMBER->BOARD* LST LEN) (IF (^BM^NLISTP LST) (^NIL) (^BM^CONS (IF (EQUAL (^BM^CAR LST) (^BM^MINUS (^INT (^BM^CONS (^2) (^BM^ZERO))))) (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (IF (EQUAL (^BM^CAR LST) (^BM^MINUS (^INT (^BM^CONS (^1) (^BM^ZERO))))) (^BM^PACK (^BM^CONS (^D) (^BM^CONS (^R) (^BM^CONS (^A) (^BM^CONS (^W) (^BM^ZERO)))))) (^BM^NUMBER->BOARD (^BM^CAR LST) LEN))) (^BM^NUMBER->BOARD* (^BM^CDR LST) LEN)))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NUMBERP X) (^BM^LESSP X Y)) (EQUAL (^BM^REMAINDER (^BM^PLUS X (^BM^TIMES Y Z)) Y) X))) 

(LEMMA (^BM^IMPLIES (^BM^NOT (^BM^ZEROP Y)) (EQUAL (^BM^REMAINDER (^BM^TIMES Y Z) Y) (^INT (^BM^ZERO))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NUMBERP Z) (^BM^LESSP X Y)) (EQUAL (^BM^QUOTIENT (^BM^PLUS X (^BM^TIMES Y Z)) Y) Z))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NUMBERP Z) (^BM^NOT (^BM^ZEROP Y))) (EQUAL (^BM^QUOTIENT (^BM^TIMES Y Z) Y) Z))) 

(LEMMA (^BM^IMPLIES (^BM^BOARDP BOARD) (EQUAL (^BM^NUMBER->BOARD (^BM^BOARD->NUMBER BOARD) (^BM^LENGTH BOARD)) BOARD))) 

(DEFINE (^BM^MOVEN X I BOARD) (IF (^BM^ZEROP I) (^BM^PLUS X (^BM^TIMES (^INT (^BM^CONS (^4) (^BM^ZERO))) (^BM^QUOTIENT BOARD (^INT (^BM^CONS (^4) (^BM^ZERO)))))) (IF (^BM^TRUE) (^BM^PLUS (^BM^REMAINDER BOARD (^INT (^BM^CONS (^4) (^BM^ZERO)))) (^BM^TIMES (^INT (^BM^CONS (^4) (^BM^ZERO))) (^BM^MOVEN X (^BM^SUB1 I) (^BM^QUOTIENT BOARD (^INT (^BM^CONS (^4) (^BM^ZERO))))))) (^NIL)))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^OR (EQUAL X (^BM^PACK (^BM^CONS (^X) (^BM^ZERO)))) (EQUAL X (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))))) (^BM^BOARDP BOARD)) (EQUAL (^BM^MOVE X I BOARD) (^BM^NUMBER->BOARD (^BM^MOVEN (^BM^PIECE->NUMBER X) I (^BM^BOARD->NUMBER BOARD)) (^BM^LENGTH BOARD))))) 

(DEFINE (^BM^NTHN I BOARD) (IF (^BM^ZEROP I) (^BM^REMAINDER BOARD (^INT (^BM^CONS (^4) (^BM^ZERO)))) (^BM^NTHN (^BM^SUB1 I) (^BM^QUOTIENT BOARD (^INT (^BM^CONS (^4) (^BM^ZERO))))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^LESSP I (^BM^LENGTH BOARD)) (^BM^BOARDP BOARD)) (EQUAL (^BM^NTH I BOARD) (^BM^NUMBER->PIECE (^BM^NTHN I (^BM^BOARD->NUMBER BOARD)))))) 

(DEFINE (^BM^LEGALPN I BOARD) (^BM^AND (^BM^LESSP I (^INT (^BM^CONS (^9) (^BM^ZERO)))) (EQUAL (^BM^NTHN I BOARD) (^INT (^BM^ZERO))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^BOARDP BOARD) (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO))))) (EQUAL (^BM^LEGALP I BOARD) (^BM^LEGALPN I (^BM^BOARD->NUMBER BOARD))))) 

(DEFINE (^BM^WINP1N X I J K BOARD) (^BM^AND (EQUAL X (^BM^NTHN I BOARD)) (^BM^AND (EQUAL X (^BM^NTHN J BOARD)) (EQUAL X (^BM^NTHN K BOARD))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^LESSP I (^BM^LENGTH BOARD)) (^BM^BOARDP BOARD)) (EQUAL (^BM^PIECE->NUMBER (^BM^NTH I BOARD)) (^BM^NTHN I (^BM^BOARD->NUMBER BOARD))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^LESSP I (^BM^LENGTH BOARD)) (^BM^BOARDP BOARD)) (^BM^LESSP (^BM^NTHN I (^BM^BOARD->NUMBER BOARD)) (^INT (^BM^CONS (^3) (^BM^ZERO)))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^BOARDP BOARD) (^BM^AND (^BM^LESSP I (^BM^LENGTH BOARD)) (^BM^AND (^BM^LESSP J (^BM^LENGTH BOARD)) (^BM^AND (^BM^LESSP K (^BM^LENGTH BOARD)) (^BM^OR (EQUAL X (^BM^PACK (^BM^CONS (^X) (^BM^ZERO)))) (EQUAL X (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))))))))) (EQUAL (^BM^WINP1 X (^BM^CONS I (^BM^CONS J (^BM^CONS K (^NIL)))) BOARD) (^BM^WINP1N (^BM^PIECE->NUMBER X) I J K (^BM^BOARD->NUMBER BOARD))))) 

(DEFINE (^BM^WINPN X BOARD) (^BM^OR (^BM^WINP1N X (^INT (^BM^ZERO)) (^INT (^BM^CONS (^1) (^BM^ZERO))) (^INT (^BM^CONS (^2) (^BM^ZERO))) BOARD) (^BM^OR (^BM^WINP1N X (^INT (^BM^CONS (^3) (^BM^ZERO))) (^INT (^BM^CONS (^4) (^BM^ZERO))) (^INT (^BM^CONS (^5) (^BM^ZERO))) BOARD) (^BM^OR (^BM^WINP1N X (^INT (^BM^CONS (^6) (^BM^ZERO))) (^INT (^BM^CONS (^7) (^BM^ZERO))) (^INT (^BM^CONS (^8) (^BM^ZERO))) BOARD) (^BM^OR (^BM^WINP1N X (^INT (^BM^ZERO)) (^INT (^BM^CONS (^3) (^BM^ZERO))) (^INT (^BM^CONS (^6) (^BM^ZERO))) BOARD) (^BM^OR (^BM^WINP1N X (^INT (^BM^CONS (^1) (^BM^ZERO))) (^INT (^BM^CONS (^4) (^BM^ZERO))) (^INT (^BM^CONS (^7) (^BM^ZERO))) BOARD) (^BM^OR (^BM^WINP1N X (^INT (^BM^CONS (^2) (^BM^ZERO))) (^INT (^BM^CONS (^5) (^BM^ZERO))) (^INT (^BM^CONS (^8) (^BM^ZERO))) BOARD) (^BM^OR (^BM^WINP1N X (^INT (^BM^ZERO)) (^INT (^BM^CONS (^4) (^BM^ZERO))) (^INT (^BM^CONS (^8) (^BM^ZERO))) BOARD) (^BM^WINP1N X (^INT (^BM^CONS (^2) (^BM^ZERO))) (^INT (^BM^CONS (^4) (^BM^ZERO))) (^INT (^BM^CONS (^6) (^BM^ZERO))) BOARD))))))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^AND (^BM^BOARDP BOARD) (^BM^OR (EQUAL X (^BM^PACK (^BM^CONS (^X) (^BM^ZERO)))) (EQUAL X (^BM^PACK (^BM^CONS (^O) (^BM^ZERO))))))) (EQUAL (^BM^WINP X BOARD) (^BM^WINPN (^BM^PIECE->NUMBER X) (^BM^BOARD->NUMBER BOARD))))) 

(LEMMA (^BM^IMPLIES (^BM^NOT (^BM^ZEROP N)) (^BM^LESSP (^BM^QUOTIENT N (^INT (^BM^CONS (^4) (^BM^ZERO)))) N))) 

(DEFINE (^BM^PICK-MOVE1N BOARD I LEN) (IF (^BM^ZEROP LEN) (^INT (^BM^ZERO)) (IF (^BM^ZEROP (^BM^REMAINDER BOARD (^INT (^BM^CONS (^4) (^BM^ZERO))))) I (IF (^BM^TRUE) (^BM^PICK-MOVE1N (^BM^QUOTIENT BOARD (^INT (^BM^CONS (^4) (^BM^ZERO)))) (^BM^ADD1 I) (^BM^SUB1 LEN)) (^NIL))))) 

(DEFINE (^BM^BOARD->NUMBER-ALIST ALIST) (IF (^BM^NLISTP ALIST) (^NIL) (^BM^CONS (^BM^CONS (^BM^BOARD->NUMBER (^BM^CAR (^BM^CAR ALIST))) (^BM^CDR (^BM^CAR ALIST))) (^BM^BOARD->NUMBER-ALIST (^BM^CDR ALIST))))) 

(DEFINE (^BM^BOARDP-ALISTP ALIST) (IF (^BM^NLISTP ALIST) (EQUAL ALIST (^NIL)) (^BM^AND (^BM^BOARDP (^BM^CAR (^BM^CAR ALIST))) (^BM^AND (EQUAL (^BM^LENGTH (^BM^CAR (^BM^CAR ALIST))) (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^BOARDP-ALISTP (^BM^CDR ALIST)))))) 

(DEFINE (^BM^PICK-MOVEN BOARD) (IF (^BM^ASSOC BOARD (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^9) (^BM^CONS (^1) (^BM^CONS (^6) (^BM^CONS (^4) (^BM^CONS (^8) (^BM^ZERO))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^9) (^BM^CONS (^0) (^BM^CONS (^6) (^BM^CONS (^8) (^BM^CONS (^8) (^BM^ZERO))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^9) (^BM^CONS (^2) (^BM^CONS (^6) (^BM^CONS (^9) (^BM^CONS (^2) (^BM^ZERO))))))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^9) (^BM^CONS (^2) (^BM^CONS (^6) (^BM^CONS (^8) (^BM^CONS (^9) (^BM^ZERO))))))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^9) (^BM^CONS (^0) (^BM^CONS (^6) (^BM^CONS (^4) (^BM^CONS (^0) (^BM^ZERO))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^9) (^BM^CONS (^0) (^BM^CONS (^6) (^BM^CONS (^2) (^BM^CONS (^8) (^BM^ZERO))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^9) (^BM^CONS (^0) (^BM^CONS (^6) (^BM^CONS (^2) (^BM^CONS (^5) (^BM^ZERO))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^8) (^BM^CONS (^2) (^BM^CONS (^4) (^BM^CONS (^3) (^BM^CONS (^2) (^BM^ZERO))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^1) (^BM^CONS (^0) (^BM^CONS (^3) (^BM^CONS (^9) (^BM^CONS (^3) (^BM^CONS (^6) (^BM^ZERO)))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^1) (^BM^CONS (^0) (^BM^CONS (^2) (^BM^CONS (^9) (^BM^CONS (^7) (^BM^CONS (^6) (^BM^ZERO)))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^1) (^BM^CONS (^0) (^BM^CONS (^2) (^BM^CONS (^9) (^BM^CONS (^2) (^BM^CONS (^8) (^BM^ZERO)))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^1) (^BM^CONS (^0) (^BM^CONS (^2) (^BM^CONS (^9) (^BM^CONS (^3) (^BM^CONS (^4) (^BM^ZERO)))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^7) (^BM^CONS (^0) (^BM^CONS (^1) (^BM^CONS (^4) (^BM^CONS (^4) (^BM^ZERO))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^8) (^BM^CONS (^3) (^BM^CONS (^4) (^BM^CONS (^8) (^BM^CONS (^8) (^BM^ZERO))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^1) (^BM^CONS (^0) (^BM^CONS (^4) (^BM^CONS (^0) (^BM^CONS (^3) (^BM^CONS (^2) (^BM^ZERO)))))))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^7) (^BM^CONS (^1) (^BM^CONS (^2) (^BM^CONS (^0) (^BM^CONS (^0) (^BM^ZERO))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^6) (^BM^CONS (^7) (^BM^CONS (^1) (^BM^CONS (^6) (^BM^CONS (^8) (^BM^ZERO))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^6) (^BM^CONS (^7) (^BM^CONS (^1) (^BM^CONS (^0) (^BM^CONS (^8) (^BM^ZERO))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^6) (^BM^CONS (^7) (^BM^CONS (^1) (^BM^CONS (^0) (^BM^CONS (^5) (^BM^ZERO))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^6) (^BM^CONS (^7) (^BM^CONS (^0) (^BM^CONS (^7) (^BM^CONS (^2) (^BM^ZERO))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^9) (^BM^CONS (^0) (^BM^CONS (^6) (^BM^CONS (^8) (^BM^CONS (^8) (^BM^ZERO))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^7) (^BM^CONS (^5) (^BM^CONS (^3) (^BM^CONS (^2) (^BM^CONS (^8) (^BM^ZERO))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^7) (^BM^CONS (^4) (^BM^CONS (^3) (^BM^CONS (^2) (^BM^CONS (^0) (^BM^ZERO))))))) (^INT (^BM^CONS (^5) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^7) (^BM^CONS (^4) (^BM^CONS (^3) (^BM^CONS (^0) (^BM^CONS (^8) (^BM^ZERO))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^7) (^BM^CONS (^4) (^BM^CONS (^3) (^BM^CONS (^0) (^BM^CONS (^5) (^BM^ZERO))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT 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(^BM^CONS (^1) (^BM^CONS (^5) (^BM^CONS (^3) (^BM^ZERO))))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^9) (^BM^CONS (^7) (^BM^CONS (^9) (^BM^CONS (^3) (^BM^ZERO)))))) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^7) (^BM^CONS (^4) (^BM^CONS (^3) (^BM^CONS (^2) (^BM^CONS (^9) (^BM^ZERO))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^5) (^BM^CONS (^7) (^BM^CONS (^7) (^BM^ZERO))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^6) (^BM^CONS (^6) (^BM^CONS (^0) (^BM^CONS (^7) (^BM^CONS (^3) (^BM^ZERO))))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^1) (^BM^CONS (^8) (^BM^CONS (^0) (^BM^CONS (^7) (^BM^CONS (^3) (^BM^ZERO))))))) (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^4) (^BM^CONS (^6) (^BM^CONS (^3) (^BM^CONS (^3) (^BM^ZERO)))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^1) (^BM^CONS (^5) (^BM^CONS (^6) (^BM^CONS (^1) (^BM^ZERO)))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^6) (^BM^CONS (^0) (^BM^CONS (^1) (^BM^ZERO))))) (^INT (^BM^CONS (^7) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^6) (^BM^CONS (^6) (^BM^CONS (^0) (^BM^CONS (^8) (^BM^CONS (^5) (^BM^ZERO))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^1) (^BM^CONS (^6) (^BM^CONS (^9) (^BM^CONS (^3) (^BM^CONS (^3) (^BM^ZERO))))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^1) (^BM^CONS (^5) (^BM^CONS (^7) (^BM^CONS (^3) (^BM^ZERO)))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^6) (^BM^CONS (^1) (^BM^CONS (^3) (^BM^ZERO))))) (^INT (^BM^CONS (^6) (^BM^ZERO)))) (^BM^CONS (^BM^CONS (^INT (^BM^CONS (^1) (^BM^ZERO))) (^INT (^BM^CONS (^4) (^BM^ZERO)))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (^BM^PICK-MOVE1N BOARD (^INT (^BM^ZERO)) (^INT (^BM^CONS (^9) (^BM^ZERO)))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (EQUAL (^BM^LENGTH BOARD1) (^BM^LENGTH BOARD2)) (^BM^AND (^BM^BOARDP BOARD1) (^BM^BOARDP BOARD2))) (EQUAL (EQUAL (^BM^BOARD->NUMBER BOARD1) (^BM^BOARD->NUMBER BOARD2)) (EQUAL BOARD1 BOARD2)))) 

(LEMMA (^BM^IMPLIES (^BM^AND (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^AND (^BM^BOARDP BOARD) (^BM^BOARDP-ALISTP ALIST))) (^BM^IFF (^BM^ASSOC BOARD ALIST) (^BM^ASSOC (^BM^BOARD->NUMBER BOARD) (^BM^BOARD->NUMBER-ALIST ALIST))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^AND (^BM^BOARDP BOARD) (^BM^BOARDP-ALISTP ALIST))) (EQUAL (^BM^CDR (^BM^ASSOC BOARD ALIST)) (^BM^CDR (^BM^ASSOC (^BM^BOARD->NUMBER BOARD) (^BM^BOARD->NUMBER-ALIST ALIST)))))) 

(LEMMA (^BM^IMPLIES (^BM^BOARDP BOARD) (EQUAL (^BM^PICK-MOVE1 BOARD I) (^BM^PICK-MOVE1N (^BM^BOARD->NUMBER BOARD) I (^BM^LENGTH BOARD))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^BOARDP BOARD)) (EQUAL (^BM^PICK-MOVE BOARD) (^BM^PICK-MOVEN (^BM^BOARD->NUMBER BOARD))))) 

(DEFINE (^BM^TIC-TAC-TOE1-B XMOVES BOARD I) (IF (^BM^LEGALPN (^BM^CAR XMOVES) BOARD) (IF (^BM^LESSP I (^INT (^BM^CONS (^9) (^BM^ZERO)))) (IF (^BM^WINPN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD))) (^BM^CONS (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^CONS (^BM^MINUS (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^NIL)))) (^BM^CONS (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^TIC-TAC-TOE1-B (^BM^CDR XMOVES) (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^ADD1 (^BM^ADD1 I)))))) (^BM^CONS (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^MINUS (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^NIL)))) (^BM^CONS (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) (^BM^CONS (^BM^MINUS (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^NIL))))) 

(DEFINE (^BM^TIC-TAC-TOE-B XMOVES) (^BM^CONS (^INT (^BM^ZERO)) (^BM^TIC-TAC-TOE1-B XMOVES (^INT (^BM^ZERO)) (^INT (^BM^CONS (^1) (^BM^ZERO)))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^LEGALPN I (^BM^BOARD->NUMBER BOARD)) (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO))))) (EQUAL (^BM^LESSP I (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^TRUE)))) 

(LEMMA (EQUAL (^BM^LENGTH (^BM^NUMBER->BOARD N LEN)) (^BM^FIX LEN))) 

(LEMMA (^BM^BOARDP (^BM^NUMBER->BOARD N LEN))) 

(DEFINE (^BM^BOARDPN N) (IF (^BM^ZEROP N) (^BM^TRUE) (IF (^BM^LESSP (^BM^REMAINDER N (^INT (^BM^CONS (^4) (^BM^ZERO)))) (^INT (^BM^CONS (^3) (^BM^ZERO)))) (^BM^BOARDPN (^BM^QUOTIENT N (^INT (^BM^CONS (^4) (^BM^ZERO))))) (^BM^FALSE)))) 

(LEMMA (^BM^IMPLIES (^BM^BOARDP BOARD) (^BM^BOARDPN (^BM^BOARD->NUMBER BOARD)))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NUMBERP BOARD) (^BM^AND (^BM^BOARDPN BOARD) (^BM^OR (EQUAL X (^INT (^BM^CONS (^1) (^BM^ZERO)))) (EQUAL X (^INT (^BM^CONS (^2) (^BM^ZERO))))))) (^BM^BOARDPN (^BM^MOVEN X I BOARD)))) 

(DEFINE (^BM^LENGTHN BOARD) (IF (^BM^ZEROP BOARD) (^INT (^BM^ZERO)) (^BM^ADD1 (^BM^LENGTHN (^BM^QUOTIENT BOARD (^INT (^BM^CONS (^4) (^BM^ZERO)))))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NUMBERP BOARD) (^BM^AND (^BM^BOARDPN BOARD) (^BM^NOT (^BM^LESSP LEN (^BM^LENGTHN BOARD))))) (EQUAL (^BM^BOARD->NUMBER (^BM^NUMBER->BOARD BOARD LEN)) BOARD))) 

(LEMMA (^BM^NOT (^BM^LESSP (^BM^LENGTH BOARD) (^BM^LENGTHN (^BM^BOARD->NUMBER BOARD))))) 

(LEMMA (^BM^IMPLIES (^BM^OR (EQUAL X (^INT (^BM^CONS (^1) (^BM^ZERO)))) (EQUAL X (^INT (^BM^CONS (^2) (^BM^ZERO))))) (EQUAL (^BM^LENGTHN (^BM^MOVEN X I BOARD)) (IF (^BM^LESSP I (^BM^LENGTHN BOARD)) (^BM^LENGTHN BOARD) (^BM^ADD1 I))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^LESSP I (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^AND (^BM^BOARDP BOARD) (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))))) (^BM^NOT (^BM^LESSP (^INT (^BM^CONS (^9) (^BM^ZERO))) (^BM^LENGTHN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) I (^BM^BOARD->NUMBER BOARD))))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^LESSP I (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^AND (^BM^BOARDP BOARD) (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))))) (^BM^LESSP (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) I (^BM^BOARD->NUMBER BOARD))) (^INT (^BM^CONS (^9) (^BM^ZERO)))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^LESSP I (^INT (^BM^CONS (^9) (^BM^ZERO)))) (^BM^AND (^BM^BOARDP BOARD) (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO)))))) (^BM^NOT (^BM^LESSP (^INT (^BM^CONS (^9) (^BM^ZERO))) (^BM^LENGTHN (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) I (^BM^BOARD->NUMBER BOARD))) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) I (^BM^BOARD->NUMBER BOARD)))))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^BOARDP BOARD) (EQUAL (^BM^LENGTH BOARD) (^INT (^BM^CONS (^9) (^BM^ZERO))))) (EQUAL (^BM^TIC-TAC-TOE1-A XMOVES BOARD I) (^BM^NUMBER->BOARD* (^BM^TIC-TAC-TOE1-B XMOVES (^BM^BOARD->NUMBER BOARD) I) (^INT (^BM^CONS (^9) (^BM^ZERO))))))) 

(LEMMA (EQUAL (^BM^TIC-TAC-TOE-A XMOVES) (^BM^NUMBER->BOARD* (^BM^TIC-TAC-TOE-B XMOVES) (^INT (^BM^CONS (^9) (^BM^ZERO)))))) 

(DEFINE (^BM^ARRAY->LST I ARRAY) (IF (^BM^NOT (^BM^LESSP I (^BM^LENGTH ARRAY))) (^NIL) (IF (^BM^NUMBERP (^BM^NTH I ARRAY)) (^BM^CONS (^BM^NTH I ARRAY) (^BM^ARRAY->LST (^BM^ADD1 I) ARRAY)) (IF (^BM^TRUE) (^BM^CONS (^BM^NTH I ARRAY) (^NIL)) (^NIL))))) 

(DEFINE (^BM^PUT VAL N LST) (IF (^BM^ZEROP N) (IF (^BM^LISTP LST) (^BM^CONS VAL (^BM^CDR LST)) (^BM^CONS VAL (^NIL))) (^BM^CONS (^BM^CAR LST) (^BM^PUT VAL (^BM^SUB1 N) (^BM^CDR LST))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NUMBERP I) (^BM^AND (^BM^NUMBERP J) (^BM^LESSP J (^BM^LENGTH ARRAY)))) (EQUAL (^BM^NTH I (^BM^PUT VAL J ARRAY)) (IF (EQUAL I J) VAL (^BM^NTH I ARRAY))))) 

(DEFINE (^BM^TIC-TAC-TOE1-C XMOVES BOARD I T3) (IF (^BM^LEGALPN (^BM^CAR XMOVES) BOARD) (IF (^BM^LESSP I (^INT (^BM^CONS (^9) (^BM^ZERO)))) (IF (^BM^WINPN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD))) (^BM^PUT (^BM^MINUS (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^ADD1 (^BM^ADD1 I)) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^ADD1 I) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) I T3))) (^BM^TIC-TAC-TOE1-C (^BM^CDR XMOVES) (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^ADD1 (^BM^ADD1 I)) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD)) (^BM^ADD1 I) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) I T3)))) (^BM^PUT (^BM^MINUS (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^ADD1 I) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) I T3))) (^BM^PUT (^BM^MINUS (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^ADD1 I) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CAR XMOVES) BOARD) I T3)))) 

(DEFINE (^BM^TIC-TAC-TOE-C XMOVES) (^BM^TIC-TAC-TOE1-C XMOVES (^INT (^BM^ZERO)) (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^NIL)))))))))))))) 

(LEMMA (^BM^IMPLIES (^BM^LESSP I (^BM^LENGTH ARRAY)) (EQUAL (^BM^LENGTH (^BM^PUT VAL I ARRAY)) (^BM^LENGTH ARRAY)))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^LESSP J (^BM^LENGTH ARRAY)) (^BM^LESSP I (^BM^LENGTH ARRAY))) (EQUAL (^BM^ARRAY->LST I (^BM^PUT VAL J ARRAY)) (IF (^BM^NUMBERP (^BM^NTH I (^BM^PUT VAL J ARRAY))) (^BM^CONS (^BM^NTH I (^BM^PUT VAL J ARRAY)) (^BM^ARRAY->LST (^BM^ADD1 I) (^BM^PUT VAL J ARRAY))) (^BM^CONS (^BM^NTH I (^BM^PUT VAL J ARRAY)) (^NIL)))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NUMBERP I) (^BM^AND (^BM^NUMBERP J) (^BM^AND (^BM^LESSP J (^BM^LENGTH ARRAY)) (^BM^LESSP J I)))) (EQUAL (^BM^ARRAY->LST I (^BM^PUT VAL J ARRAY)) (^BM^ARRAY->LST I ARRAY)))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NUMBERP BOARD) (^BM^AND (^BM^NUMBERP I) (^BM^AND (EQUAL (^BM^REMAINDER I (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^AND (^BM^LESSP I (^INT (^BM^CONS (^1) (^BM^CONS (^0) (^BM^ZERO))))) (EQUAL (^BM^LENGTH T3) (^INT (^BM^CONS (^1) (^BM^CONS (^1) (^BM^ZERO))))))))) (EQUAL (^BM^LENGTH (^BM^TIC-TAC-TOE1-C XMOVES BOARD I T3)) (^INT (^BM^CONS (^1) (^BM^CONS (^1) (^BM^ZERO))))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NUMBERP BOARD) (^BM^AND (^BM^NUMBERP I) (^BM^AND (EQUAL (^BM^REMAINDER I (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^AND (^BM^LESSP I (^INT (^BM^CONS (^1) (^BM^CONS (^0) (^BM^ZERO))))) (^BM^AND (EQUAL (^BM^LENGTH T3) (^INT (^BM^CONS (^1) (^BM^CONS (^1) (^BM^ZERO))))) (^BM^AND (^BM^NUMBERP N) (^BM^LESSP N I))))))) (EQUAL (^BM^NTH N (^BM^TIC-TAC-TOE1-C XMOVES BOARD I T3)) (^BM^NTH N T3)))) 

(LEMMA (EQUAL (^BM^REMAINDER (^BM^ADD1 (^BM^ADD1 I)) (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^REMAINDER I (^INT (^BM^CONS (^2) (^BM^ZERO)))))) 

(LEMMA (^BM^IMPLIES (^BM^AND (EQUAL (^BM^REMAINDER I (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^LESSP I (^INT (^BM^CONS (^9) (^BM^ZERO))))) (EQUAL (^BM^LESSP I (^INT (^BM^CONS (^8) (^BM^ZERO)))) (^BM^TRUE)))) 

(LEMMA (^BM^IMPLIES (^BM^AND (^BM^NUMBERP BOARD) (^BM^AND (^BM^NUMBERP I) (^BM^AND (EQUAL (^BM^REMAINDER I (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^AND (^BM^LESSP I (^INT (^BM^CONS (^1) (^BM^CONS (^0) (^BM^ZERO))))) (EQUAL (^BM^LENGTH T3) (^INT (^BM^CONS (^1) (^BM^CONS (^1) (^BM^ZERO))))))))) (EQUAL (^BM^TIC-TAC-TOE1-B XMOVES BOARD I) (^BM^ARRAY->LST I (^BM^TIC-TAC-TOE1-C XMOVES BOARD I T3))))) 

(LEMMA (EQUAL (^BM^TIC-TAC-TOE-B XMOVES) (^BM^ARRAY->LST (^INT (^BM^ZERO)) (^BM^TIC-TAC-TOE-C XMOVES)))) 

(DEFINE (^BM^TIC-TAC-TOE1-D XMOVES J BOARD I T3) (IF (^BM^LEGALPN (^BM^NTH J XMOVES) BOARD) (IF (^BM^LESSP I (^INT (^BM^CONS (^9) (^BM^ZERO)))) (IF (^BM^WINPN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD))) (^BM^PUT (^BM^MINUS (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^ADD1 (^BM^ADD1 I)) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD)) (^BM^ADD1 I) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD) I T3))) (^BM^TIC-TAC-TOE1-D XMOVES (^BM^ADD1 J) (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD)) (^BM^ADD1 (^BM^ADD1 I)) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^2) (^BM^ZERO))) (^BM^PICK-MOVEN (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD)) (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD)) (^BM^ADD1 I) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD) I T3)))) (^BM^PUT (^BM^MINUS (^INT (^BM^CONS (^1) (^BM^ZERO)))) (^BM^ADD1 I) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD) I T3))) (^BM^PUT (^BM^MINUS (^INT (^BM^CONS (^2) (^BM^ZERO)))) (^BM^ADD1 I) (^BM^PUT (^BM^MOVEN (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^NTH J XMOVES) BOARD) I T3)))) 

(DEFINE (^BM^TIC-TAC-TOE-D XMOVES) (^BM^TIC-TAC-TOE1-D XMOVES (^INT (^BM^ZERO)) (^INT (^BM^ZERO)) (^INT (^BM^CONS (^1) (^BM^ZERO))) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^BM^CONS (^INT (^BM^ZERO)) (^NIL)))))))))))))) 

(DEFINE (^BM^NTH-CDR J LST) (IF (^BM^ZEROP J) LST (^BM^NTH-CDR (^BM^SUB1 J) (^BM^CDR LST)))) 

(LEMMA (EQUAL (^BM^CAR (^BM^NTH-CDR J LST)) (^BM^NTH J LST))) 

(LEMMA (EQUAL (^BM^CDR (^BM^NTH-CDR J LST)) (^BM^NTH-CDR J (^BM^CDR LST)))) 

(LEMMA (EQUAL (^BM^TIC-TAC-TOE1-C (^BM^NTH-CDR J XMOVES) BOARD I T3) (^BM^TIC-TAC-TOE1-D XMOVES J BOARD I T3))) 

(LEMMA (EQUAL (^BM^TIC-TAC-TOE-C XMOVES) (^BM^TIC-TAC-TOE-D XMOVES))) 

(DEFINE (^BM^UP T3) (^BM^NUMBER->BOARD* (^BM^ARRAY->LST (^INT (^BM^ZERO)) T3) (^INT (^BM^CONS (^9) (^BM^ZERO))))) 

(LEMMA (^BM^AND (^BM^MEMBER (^BM^TIC-TAC-TOEP (^BM^UP (^BM^TIC-TAC-TOE-D XMOVES))) (^BM^CONS (^BM^PACK (^BM^CONS (^D) (^BM^CONS (^R) (^BM^CONS (^A) (^BM^CONS (^W) (^BM^ZERO)))))) (^BM^CONS (^BM^PACK (^BM^CONS (^O) (^BM^CONS (^-) (^BM^CONS (^W) (^BM^CONS (^I) (^BM^CONS (^N) (^BM^ZERO))))))) (^BM^PACK (^BM^CONS (^N) (^BM^CONS (^I) (^BM^CONS (^L) (^BM^ZERO)))))))) (^BM^AND (^BM^X-MOVES-HONORED XMOVES (^BM^UP (^BM^TIC-TAC-TOE-D XMOVES))) (EQUAL (^BM^INIT-GAME (^BM^LENGTH OPENING) (^BM^UP (^BM^TIC-TAC-TOE-D (^BM^APPEND OPENING XMOVES1)))) (^BM^INIT-GAME (^BM^LENGTH OPENING) (^BM^UP (^BM^TIC-TAC-TOE-D (^BM^APPEND OPENING XMOVES2))))))))